%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN487-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:39:18 AM UTC 2025
% Result : Unsatisfiable 0.78s 0.95s
% Output : Proof 1.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN487-1 : TPTP v9.0.0. Released v2.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:36:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.78/0.95 % SZS status Unsatisfiable
% 0.78/0.95 % SZS output start Proof
% 0.78/0.95 tff(c1_1_type, type, (
% 0.78/0.95 c1_1: $i > $o)).
% 0.78/0.95 tff(a2308_type, type, (
% 0.78/0.95 a2308: $i)).
% 0.78/0.95 tff(hskp18_type, type, (
% 0.78/0.95 hskp18: $o)).
% 0.78/0.95 tff(a2282_type, type, (
% 0.78/0.95 a2282: $i)).
% 0.78/0.95 tff(hskp23_type, type, (
% 0.78/0.95 hskp23: $o)).
% 0.78/0.95 tff(hskp25_type, type, (
% 0.78/0.95 hskp25: $o)).
% 0.78/0.95 tff(c3_1_type, type, (
% 0.78/0.95 c3_1: $i > $o)).
% 0.78/0.95 tff(c0_1_type, type, (
% 0.78/0.95 c0_1: $i > $o)).
% 0.78/0.95 tff(c2_1_type, type, (
% 0.78/0.95 c2_1: $i > $o)).
% 0.78/0.95 tff(ndr1_0_type, type, (
% 0.78/0.95 ndr1_0: $o)).
% 0.78/0.95 tff(hskp12_type, type, (
% 0.78/0.95 hskp12: $o)).
% 0.78/0.95 tff(hskp19_type, type, (
% 0.78/0.95 hskp19: $o)).
% 0.78/0.95 tff(a2342_type, type, (
% 0.78/0.95 a2342: $i)).
% 0.78/0.95 tff(hskp1_type, type, (
% 0.78/0.95 hskp1: $o)).
% 0.78/0.95 tff(a2277_type, type, (
% 0.78/0.95 a2277: $i)).
% 0.78/0.95 tff(a2278_type, type, (
% 0.78/0.95 a2278: $i)).
% 0.78/0.95 tff(hskp28_type, type, (
% 0.78/0.95 hskp28: $o)).
% 0.78/0.95 tff(a2323_type, type, (
% 0.78/0.95 a2323: $i)).
% 0.78/0.95 tff(a2285_type, type, (
% 0.78/0.95 a2285: $i)).
% 0.78/0.95 tff(hskp4_type, type, (
% 0.78/0.95 hskp4: $o)).
% 0.78/0.95 tff(hskp20_type, type, (
% 0.78/0.95 hskp20: $o)).
% 0.78/0.95 tff(a2302_type, type, (
% 0.78/0.95 a2302: $i)).
% 0.78/0.95 tff(hskp14_type, type, (
% 0.78/0.95 hskp14: $o)).
% 0.78/0.95 tff(hskp2_type, type, (
% 0.78/0.95 hskp2: $o)).
% 0.78/0.95 tff(hskp6_type, type, (
% 0.78/0.95 hskp6: $o)).
% 0.78/0.95 tff(hskp0_type, type, (
% 0.78/0.95 hskp0: $o)).
% 0.78/0.95 tff(hskp17_type, type, (
% 0.78/0.95 hskp17: $o)).
% 0.78/0.95 tff(a2294_type, type, (
% 0.78/0.95 a2294: $i)).
% 0.78/0.95 tff(a2327_type, type, (
% 0.78/0.95 a2327: $i)).
% 0.78/0.95 tff(hskp7_type, type, (
% 0.78/0.95 hskp7: $o)).
% 0.78/0.95 tff(hskp31_type, type, (
% 0.78/0.95 hskp31: $o)).
% 0.78/0.95 tff(a2306_type, type, (
% 0.78/0.95 a2306: $i)).
% 0.78/0.95 tff(hskp11_type, type, (
% 0.78/0.95 hskp11: $o)).
% 0.78/0.95 tff(hskp30_type, type, (
% 0.78/0.95 hskp30: $o)).
% 0.78/0.95 tff(a2295_type, type, (
% 0.78/0.95 a2295: $i)).
% 0.78/0.95 tff(a2280_type, type, (
% 0.78/0.95 a2280: $i)).
% 0.78/0.95 tff(hskp3_type, type, (
% 0.78/0.95 hskp3: $o)).
% 0.78/0.95 tff(a2325_type, type, (
% 0.78/0.95 a2325: $i)).
% 0.78/0.95 tff(hskp22_type, type, (
% 0.78/0.95 hskp22: $o)).
% 0.78/0.95 tff(a2279_type, type, (
% 0.78/0.95 a2279: $i)).
% 0.78/0.95 tff(a2315_type, type, (
% 0.78/0.95 a2315: $i)).
% 0.78/0.95 tff(a2276_type, type, (
% 0.78/0.95 a2276: $i)).
% 0.78/0.95 tff(hskp9_type, type, (
% 0.78/0.95 hskp9: $o)).
% 0.78/0.95 tff(a2291_type, type, (
% 0.78/0.95 a2291: $i)).
% 0.78/0.95 tff(a2286_type, type, (
% 0.78/0.95 a2286: $i)).
% 0.78/0.95 tff(hskp26_type, type, (
% 0.78/0.95 hskp26: $o)).
% 0.78/0.95 tff(hskp16_type, type, (
% 0.78/0.95 hskp16: $o)).
% 0.78/0.95 tff(a2304_type, type, (
% 0.78/0.95 a2304: $i)).
% 0.78/0.95 tff(a2345_type, type, (
% 0.78/0.95 a2345: $i)).
% 0.78/0.95 tff(hskp10_type, type, (
% 0.78/0.95 hskp10: $o)).
% 0.78/0.95 tff(a2293_type, type, (
% 0.78/0.95 a2293: $i)).
% 0.78/0.95 tff(a2287_type, type, (
% 0.78/0.95 a2287: $i)).
% 0.78/0.95 tff(hskp8_type, type, (
% 0.78/0.95 hskp8: $o)).
% 0.78/0.95 tff(hskp13_type, type, (
% 0.78/0.95 hskp13: $o)).
% 0.78/0.95 tff(a2299_type, type, (
% 0.78/0.95 a2299: $i)).
% 0.78/0.95 tff(a2303_type, type, (
% 0.78/0.95 a2303: $i)).
% 0.78/0.95 tff(hskp15_type, type, (
% 0.78/0.95 hskp15: $o)).
% 0.78/0.95 tff(a2367_type, type, (
% 0.78/0.95 a2367: $i)).
% 0.78/0.95 tff(hskp27_type, type, (
% 0.78/0.95 hskp27: $o)).
% 0.78/0.95 tff(a2316_type, type, (
% 0.78/0.95 a2316: $i)).
% 0.78/0.95 tff(hskp21_type, type, (
% 0.78/0.95 hskp21: $o)).
% 0.78/0.95 tff(a2324_type, type, (
% 0.78/0.95 a2324: $i)).
% 0.78/0.95 tff(hskp24_type, type, (
% 0.78/0.95 hskp24: $o)).
% 0.78/0.95 tff(a2337_type, type, (
% 0.78/0.95 a2337: $i)).
% 0.78/0.95 tff(1,plain,
% 0.78/0.95 (^[U: $i] : refl((hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(2,plain,
% 0.78/0.95 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1])).
% 0.78/0.95 tff(3,plain,
% 0.78/0.95 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(4,plain,
% 0.78/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp19) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp19) <=> (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(5,plain,
% 0.78/0.95 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp19) <=> ![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[4])).
% 0.78/0.95 tff(6,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp12) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.78/0.95 tff(7,plain,
% 0.78/0.95 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.78/0.95 tff(8,plain,
% 0.78/0.95 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.78/0.95 tff(9,plain,(
% 0.78/0.95 ![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.78/0.95 inference(skolemize,[status(sab)],[8])).
% 0.78/0.95 tff(10,plain,
% 0.78/0.95 (![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.78/0.95 tff(11,assumption,(hskp25), introduced(assumption)).
% 0.78/0.95 tff(12,plain,
% 0.78/0.95 (((~hskp25) | (~c2_1(a2342))) <=> ((~hskp25) | (~c2_1(a2342)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(13,plain,
% 0.78/0.95 (((~c2_1(a2342)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a2342)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(14,axiom,((~c2_1(a2342)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.78/0.95 tff(15,plain,
% 0.78/0.95 ((~hskp25) | (~c2_1(a2342))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.78/0.95 tff(16,plain,
% 0.78/0.95 ((~hskp25) | (~c2_1(a2342))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.78/0.95 tff(17,plain,
% 0.78/0.95 (~c2_1(a2342)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.78/0.95 tff(18,plain,
% 0.78/0.95 (((~hskp25) | c3_1(a2342)) <=> ((~hskp25) | c3_1(a2342))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(19,axiom,((~hskp25) | c3_1(a2342)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.78/0.95 tff(20,plain,
% 0.78/0.95 ((~hskp25) | c3_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.78/0.95 tff(21,plain,
% 0.78/0.95 ((~hskp25) | c3_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[20, 18])).
% 0.78/0.95 tff(22,plain,
% 0.78/0.95 ((~hskp25) | c3_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.78/0.95 tff(23,plain,
% 0.78/0.95 ((~hskp25) | c3_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.78/0.95 tff(24,plain,
% 0.78/0.95 ((~hskp25) | c3_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.78/0.95 tff(25,plain,
% 0.78/0.95 (c3_1(a2342)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[24, 11])).
% 0.78/0.95 tff(26,plain,
% 0.78/0.95 (((~hskp25) | c0_1(a2342)) <=> ((~hskp25) | c0_1(a2342))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(27,axiom,((~hskp25) | c0_1(a2342)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.78/0.95 tff(28,plain,
% 0.78/0.95 ((~hskp25) | c0_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.78/0.95 tff(29,plain,
% 0.78/0.95 ((~hskp25) | c0_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.78/0.95 tff(30,plain,
% 0.78/0.95 ((~hskp25) | c0_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.78/0.95 tff(31,plain,
% 0.78/0.95 ((~hskp25) | c0_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.78/0.95 tff(32,plain,
% 0.78/0.95 ((~hskp25) | c0_1(a2342)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.78/0.95 tff(33,plain,
% 0.78/0.95 (c0_1(a2342)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[32, 11])).
% 0.78/0.95 tff(34,assumption,(~c2_1(a2277)), introduced(assumption)).
% 0.78/0.95 tff(35,assumption,(~hskp28), introduced(assumption)).
% 0.78/0.95 tff(36,assumption,(~hskp1), introduced(assumption)).
% 0.78/0.95 tff(37,assumption,(~c1_1(a2282)), introduced(assumption)).
% 0.78/0.95 tff(38,plain,
% 0.78/0.95 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(39,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[38])).
% 0.78/0.95 tff(40,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(41,plain,
% 0.78/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_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) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_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) | (~c0_1(U)) | (~c1_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) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_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) | (~c0_1(U)) | (~c1_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)) | hskp23) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp23))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_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)) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(42,plain,
% 0.78/0.95 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[41])).
% 0.78/0.95 tff(43,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)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 0.78/0.95 tff(44,plain,
% 0.78/0.95 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.78/0.96 tff(45,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.78/0.96 tff(46,plain,(
% 0.78/0.96 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[45])).
% 0.78/0.96 tff(47,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.78/0.96 tff(48,plain,
% 0.78/0.96 (^[U: $i] : refl((hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(49,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[48])).
% 0.78/0.96 tff(50,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(51,plain,
% 0.78/0.96 (^[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)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp4) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp4) <=> (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(52,plain,
% 0.78/0.96 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp4) <=> ![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[51])).
% 0.78/0.96 tff(53,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 0.78/0.96 tff(54,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.78/0.96 tff(55,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.78/0.96 tff(56,plain,(
% 0.78/0.96 ![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[55])).
% 0.78/0.96 tff(57,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.78/0.96 tff(58,plain,
% 0.78/0.96 (^[U: $i] : refl((hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(59,plain,
% 0.78/0.96 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[58])).
% 0.78/0.96 tff(60,plain,
% 0.78/0.96 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(61,plain,
% 0.78/0.96 (^[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)) | hskp20) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp20))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(62,plain,
% 0.78/0.96 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp20) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[61])).
% 0.78/0.96 tff(63,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.78/0.96 tff(64,plain,
% 0.78/0.96 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.78/0.96 tff(65,plain,
% 0.78/0.96 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.78/0.96 tff(66,plain,(
% 0.78/0.96 ![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[65])).
% 0.78/0.96 tff(67,plain,
% 0.78/0.96 (![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.78/0.96 tff(68,plain,
% 0.78/0.96 (^[U: $i] : refl((hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(69,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[68])).
% 0.78/0.96 tff(70,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(71,plain,
% 0.78/0.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp4) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp4) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(72,plain,
% 0.78/0.96 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp4) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[71])).
% 0.78/0.96 tff(73,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp2) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.78/0.96 tff(74,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.78/0.96 tff(75,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.78/0.96 tff(76,plain,(
% 0.78/0.96 ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[75])).
% 0.78/0.96 tff(77,plain,
% 0.78/0.96 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.78/0.96 tff(78,assumption,(~hskp14), introduced(assumption)).
% 0.78/0.96 tff(79,plain,
% 0.78/0.96 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(80,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_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) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[79])).
% 0.78/0.96 tff(81,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_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) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(82,plain,
% 0.78/0.96 (^[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))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_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)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(83,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[82])).
% 0.78/0.96 tff(84,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause203')).
% 0.78/0.96 tff(85,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.78/0.96 tff(86,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.78/0.96 tff(87,plain,(
% 0.78/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[86])).
% 0.78/0.96 tff(88,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.78/0.96 tff(89,plain,
% 0.78/0.96 (^[U: $i] : refl((hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(90,plain,
% 0.78/0.96 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[89])).
% 0.78/0.96 tff(91,plain,
% 0.78/0.96 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(92,plain,
% 0.78/0.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_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)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp14) <=> ((hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp14))), rewrite(((hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp14) <=> (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp14) <=> (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(93,plain,
% 0.78/0.96 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp14) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[92])).
% 0.78/0.96 tff(94,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 0.78/0.96 tff(95,plain,
% 0.78/0.96 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.78/0.96 tff(96,plain,
% 0.78/0.96 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.78/0.96 tff(97,plain,(
% 0.78/0.96 ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[96])).
% 0.78/0.96 tff(98,plain,
% 0.78/0.96 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.78/0.96 tff(99,plain,
% 0.78/0.96 ((hskp20 | hskp14 | hskp1) <=> (hskp20 | hskp14 | hskp1)),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(100,plain,
% 0.78/0.96 (((hskp1 | hskp14) | hskp20) <=> (hskp20 | hskp14 | hskp1)),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(101,axiom,((hskp1 | hskp14) | hskp20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.78/0.96 tff(102,plain,
% 0.78/0.96 (hskp20 | hskp14 | hskp1),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.78/0.96 tff(103,plain,
% 0.78/0.96 (hskp20 | hskp14 | hskp1),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.78/0.96 tff(104,plain,
% 0.78/0.96 (hskp20 | hskp14 | hskp1),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.78/0.96 tff(105,plain,
% 0.78/0.96 (hskp20 | hskp14 | hskp1),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[104, 99])).
% 0.78/0.96 tff(106,plain,
% 0.78/0.96 (hskp20 | hskp14 | hskp1),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[105, 99])).
% 0.78/0.96 tff(107,plain,
% 0.78/0.96 (hskp20),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[106, 36, 78])).
% 0.78/0.96 tff(108,plain,
% 0.78/0.96 (((~hskp20) | (~c1_1(a2323))) <=> ((~hskp20) | (~c1_1(a2323)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(109,plain,
% 0.78/0.96 (((~c1_1(a2323)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a2323)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(110,axiom,((~c1_1(a2323)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.78/0.96 tff(111,plain,
% 0.78/0.96 ((~hskp20) | (~c1_1(a2323))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.78/0.96 tff(112,plain,
% 0.78/0.96 ((~hskp20) | (~c1_1(a2323))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.78/0.96 tff(113,plain,
% 0.78/0.96 (~c1_1(a2323)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[112, 107])).
% 0.78/0.96 tff(114,plain,
% 0.78/0.96 (((~hskp20) | c3_1(a2323)) <=> ((~hskp20) | c3_1(a2323))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(115,axiom,((~hskp20) | c3_1(a2323)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.78/0.96 tff(116,plain,
% 0.78/0.96 ((~hskp20) | c3_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.78/0.96 tff(117,plain,
% 0.78/0.96 ((~hskp20) | c3_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[116, 114])).
% 0.78/0.96 tff(118,plain,
% 0.78/0.96 ((~hskp20) | c3_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.78/0.96 tff(119,plain,
% 0.78/0.96 ((~hskp20) | c3_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.78/0.96 tff(120,plain,
% 0.78/0.96 ((~hskp20) | c3_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[119, 114])).
% 0.78/0.96 tff(121,plain,
% 0.78/0.96 (c3_1(a2323)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[120, 107])).
% 0.78/0.96 tff(122,plain,
% 0.78/0.96 (((~hskp20) | c2_1(a2323)) <=> ((~hskp20) | c2_1(a2323))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(123,axiom,((~hskp20) | c2_1(a2323)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.78/0.96 tff(124,plain,
% 0.78/0.96 ((~hskp20) | c2_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.78/0.96 tff(125,plain,
% 0.78/0.96 ((~hskp20) | c2_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[124, 122])).
% 0.78/0.96 tff(126,plain,
% 0.78/0.96 ((~hskp20) | c2_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[125, 122])).
% 0.78/0.96 tff(127,plain,
% 0.78/0.96 ((~hskp20) | c2_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.78/0.96 tff(128,plain,
% 0.78/0.96 ((~hskp20) | c2_1(a2323)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[127, 122])).
% 0.78/0.96 tff(129,plain,
% 0.78/0.96 (c2_1(a2323)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[128, 107])).
% 0.78/0.96 tff(130,assumption,(~ndr1_0), introduced(assumption)).
% 0.78/0.96 tff(131,plain,
% 0.78/0.96 ((ndr1_0 | (~hskp7)) <=> (ndr1_0 | (~hskp7))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(132,plain,
% 0.78/0.96 (((~hskp7) | ndr1_0) <=> (ndr1_0 | (~hskp7))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(133,axiom,((~hskp7) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause25')).
% 0.78/0.96 tff(134,plain,
% 0.78/0.96 (ndr1_0 | (~hskp7)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.78/0.96 tff(135,plain,
% 0.78/0.96 (ndr1_0 | (~hskp7)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[134, 131])).
% 0.78/0.96 tff(136,plain,
% 0.78/0.96 (~hskp7),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[135, 130])).
% 0.78/0.96 tff(137,plain,
% 0.78/0.96 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(138,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.78/0.96 tff(139,plain,
% 0.78/0.96 ((~hskp31) | ndr1_0),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.78/0.96 tff(140,plain,
% 0.78/0.96 ((~hskp31) | ndr1_0),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[139, 137])).
% 0.78/0.96 tff(141,plain,
% 0.78/0.96 ((~hskp31) | ndr1_0),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[140, 137])).
% 0.78/0.96 tff(142,plain,
% 0.78/0.96 ((~hskp31) | ndr1_0),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.78/0.96 tff(143,plain,
% 0.78/0.96 ((~hskp31) | ndr1_0),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[142, 137])).
% 0.78/0.96 tff(144,plain,
% 0.78/0.96 (~hskp31),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[143, 130])).
% 0.78/0.96 tff(145,plain,
% 0.78/0.96 ((ndr1_0 | (~hskp14)) <=> (ndr1_0 | (~hskp14))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(146,plain,
% 0.78/0.96 (((~hskp14) | ndr1_0) <=> (ndr1_0 | (~hskp14))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(147,axiom,((~hskp14) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause18')).
% 0.78/0.96 tff(148,plain,
% 0.78/0.96 (ndr1_0 | (~hskp14)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.78/0.96 tff(149,plain,
% 0.78/0.96 (ndr1_0 | (~hskp14)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[148, 145])).
% 0.78/0.96 tff(150,plain,
% 0.78/0.96 (~hskp14),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[149, 130])).
% 0.78/0.96 tff(151,plain,
% 0.78/0.96 ((hskp31 | hskp14 | hskp7) <=> (hskp31 | hskp14 | hskp7)),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(152,plain,
% 0.78/0.96 (((hskp31 | hskp7) | hskp14) <=> (hskp31 | hskp14 | hskp7)),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(153,axiom,((hskp31 | hskp7) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.78/0.96 tff(154,plain,
% 0.78/0.96 (hskp31 | hskp14 | hskp7),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.78/0.96 tff(155,plain,
% 0.78/0.96 (hskp31 | hskp14 | hskp7),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[154, 151])).
% 0.78/0.96 tff(156,plain,
% 0.78/0.96 (hskp31 | hskp14 | hskp7),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.78/0.96 tff(157,plain,
% 0.78/0.96 (hskp31 | hskp14 | hskp7),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[156, 151])).
% 0.78/0.96 tff(158,plain,
% 0.78/0.96 (hskp31 | hskp14 | hskp7),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[157, 151])).
% 0.78/0.96 tff(159,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[158, 150, 144, 136])).
% 0.78/0.96 tff(160,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(161,plain,
% 0.78/0.96 (((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(162,plain,
% 0.78/0.96 ((hskp4 | hskp1 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323))) <=> (hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(163,plain,
% 0.78/0.96 (((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[162])).
% 0.78/0.96 tff(164,plain,
% 0.78/0.96 (((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[163, 161])).
% 0.78/0.96 tff(165,plain,
% 0.78/0.96 ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp1 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(166,plain,
% 0.78/0.96 ((~![U: $i] : (hskp4 | hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp1 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.78/0.96 tff(167,plain,
% 0.78/0.96 (hskp4),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[166, 160, 36, 129, 121, 113, 57])).
% 0.78/0.96 tff(168,plain,
% 0.78/0.96 (((~hskp4) | (~c3_1(a2282))) <=> ((~hskp4) | (~c3_1(a2282)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(169,plain,
% 0.78/0.96 (((~c3_1(a2282)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a2282)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(170,axiom,((~c3_1(a2282)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 0.78/0.96 tff(171,plain,
% 0.78/0.96 ((~hskp4) | (~c3_1(a2282))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.78/0.96 tff(172,plain,
% 0.78/0.96 ((~hskp4) | (~c3_1(a2282))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[171, 168])).
% 0.78/0.96 tff(173,plain,
% 0.78/0.96 (~c3_1(a2282)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[172, 167])).
% 0.78/0.96 tff(174,plain,
% 0.78/0.96 (((~hskp4) | (~c0_1(a2282))) <=> ((~hskp4) | (~c0_1(a2282)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(175,plain,
% 0.78/0.96 (((~c0_1(a2282)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a2282)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(176,axiom,((~c0_1(a2282)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.78/0.96 tff(177,plain,
% 0.78/0.96 ((~hskp4) | (~c0_1(a2282))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.78/0.96 tff(178,plain,
% 0.78/0.96 ((~hskp4) | (~c0_1(a2282))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[177, 174])).
% 0.78/0.96 tff(179,plain,
% 0.78/0.96 (~c0_1(a2282)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[178, 167])).
% 0.78/0.96 tff(180,plain,
% 0.78/0.96 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(181,plain,
% 0.78/0.96 ((hskp14 | hskp1 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))) <=> (hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(182,plain,
% 0.78/0.96 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[181])).
% 0.78/0.96 tff(183,plain,
% 0.78/0.96 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[182, 180])).
% 0.78/0.96 tff(184,plain,
% 0.78/0.96 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(185,plain,
% 0.78/0.96 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp14 | hskp1 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.78/0.96 tff(186,plain,
% 0.78/0.96 (~c1_1(a2282)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[185, 160, 78, 36, 179, 173, 98])).
% 0.78/0.96 tff(187,plain,
% 0.78/0.96 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(188,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[187])).
% 0.78/0.96 tff(189,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(190,plain,
% 0.78/0.96 (^[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)) | (~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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(191,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[190])).
% 0.78/0.96 tff(192,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 0.78/0.97 tff(193,plain,
% 0.78/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.78/0.97 tff(194,plain,
% 0.78/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.78/0.97 tff(195,plain,(
% 0.78/0.97 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.78/0.97 inference(skolemize,[status(sab)],[194])).
% 0.78/0.97 tff(196,plain,
% 0.78/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.78/0.97 tff(197,plain,
% 0.78/0.97 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(198,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[197])).
% 0.78/0.97 tff(199,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(200,plain,
% 0.78/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(201,plain,
% 0.78/0.97 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | 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) | c0_1(V))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[200])).
% 0.78/0.97 tff(202,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.78/0.97 tff(203,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.78/0.97 tff(204,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.78/0.97 tff(205,plain,(
% 0.78/0.97 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.97 inference(skolemize,[status(sab)],[204])).
% 0.78/0.97 tff(206,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.78/0.97 tff(207,plain,
% 0.78/0.97 (^[U: $i] : refl((hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(208,plain,
% 0.78/0.97 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[207])).
% 0.78/0.97 tff(209,plain,
% 0.78/0.97 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(210,plain,
% 0.78/0.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp17) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp17))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(211,plain,
% 0.78/0.97 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp17) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[210])).
% 0.78/0.97 tff(212,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.78/0.97 tff(213,plain,
% 0.78/0.97 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.78/0.97 tff(214,plain,
% 0.78/0.97 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.78/0.97 tff(215,plain,(
% 0.78/0.97 ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.97 inference(skolemize,[status(sab)],[214])).
% 0.78/0.97 tff(216,plain,
% 0.78/0.97 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.78/0.97 tff(217,plain,
% 0.78/0.97 (((~hskp4) | c2_1(a2282)) <=> ((~hskp4) | c2_1(a2282))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(218,axiom,((~hskp4) | c2_1(a2282)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.78/0.97 tff(219,plain,
% 0.78/0.97 ((~hskp4) | c2_1(a2282)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.78/0.97 tff(220,plain,
% 0.78/0.97 ((~hskp4) | c2_1(a2282)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[219, 217])).
% 0.78/0.97 tff(221,plain,
% 0.78/0.97 ((~hskp4) | c2_1(a2282)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[220, 217])).
% 0.78/0.97 tff(222,plain,
% 0.78/0.97 ((~hskp4) | c2_1(a2282)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.78/0.97 tff(223,plain,
% 0.78/0.97 ((~hskp4) | c2_1(a2282)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[222, 217])).
% 0.78/0.97 tff(224,plain,
% 0.78/0.97 (c2_1(a2282)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[223, 167])).
% 0.78/0.97 tff(225,plain,
% 0.78/0.97 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(226,plain,
% 0.78/0.97 ((hskp17 | hskp14 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(227,plain,
% 0.78/0.97 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[226])).
% 0.78/0.97 tff(228,plain,
% 0.78/0.97 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[227, 225])).
% 0.78/0.97 tff(229,plain,
% 0.78/0.97 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(230,plain,
% 0.78/0.97 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c2_1(a2282))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.78/0.97 tff(231,plain,
% 0.78/0.97 (hskp17),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[230, 160, 78, 224, 179, 173, 216])).
% 0.78/0.97 tff(232,plain,
% 0.78/0.97 (((~hskp17) | (~c2_1(a2306))) <=> ((~hskp17) | (~c2_1(a2306)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(233,plain,
% 0.78/0.97 (((~c2_1(a2306)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a2306)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(234,axiom,((~c2_1(a2306)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.78/0.97 tff(235,plain,
% 0.78/0.97 ((~hskp17) | (~c2_1(a2306))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.78/0.97 tff(236,plain,
% 0.78/0.97 ((~hskp17) | (~c2_1(a2306))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[235, 232])).
% 0.78/0.97 tff(237,plain,
% 0.78/0.97 (~c2_1(a2306)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[236, 231])).
% 0.78/0.97 tff(238,plain,
% 0.78/0.97 (((~hskp17) | (~c1_1(a2306))) <=> ((~hskp17) | (~c1_1(a2306)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(239,plain,
% 0.78/0.97 (((~c1_1(a2306)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a2306)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(240,axiom,((~c1_1(a2306)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.78/0.97 tff(241,plain,
% 0.78/0.97 ((~hskp17) | (~c1_1(a2306))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.78/0.97 tff(242,plain,
% 0.78/0.97 ((~hskp17) | (~c1_1(a2306))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[241, 238])).
% 0.78/0.97 tff(243,plain,
% 0.78/0.97 (~c1_1(a2306)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[242, 231])).
% 0.78/0.97 tff(244,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(245,plain,
% 0.78/0.97 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306)) <=> (hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(246,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306)))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[245])).
% 0.78/0.97 tff(247,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306))),
% 0.78/0.97 inference(transitivity,[status(thm)],[246, 244])).
% 0.78/0.97 tff(248,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(249,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c0_1(a2306)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.78/0.97 tff(250,plain,
% 0.78/0.97 (c0_1(a2306)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[249, 160, 36, 224, 243, 237, 173, 206, 186])).
% 0.78/0.97 tff(251,plain,
% 0.78/0.97 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(252,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[251])).
% 0.78/0.97 tff(253,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(254,plain,
% 0.78/0.97 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(255,plain,
% 0.78/0.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[254])).
% 0.78/0.97 tff(256,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 0.78/0.97 tff(257,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.78/0.97 tff(258,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[257, 253])).
% 0.78/0.97 tff(259,plain,(
% 0.78/0.97 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(skolemize,[status(sab)],[258])).
% 0.78/0.97 tff(260,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[259, 252])).
% 0.78/0.97 tff(261,plain,
% 0.78/0.97 (((~hskp17) | (~c3_1(a2306))) <=> ((~hskp17) | (~c3_1(a2306)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(262,plain,
% 0.78/0.97 (((~c3_1(a2306)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a2306)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(263,axiom,((~c3_1(a2306)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.78/0.97 tff(264,plain,
% 0.78/0.97 ((~hskp17) | (~c3_1(a2306))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.78/0.97 tff(265,plain,
% 0.78/0.97 ((~hskp17) | (~c3_1(a2306))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[264, 261])).
% 0.78/0.97 tff(266,plain,
% 0.78/0.97 (~c3_1(a2306)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[265, 231])).
% 0.78/0.97 tff(267,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(268,plain,
% 0.78/0.97 ((hskp23 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(269,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[268])).
% 0.78/0.97 tff(270,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[269, 267])).
% 0.78/0.97 tff(271,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(272,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.78/0.97 tff(273,plain,
% 0.78/0.97 (hskp23),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[272, 160, 243, 237, 266, 260, 250])).
% 0.78/0.97 tff(274,plain,
% 0.78/0.97 (((~hskp23) | (~c2_1(a2327))) <=> ((~hskp23) | (~c2_1(a2327)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(275,plain,
% 0.78/0.97 (((~c2_1(a2327)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a2327)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(276,axiom,((~c2_1(a2327)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.78/0.97 tff(277,plain,
% 0.78/0.97 ((~hskp23) | (~c2_1(a2327))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.78/0.97 tff(278,plain,
% 0.78/0.97 ((~hskp23) | (~c2_1(a2327))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[277, 274])).
% 0.78/0.97 tff(279,plain,
% 0.78/0.97 (~c2_1(a2327)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[278, 273])).
% 0.78/0.97 tff(280,plain,
% 0.78/0.97 (((~hskp23) | c3_1(a2327)) <=> ((~hskp23) | c3_1(a2327))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(281,axiom,((~hskp23) | c3_1(a2327)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.78/0.97 tff(282,plain,
% 0.78/0.97 ((~hskp23) | c3_1(a2327)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.78/0.97 tff(283,plain,
% 0.78/0.97 ((~hskp23) | c3_1(a2327)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[282, 280])).
% 0.78/0.97 tff(284,plain,
% 0.78/0.97 ((~hskp23) | c3_1(a2327)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[283, 280])).
% 0.78/0.97 tff(285,plain,
% 0.78/0.97 ((~hskp23) | c3_1(a2327)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.78/0.97 tff(286,plain,
% 0.78/0.97 ((~hskp23) | c3_1(a2327)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[285, 280])).
% 0.78/0.97 tff(287,plain,
% 0.78/0.97 (c3_1(a2327)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[286, 273])).
% 0.78/0.97 tff(288,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(289,plain,
% 0.78/0.97 (((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282))) <=> (c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(290,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[289])).
% 0.78/0.97 tff(291,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[290, 288])).
% 0.78/0.97 tff(292,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(293,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2327) | c1_1(a2323) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)) | (~c3_1(a2327)) | (~c1_1(a2327))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.78/0.97 tff(294,plain,
% 0.78/0.97 (~c1_1(a2327)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[293, 160, 287, 129, 121, 224, 279, 113, 179, 196, 186])).
% 0.78/0.97 tff(295,plain,
% 0.78/0.97 (((~hskp23) | (~c0_1(a2327))) <=> ((~hskp23) | (~c0_1(a2327)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(296,plain,
% 0.78/0.97 (((~c0_1(a2327)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a2327)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(297,axiom,((~c0_1(a2327)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.78/0.97 tff(298,plain,
% 0.78/0.97 ((~hskp23) | (~c0_1(a2327))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.78/0.97 tff(299,plain,
% 0.78/0.97 ((~hskp23) | (~c0_1(a2327))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[298, 295])).
% 0.78/0.97 tff(300,plain,
% 0.78/0.97 (~c0_1(a2327)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[299, 273])).
% 0.78/0.97 tff(301,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(302,plain,
% 0.78/0.97 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(303,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327)))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[302])).
% 0.78/0.97 tff(304,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327))),
% 0.78/0.97 inference(transitivity,[status(thm)],[303, 301])).
% 0.78/0.97 tff(305,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(306,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2327)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.78/0.97 tff(307,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[306, 160, 36, 224, 300, 279, 173, 206, 186, 294])).
% 0.78/0.97 tff(308,plain,(hskp1 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(309,plain,
% 0.78/0.97 (hskp1),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[308, 78])).
% 0.78/0.97 tff(310,plain,
% 0.78/0.97 (((~hskp1) | (~c2_1(a2277))) <=> ((~hskp1) | (~c2_1(a2277)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(311,plain,
% 0.78/0.97 (((~c2_1(a2277)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2277)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(312,axiom,((~c2_1(a2277)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.78/0.97 tff(313,plain,
% 0.78/0.97 ((~hskp1) | (~c2_1(a2277))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.78/0.97 tff(314,plain,
% 0.78/0.97 ((~hskp1) | (~c2_1(a2277))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[313, 310])).
% 0.78/0.97 tff(315,plain,
% 0.78/0.97 (~c2_1(a2277)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[314, 309])).
% 0.78/0.97 tff(316,assumption,(hskp17), introduced(assumption)).
% 0.78/0.97 tff(317,plain,
% 0.78/0.97 (~c3_1(a2306)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[265, 316])).
% 0.78/0.97 tff(318,plain,
% 0.78/0.97 (~c2_1(a2306)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[236, 316])).
% 0.78/0.97 tff(319,plain,
% 0.78/0.97 (~c1_1(a2306)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[242, 316])).
% 0.78/0.97 tff(320,plain,
% 0.78/0.97 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(321,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[320])).
% 0.78/0.98 tff(322,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(323,plain,
% 0.78/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(324,plain,
% 0.78/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[323])).
% 0.78/0.98 tff(325,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 0.78/0.98 tff(326,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.78/0.98 tff(327,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.78/0.98 tff(328,plain,(
% 0.78/0.98 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.98 inference(skolemize,[status(sab)],[327])).
% 0.78/0.98 tff(329,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[328, 321])).
% 0.78/0.98 tff(330,plain,
% 0.78/0.98 (((~hskp1) | c1_1(a2277)) <=> ((~hskp1) | c1_1(a2277))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(331,axiom,((~hskp1) | c1_1(a2277)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.78/0.98 tff(332,plain,
% 0.78/0.98 ((~hskp1) | c1_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.78/0.98 tff(333,plain,
% 0.78/0.98 ((~hskp1) | c1_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[332, 330])).
% 0.78/0.98 tff(334,plain,
% 0.78/0.98 ((~hskp1) | c1_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[333, 330])).
% 0.78/0.98 tff(335,plain,
% 0.78/0.98 ((~hskp1) | c1_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[334, 330])).
% 0.78/0.98 tff(336,plain,
% 0.78/0.98 ((~hskp1) | c1_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[335, 330])).
% 0.78/0.98 tff(337,plain,
% 0.78/0.98 (c1_1(a2277)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[336, 309])).
% 0.78/0.98 tff(338,plain,
% 0.78/0.98 (((~hskp1) | c0_1(a2277)) <=> ((~hskp1) | c0_1(a2277))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(339,axiom,((~hskp1) | c0_1(a2277)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.78/0.98 tff(340,plain,
% 0.78/0.98 ((~hskp1) | c0_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.78/0.98 tff(341,plain,
% 0.78/0.98 ((~hskp1) | c0_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[340, 338])).
% 0.78/0.98 tff(342,plain,
% 0.78/0.98 ((~hskp1) | c0_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[341, 338])).
% 0.78/0.98 tff(343,plain,
% 0.78/0.98 ((~hskp1) | c0_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[342, 338])).
% 0.78/0.98 tff(344,plain,
% 0.78/0.98 ((~hskp1) | c0_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[343, 338])).
% 0.78/0.98 tff(345,plain,
% 0.78/0.98 (c0_1(a2277)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[344, 309])).
% 0.78/0.98 tff(346,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(347,plain,
% 0.78/0.98 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277))) <=> (hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(348,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277)))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[347])).
% 0.78/0.98 tff(349,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 0.78/0.98 inference(transitivity,[status(thm)],[348, 346])).
% 0.78/0.98 tff(350,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(351,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.78/0.98 tff(352,plain,
% 0.78/0.98 (c3_1(a2277)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[351, 160, 78, 345, 337, 315, 329])).
% 0.78/0.98 tff(353,plain,
% 0.78/0.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(354,plain,
% 0.78/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[353])).
% 0.78/0.98 tff(355,plain,
% 0.78/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(356,plain,
% 0.78/0.98 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(357,plain,
% 0.78/0.98 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[356])).
% 0.78/0.98 tff(358,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause201')).
% 0.78/0.98 tff(359,plain,
% 0.78/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.78/0.98 tff(360,plain,
% 0.78/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[359, 355])).
% 0.78/0.98 tff(361,plain,(
% 0.78/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.78/0.98 inference(skolemize,[status(sab)],[360])).
% 0.78/0.98 tff(362,plain,
% 0.78/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[361, 354])).
% 0.78/0.98 tff(363,assumption,(~c3_1(a2306)), introduced(assumption)).
% 0.78/0.98 tff(364,assumption,(~c2_1(a2306)), introduced(assumption)).
% 0.78/0.98 tff(365,assumption,(~c1_1(a2306)), introduced(assumption)).
% 0.78/0.98 tff(366,assumption,(hskp6), introduced(assumption)).
% 0.78/0.98 tff(367,plain,
% 0.78/0.98 (((~hskp6) | c1_1(a2285)) <=> ((~hskp6) | c1_1(a2285))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(368,axiom,((~hskp6) | c1_1(a2285)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.78/0.98 tff(369,plain,
% 0.78/0.98 ((~hskp6) | c1_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.78/0.98 tff(370,plain,
% 0.78/0.98 ((~hskp6) | c1_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[369, 367])).
% 0.78/0.98 tff(371,plain,
% 0.78/0.98 ((~hskp6) | c1_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[370, 367])).
% 0.78/0.98 tff(372,plain,
% 0.78/0.98 ((~hskp6) | c1_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.78/0.98 tff(373,plain,
% 0.78/0.98 ((~hskp6) | c1_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[372, 367])).
% 0.78/0.98 tff(374,plain,
% 0.78/0.98 (c1_1(a2285)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[373, 366])).
% 0.78/0.98 tff(375,plain,
% 0.78/0.98 (((~hskp6) | c0_1(a2285)) <=> ((~hskp6) | c0_1(a2285))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(376,axiom,((~hskp6) | c0_1(a2285)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.78/0.98 tff(377,plain,
% 0.78/0.98 ((~hskp6) | c0_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.78/0.98 tff(378,plain,
% 0.78/0.98 ((~hskp6) | c0_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[377, 375])).
% 0.78/0.98 tff(379,plain,
% 0.78/0.98 ((~hskp6) | c0_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[378, 375])).
% 0.78/0.98 tff(380,plain,
% 0.78/0.98 ((~hskp6) | c0_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[379, 375])).
% 0.78/0.98 tff(381,plain,
% 0.78/0.98 ((~hskp6) | c0_1(a2285)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[380, 375])).
% 0.78/0.98 tff(382,plain,
% 0.78/0.98 (c0_1(a2285)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[381, 366])).
% 0.78/0.98 tff(383,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(384,plain,
% 0.78/0.98 (((~ndr1_0) | (~c0_1(a2285)) | (~c1_1(a2285)) | (~c2_1(a2285)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306)) <=> (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(385,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2285)) | (~c1_1(a2285)) | (~c2_1(a2285)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[384])).
% 0.78/0.98 tff(386,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2285)) | (~c1_1(a2285)) | (~c2_1(a2285)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[385, 383])).
% 0.78/0.98 tff(387,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2285)) | (~c1_1(a2285)) | (~c2_1(a2285)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(388,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.78/0.98 tff(389,plain,
% 0.78/0.98 (~c2_1(a2285)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[388, 160, 382, 374, 345, 365, 364, 363, 315, 362, 352])).
% 0.78/0.98 tff(390,plain,
% 0.78/0.98 (((~hskp6) | (~c3_1(a2285))) <=> ((~hskp6) | (~c3_1(a2285)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(391,plain,
% 0.78/0.98 (((~c3_1(a2285)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a2285)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(392,axiom,((~c3_1(a2285)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.78/0.98 tff(393,plain,
% 0.78/0.98 ((~hskp6) | (~c3_1(a2285))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.78/0.98 tff(394,plain,
% 0.78/0.98 ((~hskp6) | (~c3_1(a2285))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[393, 390])).
% 0.78/0.98 tff(395,plain,
% 0.78/0.98 (~c3_1(a2285)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[394, 366])).
% 0.78/0.98 tff(396,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(397,plain,
% 0.78/0.98 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285))) <=> (hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(398,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[397])).
% 0.78/0.98 tff(399,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[398, 396])).
% 0.78/0.98 tff(400,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(401,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2285) | (~c0_1(a2285))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.78/0.98 tff(402,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[401, 160, 78, 382, 345, 337, 395, 315, 329, 389])).
% 0.78/0.98 tff(403,plain,((~hskp6) | hskp14 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(404,plain,
% 0.78/0.98 (~hskp6),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[403, 319, 78, 318, 317])).
% 0.78/0.98 tff(405,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(406,plain,
% 0.78/0.98 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(407,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[406])).
% 0.78/0.98 tff(408,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[407, 405])).
% 0.78/0.98 tff(409,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(410,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2306))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.78/0.98 tff(411,plain,
% 0.78/0.98 (~c0_1(a2306)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[410, 160, 78, 345, 337, 318, 317, 315, 329])).
% 0.78/0.98 tff(412,plain,
% 0.78/0.98 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(413,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[412])).
% 0.78/0.98 tff(414,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(415,plain,
% 0.78/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(416,plain,
% 0.78/0.98 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[415])).
% 0.78/0.98 tff(417,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.78/0.98 tff(418,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.78/0.98 tff(419,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[418, 414])).
% 0.78/0.98 tff(420,plain,(
% 0.78/0.98 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.98 inference(skolemize,[status(sab)],[419])).
% 0.78/0.98 tff(421,plain,
% 0.78/0.98 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[420, 413])).
% 0.78/0.98 tff(422,assumption,(~hskp3), introduced(assumption)).
% 0.78/0.98 tff(423,plain,
% 0.78/0.98 ((hskp22 | hskp14 | hskp3) <=> (hskp22 | hskp14 | hskp3)),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(424,plain,
% 0.78/0.98 (((hskp14 | hskp3) | hskp22) <=> (hskp22 | hskp14 | hskp3)),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(425,plain,
% 0.78/0.98 ((hskp3 | hskp14) <=> (hskp14 | hskp3)),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(426,plain,
% 0.78/0.98 (((hskp3 | hskp14) | hskp22) <=> ((hskp14 | hskp3) | hskp22)),
% 0.78/0.98 inference(monotonicity,[status(thm)],[425])).
% 0.78/0.98 tff(427,plain,
% 0.78/0.98 (((hskp3 | hskp14) | hskp22) <=> (hskp22 | hskp14 | hskp3)),
% 0.78/0.98 inference(transitivity,[status(thm)],[426, 424])).
% 0.78/0.98 tff(428,axiom,((hskp3 | hskp14) | hskp22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.78/0.98 tff(429,plain,
% 0.78/0.98 (hskp22 | hskp14 | hskp3),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.78/0.98 tff(430,plain,
% 0.78/0.98 (hskp22 | hskp14 | hskp3),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[429, 423])).
% 0.78/0.98 tff(431,plain,
% 0.78/0.98 (hskp22 | hskp14 | hskp3),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[430, 423])).
% 0.78/0.98 tff(432,plain,
% 0.78/0.98 (hskp22 | hskp14 | hskp3),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[431, 423])).
% 0.78/0.98 tff(433,plain,
% 0.78/0.98 (hskp22 | hskp14 | hskp3),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[432, 423])).
% 0.78/0.98 tff(434,plain,
% 0.78/0.98 (hskp22),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[433, 422, 78])).
% 0.78/0.98 tff(435,plain,
% 0.78/0.98 (((~hskp22) | (~c1_1(a2325))) <=> ((~hskp22) | (~c1_1(a2325)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(436,plain,
% 0.78/0.98 (((~c1_1(a2325)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a2325)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(437,axiom,((~c1_1(a2325)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.78/0.99 tff(438,plain,
% 0.78/0.99 ((~hskp22) | (~c1_1(a2325))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.78/0.99 tff(439,plain,
% 0.78/0.99 ((~hskp22) | (~c1_1(a2325))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[438, 435])).
% 0.78/0.99 tff(440,plain,
% 0.78/0.99 (~c1_1(a2325)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[439, 434])).
% 0.78/0.99 tff(441,plain,
% 0.78/0.99 (((~hskp22) | (~c0_1(a2325))) <=> ((~hskp22) | (~c0_1(a2325)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(442,plain,
% 0.78/0.99 (((~c0_1(a2325)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a2325)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(443,axiom,((~c0_1(a2325)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.78/0.99 tff(444,plain,
% 0.78/0.99 ((~hskp22) | (~c0_1(a2325))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.78/0.99 tff(445,plain,
% 0.78/0.99 ((~hskp22) | (~c0_1(a2325))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[444, 441])).
% 0.78/0.99 tff(446,plain,
% 0.78/0.99 (~c0_1(a2325)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[445, 434])).
% 0.78/0.99 tff(447,plain,
% 0.78/0.99 (((~hskp22) | c2_1(a2325)) <=> ((~hskp22) | c2_1(a2325))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(448,axiom,((~hskp22) | c2_1(a2325)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.78/0.99 tff(449,plain,
% 0.78/0.99 ((~hskp22) | c2_1(a2325)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.78/0.99 tff(450,plain,
% 0.78/0.99 ((~hskp22) | c2_1(a2325)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[449, 447])).
% 0.78/0.99 tff(451,plain,
% 0.78/0.99 ((~hskp22) | c2_1(a2325)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[450, 447])).
% 0.78/0.99 tff(452,plain,
% 0.78/0.99 ((~hskp22) | c2_1(a2325)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[451, 447])).
% 0.78/0.99 tff(453,plain,
% 0.78/0.99 ((~hskp22) | c2_1(a2325)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[452, 447])).
% 0.78/0.99 tff(454,plain,
% 0.78/0.99 (c2_1(a2325)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[453, 434])).
% 0.78/0.99 tff(455,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(456,plain,
% 0.78/0.99 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2325) | (~c2_1(a2325)) | (~c3_1(a2325)) | c0_1(a2325) | c1_1(a2325) | (~c2_1(a2325))) <=> (c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(457,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2325) | (~c2_1(a2325)) | (~c3_1(a2325)) | c0_1(a2325) | c1_1(a2325) | (~c2_1(a2325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[456])).
% 0.78/0.99 tff(458,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2325) | (~c2_1(a2325)) | (~c3_1(a2325)) | c0_1(a2325) | c1_1(a2325) | (~c2_1(a2325)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[457, 455])).
% 0.78/0.99 tff(459,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2325) | (~c2_1(a2325)) | (~c3_1(a2325)) | c0_1(a2325) | c1_1(a2325) | (~c2_1(a2325)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(460,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2325) | c1_1(a2325) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2325)) | (~c3_1(a2325))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.78/0.99 tff(461,plain,
% 0.78/0.99 (~c3_1(a2325)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[460, 160, 454, 337, 446, 440, 315, 196, 352])).
% 0.78/0.99 tff(462,plain,
% 0.78/0.99 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(463,plain,
% 0.78/0.99 ((hskp17 | hskp14 | (~ndr1_0) | c0_1(a2325) | c3_1(a2325) | (~c2_1(a2325))) <=> (hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(464,plain,
% 0.78/0.99 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2325) | c3_1(a2325) | (~c2_1(a2325)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325)))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[463])).
% 0.78/0.99 tff(465,plain,
% 0.78/0.99 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2325) | c3_1(a2325) | (~c2_1(a2325)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325))),
% 0.78/0.99 inference(transitivity,[status(thm)],[464, 462])).
% 0.78/0.99 tff(466,plain,
% 0.78/0.99 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2325) | c3_1(a2325) | (~c2_1(a2325)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(467,plain,
% 0.78/0.99 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp17 | hskp14 | c0_1(a2325) | (~ndr1_0) | (~c2_1(a2325)) | c3_1(a2325)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.78/0.99 tff(468,plain,
% 0.78/0.99 (hskp17),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[467, 160, 78, 454, 446, 216, 461])).
% 0.78/0.99 tff(469,plain,
% 0.78/0.99 (~c3_1(a2306)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[265, 468])).
% 0.78/0.99 tff(470,plain,
% 0.78/0.99 (~c2_1(a2306)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[236, 468])).
% 0.78/0.99 tff(471,plain,
% 0.78/0.99 (~c0_1(a2306)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[410, 160, 78, 345, 337, 470, 469, 315, 329])).
% 0.78/0.99 tff(472,plain,
% 0.78/0.99 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.78/0.99 inference(bind,[status(th)],[])).
% 0.78/0.99 tff(473,plain,
% 0.78/0.99 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/0.99 inference(quant_intro,[status(thm)],[472])).
% 0.78/0.99 tff(474,plain,
% 0.78/0.99 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(475,plain,
% 0.78/0.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.78/0.99 inference(bind,[status(th)],[])).
% 0.78/0.99 tff(476,plain,
% 0.78/0.99 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/0.99 inference(quant_intro,[status(thm)],[475])).
% 0.78/0.99 tff(477,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.78/0.99 tff(478,plain,
% 0.78/0.99 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.78/0.99 tff(479,plain,
% 0.78/0.99 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[478, 474])).
% 0.78/0.99 tff(480,plain,(
% 0.78/0.99 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/0.99 inference(skolemize,[status(sab)],[479])).
% 0.78/0.99 tff(481,plain,
% 0.78/0.99 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[480, 473])).
% 0.78/0.99 tff(482,plain,
% 0.78/0.99 (~c1_1(a2306)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[242, 468])).
% 0.78/0.99 tff(483,assumption,(hskp2), introduced(assumption)).
% 0.78/0.99 tff(484,plain,
% 0.78/0.99 (((~hskp2) | (~c3_1(a2279))) <=> ((~hskp2) | (~c3_1(a2279)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(485,plain,
% 0.78/0.99 (((~c3_1(a2279)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a2279)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(486,axiom,((~c3_1(a2279)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.78/0.99 tff(487,plain,
% 0.78/0.99 ((~hskp2) | (~c3_1(a2279))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.78/0.99 tff(488,plain,
% 0.78/0.99 ((~hskp2) | (~c3_1(a2279))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[487, 484])).
% 0.78/0.99 tff(489,plain,
% 0.78/0.99 (~c3_1(a2279)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[488, 483])).
% 0.78/0.99 tff(490,plain,
% 0.78/0.99 (((~hskp2) | (~c2_1(a2279))) <=> ((~hskp2) | (~c2_1(a2279)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(491,plain,
% 0.78/0.99 (((~c2_1(a2279)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a2279)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(492,axiom,((~c2_1(a2279)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.78/0.99 tff(493,plain,
% 0.78/0.99 ((~hskp2) | (~c2_1(a2279))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.78/0.99 tff(494,plain,
% 0.78/0.99 ((~hskp2) | (~c2_1(a2279))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[493, 490])).
% 0.78/0.99 tff(495,plain,
% 0.78/0.99 (~c2_1(a2279)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[494, 483])).
% 0.78/0.99 tff(496,plain,
% 0.78/0.99 (((~hskp2) | c0_1(a2279)) <=> ((~hskp2) | c0_1(a2279))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(497,axiom,((~hskp2) | c0_1(a2279)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.78/0.99 tff(498,plain,
% 0.78/0.99 ((~hskp2) | c0_1(a2279)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.78/0.99 tff(499,plain,
% 0.78/0.99 ((~hskp2) | c0_1(a2279)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[498, 496])).
% 0.78/0.99 tff(500,plain,
% 0.78/0.99 ((~hskp2) | c0_1(a2279)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[499, 496])).
% 0.78/0.99 tff(501,plain,
% 0.78/0.99 ((~hskp2) | c0_1(a2279)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[500, 496])).
% 0.78/0.99 tff(502,plain,
% 0.78/0.99 ((~hskp2) | c0_1(a2279)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[501, 496])).
% 0.78/0.99 tff(503,plain,
% 0.78/0.99 (c0_1(a2279)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[502, 483])).
% 0.78/0.99 tff(504,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(505,plain,
% 0.78/0.99 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279))) <=> (hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(506,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[505])).
% 0.78/0.99 tff(507,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[506, 504])).
% 0.78/0.99 tff(508,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(509,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2279) | c3_1(a2279) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2279))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[508, 507])).
% 0.78/0.99 tff(510,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[509, 160, 78, 503, 345, 337, 495, 489, 315, 329])).
% 0.78/0.99 tff(511,plain,((~hskp2) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(512,plain,
% 0.78/0.99 (~hskp2),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[511, 78])).
% 0.78/0.99 tff(513,plain,
% 0.78/0.99 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(514,plain,
% 0.78/0.99 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306)) <=> (hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(515,plain,
% 0.78/0.99 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[514])).
% 0.78/0.99 tff(516,plain,
% 0.78/0.99 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.78/0.99 inference(transitivity,[status(thm)],[515, 513])).
% 0.78/0.99 tff(517,plain,
% 0.78/0.99 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(518,plain,
% 0.78/0.99 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c1_1(a2306) | c2_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[517, 516])).
% 0.78/0.99 tff(519,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[518, 160, 422, 512, 482, 470, 481, 471])).
% 0.78/0.99 tff(520,plain,(hskp3 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(521,plain,
% 0.78/0.99 (hskp3),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[520, 78])).
% 0.78/0.99 tff(522,plain,
% 0.78/0.99 (((~hskp3) | (~c2_1(a2280))) <=> ((~hskp3) | (~c2_1(a2280)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(523,plain,
% 0.78/0.99 (((~c2_1(a2280)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a2280)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(524,axiom,((~c2_1(a2280)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.78/0.99 tff(525,plain,
% 0.78/0.99 ((~hskp3) | (~c2_1(a2280))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.78/0.99 tff(526,plain,
% 0.78/0.99 ((~hskp3) | (~c2_1(a2280))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[525, 522])).
% 0.78/0.99 tff(527,plain,
% 0.78/0.99 (~c2_1(a2280)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[526, 521])).
% 0.78/0.99 tff(528,plain,
% 0.78/0.99 (((~hskp3) | c3_1(a2280)) <=> ((~hskp3) | c3_1(a2280))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(529,axiom,((~hskp3) | c3_1(a2280)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.78/0.99 tff(530,plain,
% 0.78/0.99 ((~hskp3) | c3_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.78/0.99 tff(531,plain,
% 0.78/0.99 ((~hskp3) | c3_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[530, 528])).
% 0.78/0.99 tff(532,plain,
% 0.78/0.99 ((~hskp3) | c3_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[531, 528])).
% 0.78/0.99 tff(533,plain,
% 0.78/0.99 ((~hskp3) | c3_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[532, 528])).
% 0.78/0.99 tff(534,plain,
% 0.78/0.99 ((~hskp3) | c3_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[533, 528])).
% 0.78/0.99 tff(535,plain,
% 0.78/0.99 (c3_1(a2280)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[534, 521])).
% 0.78/0.99 tff(536,plain,
% 0.78/0.99 (((~hskp3) | c1_1(a2280)) <=> ((~hskp3) | c1_1(a2280))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(537,axiom,((~hskp3) | c1_1(a2280)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.78/0.99 tff(538,plain,
% 0.78/0.99 ((~hskp3) | c1_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.78/0.99 tff(539,plain,
% 0.78/0.99 ((~hskp3) | c1_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[538, 536])).
% 0.78/0.99 tff(540,plain,
% 0.78/0.99 ((~hskp3) | c1_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[539, 536])).
% 0.78/0.99 tff(541,plain,
% 0.78/0.99 ((~hskp3) | c1_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[540, 536])).
% 0.78/0.99 tff(542,plain,
% 0.78/0.99 ((~hskp3) | c1_1(a2280)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[541, 536])).
% 0.78/0.99 tff(543,plain,
% 0.78/0.99 (c1_1(a2280)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[542, 521])).
% 0.78/0.99 tff(544,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(545,plain,
% 0.78/0.99 ((hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306)) <=> (hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(546,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306)))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[545])).
% 0.78/0.99 tff(547,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306))),
% 0.78/0.99 inference(transitivity,[status(thm)],[546, 544])).
% 0.78/0.99 tff(548,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(549,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2306) | c2_1(a2306) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c0_1(a2306)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.78/0.99 tff(550,plain,
% 0.78/0.99 (hskp28),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[549, 160, 543, 535, 319, 318, 527, 421, 411])).
% 0.78/0.99 tff(551,plain,
% 0.78/0.99 (((~hskp28) | c3_1(a2278)) <=> ((~hskp28) | c3_1(a2278))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(552,axiom,((~hskp28) | c3_1(a2278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.78/0.99 tff(553,plain,
% 0.78/0.99 ((~hskp28) | c3_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.78/0.99 tff(554,plain,
% 0.78/0.99 ((~hskp28) | c3_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[553, 551])).
% 0.78/0.99 tff(555,plain,
% 0.78/0.99 ((~hskp28) | c3_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[554, 551])).
% 0.78/0.99 tff(556,plain,
% 0.78/0.99 ((~hskp28) | c3_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[555, 551])).
% 0.78/0.99 tff(557,plain,
% 0.78/0.99 ((~hskp28) | c3_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[556, 551])).
% 0.78/0.99 tff(558,plain,
% 0.78/0.99 (c3_1(a2278)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[557, 550])).
% 0.78/0.99 tff(559,plain,
% 0.78/0.99 (((~hskp28) | c1_1(a2278)) <=> ((~hskp28) | c1_1(a2278))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(560,axiom,((~hskp28) | c1_1(a2278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.78/0.99 tff(561,plain,
% 0.78/0.99 ((~hskp28) | c1_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.78/0.99 tff(562,plain,
% 0.78/0.99 ((~hskp28) | c1_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[561, 559])).
% 0.78/0.99 tff(563,plain,
% 0.78/0.99 ((~hskp28) | c1_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[562, 559])).
% 0.78/0.99 tff(564,plain,
% 0.78/0.99 ((~hskp28) | c1_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[563, 559])).
% 0.78/0.99 tff(565,plain,
% 0.78/0.99 ((~hskp28) | c1_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[564, 559])).
% 0.78/0.99 tff(566,plain,
% 0.78/0.99 (c1_1(a2278)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[565, 550])).
% 0.78/0.99 tff(567,plain,
% 0.78/0.99 (((~hskp28) | c0_1(a2278)) <=> ((~hskp28) | c0_1(a2278))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(568,axiom,((~hskp28) | c0_1(a2278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.78/0.99 tff(569,plain,
% 0.78/0.99 ((~hskp28) | c0_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.78/0.99 tff(570,plain,
% 0.78/0.99 ((~hskp28) | c0_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[569, 567])).
% 0.78/0.99 tff(571,plain,
% 0.78/0.99 ((~hskp28) | c0_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[570, 567])).
% 0.78/0.99 tff(572,plain,
% 0.78/0.99 ((~hskp28) | c0_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[571, 567])).
% 0.78/0.99 tff(573,plain,
% 0.78/0.99 ((~hskp28) | c0_1(a2278)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[572, 567])).
% 0.78/0.99 tff(574,plain,
% 0.78/0.99 (c0_1(a2278)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[573, 550])).
% 0.78/0.99 tff(575,assumption,(~hskp12), introduced(assumption)).
% 0.78/0.99 tff(576,assumption,(~c0_1(a2306)), introduced(assumption)).
% 0.78/0.99 tff(577,plain,
% 0.78/0.99 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.78/0.99 inference(bind,[status(th)],[])).
% 0.78/0.99 tff(578,plain,
% 0.78/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/0.99 inference(quant_intro,[status(thm)],[577])).
% 0.78/0.99 tff(579,plain,
% 0.78/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(580,plain,
% 0.78/0.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ((hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp12))), rewrite(((hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.78/0.99 inference(bind,[status(th)],[])).
% 0.78/0.99 tff(581,plain,
% 0.78/0.99 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/0.99 inference(quant_intro,[status(thm)],[580])).
% 0.78/0.99 tff(582,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 0.78/0.99 tff(583,plain,
% 0.78/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.78/0.99 tff(584,plain,
% 0.78/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[583, 579])).
% 0.78/0.99 tff(585,plain,(
% 0.78/0.99 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/0.99 inference(skolemize,[status(sab)],[584])).
% 0.78/0.99 tff(586,plain,
% 0.78/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[585, 578])).
% 0.78/0.99 tff(587,plain,
% 0.78/0.99 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(588,plain,
% 0.78/0.99 ((hskp12 | hskp11 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306)) <=> (hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(589,plain,
% 0.78/0.99 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[588])).
% 0.78/0.99 tff(590,plain,
% 0.78/0.99 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.78/0.99 inference(transitivity,[status(thm)],[589, 587])).
% 0.78/0.99 tff(591,plain,
% 0.78/0.99 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp12 | hskp11 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(592,plain,
% 0.78/0.99 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp12 | hskp11 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.78/0.99 tff(593,plain,
% 0.78/0.99 (hskp12 | hskp11),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[592, 160, 364, 363, 586, 576])).
% 0.78/0.99 tff(594,plain,
% 0.78/0.99 (hskp11),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[593, 575])).
% 0.78/0.99 tff(595,plain,
% 0.78/0.99 (((~hskp11) | (~c1_1(a2294))) <=> ((~hskp11) | (~c1_1(a2294)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(596,plain,
% 0.78/0.99 (((~c1_1(a2294)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a2294)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(597,axiom,((~c1_1(a2294)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.78/0.99 tff(598,plain,
% 0.78/0.99 ((~hskp11) | (~c1_1(a2294))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.78/0.99 tff(599,plain,
% 0.78/0.99 ((~hskp11) | (~c1_1(a2294))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[598, 595])).
% 0.78/0.99 tff(600,plain,
% 0.78/0.99 (~c1_1(a2294)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[599, 594])).
% 0.78/0.99 tff(601,assumption,(c1_1(a2277)), introduced(assumption)).
% 0.78/0.99 tff(602,assumption,(c0_1(a2277)), introduced(assumption)).
% 0.78/0.99 tff(603,plain,
% 0.78/0.99 (((~hskp11) | c0_1(a2294)) <=> ((~hskp11) | c0_1(a2294))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(604,axiom,((~hskp11) | c0_1(a2294)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.78/0.99 tff(605,plain,
% 0.78/0.99 ((~hskp11) | c0_1(a2294)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[604, 603])).
% 0.78/0.99 tff(606,plain,
% 0.78/0.99 ((~hskp11) | c0_1(a2294)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[605, 603])).
% 0.78/0.99 tff(607,plain,
% 0.78/0.99 ((~hskp11) | c0_1(a2294)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[606, 603])).
% 0.78/0.99 tff(608,plain,
% 0.78/0.99 ((~hskp11) | c0_1(a2294)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[607, 603])).
% 0.78/0.99 tff(609,plain,
% 0.78/0.99 ((~hskp11) | c0_1(a2294)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[608, 603])).
% 0.78/0.99 tff(610,plain,
% 0.78/0.99 (c0_1(a2294)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[609, 594])).
% 0.78/0.99 tff(611,assumption,(c3_1(a2278)), introduced(assumption)).
% 0.78/0.99 tff(612,assumption,(c1_1(a2278)), introduced(assumption)).
% 0.78/0.99 tff(613,assumption,(c0_1(a2278)), introduced(assumption)).
% 0.78/0.99 tff(614,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(615,plain,
% 0.78/0.99 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294))) <=> (c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(616,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[615])).
% 0.78/1.00 tff(617,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[616, 614])).
% 0.78/1.00 tff(618,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(619,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2294)) | (~c0_1(a2294))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.78/1.00 tff(620,plain,
% 0.78/1.00 (~c3_1(a2294)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[619, 160, 613, 612, 611, 610, 602, 601, 600, 34, 88])).
% 0.78/1.00 tff(621,plain,
% 0.78/1.00 (^[U: $i] : refl((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.78/1.00 inference(bind,[status(th)],[])).
% 0.78/1.00 tff(622,plain,
% 0.78/1.00 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/1.00 inference(quant_intro,[status(thm)],[621])).
% 0.78/1.00 tff(623,plain,
% 0.78/1.00 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(624,plain,
% 0.78/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.78/1.00 inference(bind,[status(th)],[])).
% 0.78/1.00 tff(625,plain,
% 0.78/1.00 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/1.00 inference(quant_intro,[status(thm)],[624])).
% 0.78/1.00 tff(626,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 0.78/1.00 tff(627,plain,
% 0.78/1.00 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.78/1.00 tff(628,plain,
% 0.78/1.00 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[627, 623])).
% 0.78/1.00 tff(629,plain,(
% 0.78/1.00 ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/1.00 inference(skolemize,[status(sab)],[628])).
% 0.78/1.00 tff(630,plain,
% 0.78/1.00 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[629, 622])).
% 0.78/1.00 tff(631,plain,
% 0.78/1.00 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(632,plain,
% 0.78/1.00 ((hskp12 | (~ndr1_0) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294))) <=> (hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(633,plain,
% 0.78/1.00 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[632])).
% 0.78/1.00 tff(634,plain,
% 0.78/1.00 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[633, 631])).
% 0.78/1.00 tff(635,plain,
% 0.78/1.00 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(636,plain,
% 0.78/1.00 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2294) | (~ndr1_0) | c3_1(a2294) | (~c0_1(a2294))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.78/1.00 tff(637,plain,
% 0.78/1.00 ($false),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[636, 160, 575, 610, 600, 630, 620])).
% 0.78/1.00 tff(638,plain,(hskp12 | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | c2_1(a2306) | c3_1(a2306) | c0_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.00 tff(639,plain,
% 0.78/1.00 (hskp12),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[638, 574, 566, 558, 345, 337, 315, 318, 317, 411])).
% 0.78/1.00 tff(640,plain,
% 0.78/1.00 (((~hskp12) | (~c3_1(a2295))) <=> ((~hskp12) | (~c3_1(a2295)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(641,plain,
% 0.78/1.00 (((~c3_1(a2295)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a2295)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(642,axiom,((~c3_1(a2295)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.78/1.00 tff(643,plain,
% 0.78/1.00 ((~hskp12) | (~c3_1(a2295))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[642, 641])).
% 0.78/1.00 tff(644,plain,
% 0.78/1.00 ((~hskp12) | (~c3_1(a2295))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[643, 640])).
% 0.78/1.00 tff(645,plain,
% 0.78/1.00 (~c3_1(a2295)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[644, 639])).
% 0.78/1.00 tff(646,plain,
% 0.78/1.00 (((~hskp12) | c0_1(a2295)) <=> ((~hskp12) | c0_1(a2295))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(647,axiom,((~hskp12) | c0_1(a2295)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.78/1.00 tff(648,plain,
% 0.78/1.00 ((~hskp12) | c0_1(a2295)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.78/1.00 tff(649,plain,
% 0.78/1.00 ((~hskp12) | c0_1(a2295)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[648, 646])).
% 0.78/1.00 tff(650,plain,
% 0.78/1.00 ((~hskp12) | c0_1(a2295)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[649, 646])).
% 0.78/1.00 tff(651,plain,
% 0.78/1.00 ((~hskp12) | c0_1(a2295)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[650, 646])).
% 0.78/1.00 tff(652,plain,
% 0.78/1.00 ((~hskp12) | c0_1(a2295)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[651, 646])).
% 0.78/1.00 tff(653,plain,
% 0.78/1.00 (c0_1(a2295)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[652, 639])).
% 0.78/1.00 tff(654,assumption,(~c2_1(a2295)), introduced(assumption)).
% 0.78/1.00 tff(655,assumption,(~c3_1(a2295)), introduced(assumption)).
% 0.78/1.00 tff(656,assumption,(c0_1(a2295)), introduced(assumption)).
% 0.78/1.00 tff(657,plain,
% 0.78/1.00 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(658,plain,
% 0.78/1.00 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(659,plain,
% 0.78/1.00 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[658])).
% 0.78/1.00 tff(660,plain,
% 0.78/1.00 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[659, 657])).
% 0.78/1.00 tff(661,plain,
% 0.78/1.00 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(662,plain,
% 0.78/1.00 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2295) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2295) | (~c0_1(a2295))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.78/1.00 tff(663,plain,
% 0.78/1.00 ($false),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[662, 160, 78, 656, 345, 337, 655, 315, 329, 654])).
% 0.78/1.00 tff(664,plain,(c2_1(a2295) | hskp14 | (~c0_1(a2295)) | c3_1(a2295)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.00 tff(665,plain,
% 0.78/1.00 (c2_1(a2295)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[664, 653, 78, 645])).
% 0.78/1.00 tff(666,plain,
% 0.78/1.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.78/1.00 inference(bind,[status(th)],[])).
% 0.78/1.00 tff(667,plain,
% 0.78/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.78/1.00 inference(quant_intro,[status(thm)],[666])).
% 0.78/1.00 tff(668,plain,
% 0.78/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(669,plain,
% 0.78/1.00 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.78/1.00 inference(bind,[status(th)],[])).
% 0.78/1.00 tff(670,plain,
% 0.78/1.00 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.78/1.00 inference(quant_intro,[status(thm)],[669])).
% 0.78/1.00 tff(671,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause202')).
% 0.78/1.00 tff(672,plain,
% 0.78/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[671, 670])).
% 0.78/1.00 tff(673,plain,
% 0.78/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[672, 668])).
% 0.78/1.00 tff(674,plain,(
% 0.78/1.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.78/1.00 inference(skolemize,[status(sab)],[673])).
% 0.78/1.00 tff(675,plain,
% 0.78/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[674, 667])).
% 0.78/1.00 tff(676,assumption,(hskp12), introduced(assumption)).
% 0.78/1.00 tff(677,plain,
% 0.78/1.00 (~c3_1(a2295)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[644, 676])).
% 0.78/1.00 tff(678,plain,
% 0.78/1.00 (c0_1(a2295)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[652, 676])).
% 0.78/1.00 tff(679,assumption,(~hskp4), introduced(assumption)).
% 0.78/1.00 tff(680,plain,
% 0.78/1.00 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(681,plain,
% 0.78/1.00 ((hskp4 | hskp2 | (~ndr1_0) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295))) <=> (hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(682,plain,
% 0.78/1.00 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[681])).
% 0.78/1.00 tff(683,plain,
% 0.78/1.00 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[682, 680])).
% 0.78/1.00 tff(684,plain,
% 0.78/1.00 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(685,plain,
% 0.78/1.00 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.78/1.00 tff(686,plain,
% 0.78/1.00 (~c2_1(a2295)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[685, 160, 679, 512, 678, 677, 77])).
% 0.78/1.00 tff(687,plain,
% 0.78/1.00 ($false),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[662, 160, 78, 678, 345, 337, 677, 315, 329, 686])).
% 0.78/1.00 tff(688,plain,((~hskp12) | hskp14 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.78/1.00 tff(689,plain,
% 0.78/1.00 (hskp4),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[688, 639, 78])).
% 0.78/1.00 tff(690,plain,
% 0.78/1.00 (~c3_1(a2282)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[172, 689])).
% 0.78/1.00 tff(691,plain,
% 0.78/1.00 (~c0_1(a2282)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[178, 689])).
% 0.78/1.00 tff(692,plain,
% 0.78/1.00 (c2_1(a2282)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[223, 689])).
% 0.78/1.00 tff(693,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(694,plain,
% 0.78/1.00 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> (c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(695,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[694])).
% 0.78/1.00 tff(696,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[695, 693])).
% 0.78/1.00 tff(697,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(698,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2295) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[697, 696])).
% 0.78/1.00 tff(699,plain,
% 0.78/1.00 ((~c1_1(a2282)) | (~c2_1(a2295))),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[698, 160, 653, 692, 645, 691, 690, 675])).
% 0.78/1.00 tff(700,plain,
% 0.78/1.00 (~c1_1(a2282)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[699, 665])).
% 0.78/1.00 tff(701,assumption,(~c2_1(a2280)), introduced(assumption)).
% 0.78/1.00 tff(702,assumption,(~c0_1(a2282)), introduced(assumption)).
% 0.78/1.00 tff(703,assumption,(hskp20), introduced(assumption)).
% 0.78/1.00 tff(704,plain,
% 0.78/1.00 (~c1_1(a2323)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[112, 703])).
% 0.78/1.00 tff(705,assumption,(c3_1(a2280)), introduced(assumption)).
% 0.78/1.00 tff(706,assumption,(c1_1(a2280)), introduced(assumption)).
% 0.78/1.00 tff(707,assumption,(c2_1(a2282)), introduced(assumption)).
% 0.78/1.00 tff(708,plain,
% 0.78/1.00 (c3_1(a2323)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[120, 703])).
% 0.78/1.00 tff(709,plain,
% 0.78/1.00 (c2_1(a2323)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[128, 703])).
% 0.78/1.00 tff(710,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(711,plain,
% 0.78/1.00 (((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282))) <=> (c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(712,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[711])).
% 0.78/1.00 tff(713,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[712, 710])).
% 0.78/1.00 tff(714,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(715,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.78/1.00 tff(716,plain,
% 0.78/1.00 ($false),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[715, 160, 709, 708, 707, 706, 705, 704, 702, 701, 196, 37])).
% 0.78/1.00 tff(717,plain,((~hskp20) | (~c2_1(a2282)) | (~c1_1(a2280)) | (~c3_1(a2280)) | c0_1(a2282) | c2_1(a2280) | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.00 tff(718,plain,
% 0.78/1.00 (~hskp20),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[717, 692, 543, 535, 691, 527, 700])).
% 0.78/1.00 tff(719,assumption,(hskp30), introduced(assumption)).
% 0.78/1.00 tff(720,plain,
% 0.78/1.00 (((~hskp30) | c3_1(a2315)) <=> ((~hskp30) | c3_1(a2315))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(721,axiom,((~hskp30) | c3_1(a2315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.78/1.00 tff(722,plain,
% 0.78/1.00 ((~hskp30) | c3_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.78/1.00 tff(723,plain,
% 0.78/1.00 ((~hskp30) | c3_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[722, 720])).
% 0.78/1.00 tff(724,plain,
% 0.78/1.00 ((~hskp30) | c3_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[723, 720])).
% 0.78/1.00 tff(725,plain,
% 0.78/1.00 ((~hskp30) | c3_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[724, 720])).
% 0.78/1.00 tff(726,plain,
% 0.78/1.00 ((~hskp30) | c3_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[725, 720])).
% 0.78/1.00 tff(727,plain,
% 0.78/1.00 (c3_1(a2315)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[726, 719])).
% 0.78/1.00 tff(728,plain,
% 0.78/1.00 (((~hskp30) | c2_1(a2315)) <=> ((~hskp30) | c2_1(a2315))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(729,axiom,((~hskp30) | c2_1(a2315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.78/1.00 tff(730,plain,
% 0.78/1.00 ((~hskp30) | c2_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[729, 728])).
% 0.78/1.00 tff(731,plain,
% 0.78/1.00 ((~hskp30) | c2_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[730, 728])).
% 0.78/1.00 tff(732,plain,
% 0.78/1.00 ((~hskp30) | c2_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[731, 728])).
% 0.78/1.00 tff(733,plain,
% 0.78/1.00 ((~hskp30) | c2_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[732, 728])).
% 0.78/1.00 tff(734,plain,
% 0.78/1.00 ((~hskp30) | c2_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[733, 728])).
% 0.78/1.00 tff(735,plain,
% 0.78/1.00 (c2_1(a2315)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[734, 719])).
% 0.78/1.00 tff(736,assumption,(~hskp20), introduced(assumption)).
% 0.78/1.00 tff(737,plain,
% 0.78/1.00 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(738,plain,
% 0.78/1.00 ((hskp20 | (~ndr1_0) | c0_1(a2315) | (~c3_1(a2315)) | (~c2_1(a2315))) <=> (hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(739,plain,
% 0.78/1.00 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2315) | (~c3_1(a2315)) | (~c2_1(a2315)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315)))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[738])).
% 0.78/1.00 tff(740,plain,
% 0.78/1.00 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2315) | (~c3_1(a2315)) | (~c2_1(a2315)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315))),
% 0.78/1.00 inference(transitivity,[status(thm)],[739, 737])).
% 0.78/1.00 tff(741,plain,
% 0.78/1.00 ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2315) | (~c3_1(a2315)) | (~c2_1(a2315)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(742,plain,
% 0.78/1.00 ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | c0_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.78/1.00 tff(743,plain,
% 0.78/1.00 (c0_1(a2315)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[742, 160, 736, 735, 727, 67])).
% 0.78/1.00 tff(744,assumption,(c3_1(a2277)), introduced(assumption)).
% 0.78/1.00 tff(745,plain,
% 0.78/1.00 (((~hskp30) | c1_1(a2315)) <=> ((~hskp30) | c1_1(a2315))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(746,axiom,((~hskp30) | c1_1(a2315)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.78/1.00 tff(747,plain,
% 0.78/1.00 ((~hskp30) | c1_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.78/1.00 tff(748,plain,
% 0.78/1.00 ((~hskp30) | c1_1(a2315)),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[747, 745])).
% 0.78/1.00 tff(749,plain,
% 0.78/1.01 ((~hskp30) | c1_1(a2315)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[748, 745])).
% 0.78/1.01 tff(750,plain,
% 0.78/1.01 ((~hskp30) | c1_1(a2315)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[749, 745])).
% 0.78/1.01 tff(751,plain,
% 0.78/1.01 ((~hskp30) | c1_1(a2315)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[750, 745])).
% 0.78/1.01 tff(752,plain,
% 0.78/1.01 (c1_1(a2315)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[751, 719])).
% 0.78/1.01 tff(753,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(754,plain,
% 0.78/1.01 (((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306)) <=> (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(755,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[754])).
% 0.78/1.01 tff(756,plain,
% 0.78/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[755, 753])).
% 0.78/1.01 tff(757,plain,
% 0.78/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(758,plain,
% 0.78/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.78/1.01 tff(759,plain,
% 0.78/1.01 ($false),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[758, 160, 752, 735, 602, 365, 364, 363, 34, 362, 744, 743])).
% 0.78/1.01 tff(760,plain,((~hskp30) | (~c0_1(a2277)) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | (~c3_1(a2277)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.78/1.01 tff(761,plain,
% 0.78/1.01 (~hskp30),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[760, 319, 345, 318, 317, 315, 352, 718])).
% 0.78/1.01 tff(762,plain,
% 0.78/1.01 ((hskp30 | hskp11 | hskp6) <=> (hskp30 | hskp11 | hskp6)),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(763,plain,
% 0.78/1.01 (((hskp11 | hskp6) | hskp30) <=> (hskp30 | hskp11 | hskp6)),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(764,plain,
% 0.78/1.01 ((hskp6 | hskp11) <=> (hskp11 | hskp6)),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(765,plain,
% 0.78/1.01 (((hskp6 | hskp11) | hskp30) <=> ((hskp11 | hskp6) | hskp30)),
% 0.78/1.01 inference(monotonicity,[status(thm)],[764])).
% 0.78/1.01 tff(766,plain,
% 0.78/1.01 (((hskp6 | hskp11) | hskp30) <=> (hskp30 | hskp11 | hskp6)),
% 0.78/1.01 inference(transitivity,[status(thm)],[765, 763])).
% 0.78/1.01 tff(767,axiom,((hskp6 | hskp11) | hskp30), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.78/1.01 tff(768,plain,
% 0.78/1.01 (hskp30 | hskp11 | hskp6),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.78/1.01 tff(769,plain,
% 0.78/1.01 (hskp30 | hskp11 | hskp6),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[768, 762])).
% 0.78/1.01 tff(770,plain,
% 0.78/1.01 (hskp30 | hskp11 | hskp6),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[769, 762])).
% 0.78/1.01 tff(771,plain,
% 0.78/1.01 (hskp30 | hskp11 | hskp6),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[770, 762])).
% 0.78/1.01 tff(772,plain,
% 0.78/1.01 (hskp30 | hskp11 | hskp6),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[771, 762])).
% 0.78/1.01 tff(773,plain,
% 0.78/1.01 (hskp11),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[772, 761, 404])).
% 0.78/1.01 tff(774,plain,
% 0.78/1.01 (~c1_1(a2294)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[599, 773])).
% 0.78/1.01 tff(775,plain,
% 0.78/1.01 (c0_1(a2294)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[609, 773])).
% 0.78/1.01 tff(776,plain,
% 0.78/1.01 (~c3_1(a2294)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[619, 160, 574, 566, 558, 775, 345, 337, 774, 315, 88])).
% 0.78/1.01 tff(777,plain,
% 0.78/1.01 (((~hskp11) | (~c2_1(a2294))) <=> ((~hskp11) | (~c2_1(a2294)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(778,plain,
% 0.78/1.01 (((~c2_1(a2294)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a2294)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(779,axiom,((~c2_1(a2294)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.78/1.01 tff(780,plain,
% 0.78/1.01 ((~hskp11) | (~c2_1(a2294))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.78/1.01 tff(781,plain,
% 0.78/1.01 ((~hskp11) | (~c2_1(a2294))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[780, 777])).
% 0.78/1.01 tff(782,plain,
% 0.78/1.01 (~c2_1(a2294)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[781, 773])).
% 0.78/1.01 tff(783,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(784,plain,
% 0.78/1.01 ((hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2294) | c3_1(a2294) | (~c0_1(a2294))) <=> (hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(785,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[784])).
% 0.78/1.01 tff(786,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[785, 783])).
% 0.78/1.01 tff(787,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(788,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a2294) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2294) | (~c0_1(a2294))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.78/1.01 tff(789,plain,
% 0.78/1.01 ($false),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[788, 160, 78, 775, 345, 337, 782, 315, 329, 776])).
% 0.78/1.01 tff(790,plain,((~hskp17) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/1.01 tff(791,plain,
% 0.78/1.01 (~hskp17),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[790, 78])).
% 0.78/1.01 tff(792,plain,
% 0.78/1.01 (^[U: $i] : refl((hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.78/1.01 inference(bind,[status(th)],[])).
% 0.78/1.01 tff(793,plain,
% 0.78/1.01 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.78/1.01 inference(quant_intro,[status(thm)],[792])).
% 0.78/1.01 tff(794,plain,
% 0.78/1.01 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(795,plain,
% 0.78/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp17) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.78/1.01 inference(bind,[status(th)],[])).
% 0.78/1.01 tff(796,plain,
% 0.78/1.01 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp17) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.78/1.01 inference(quant_intro,[status(thm)],[795])).
% 0.78/1.01 tff(797,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 0.78/1.01 tff(798,plain,
% 0.78/1.01 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.78/1.01 tff(799,plain,
% 0.78/1.01 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[798, 794])).
% 0.78/1.01 tff(800,plain,(
% 0.78/1.01 ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.78/1.01 inference(skolemize,[status(sab)],[799])).
% 0.78/1.01 tff(801,plain,
% 0.78/1.01 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[800, 793])).
% 0.78/1.01 tff(802,assumption,(hskp0), introduced(assumption)).
% 0.78/1.01 tff(803,plain,
% 0.78/1.01 (((~hskp0) | (~c0_1(a2276))) <=> ((~hskp0) | (~c0_1(a2276)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(804,plain,
% 0.78/1.01 (((~c0_1(a2276)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a2276)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(805,axiom,((~c0_1(a2276)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.78/1.01 tff(806,plain,
% 0.78/1.01 ((~hskp0) | (~c0_1(a2276))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[805, 804])).
% 0.78/1.01 tff(807,plain,
% 0.78/1.01 ((~hskp0) | (~c0_1(a2276))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[806, 803])).
% 0.78/1.01 tff(808,plain,
% 0.78/1.01 (~c0_1(a2276)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[807, 802])).
% 0.78/1.01 tff(809,plain,
% 0.78/1.01 (((~hskp0) | c3_1(a2276)) <=> ((~hskp0) | c3_1(a2276))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(810,axiom,((~hskp0) | c3_1(a2276)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.78/1.01 tff(811,plain,
% 0.78/1.01 ((~hskp0) | c3_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[810, 809])).
% 0.78/1.01 tff(812,plain,
% 0.78/1.01 ((~hskp0) | c3_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[811, 809])).
% 0.78/1.01 tff(813,plain,
% 0.78/1.01 ((~hskp0) | c3_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[812, 809])).
% 0.78/1.01 tff(814,plain,
% 0.78/1.01 ((~hskp0) | c3_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[813, 809])).
% 0.78/1.01 tff(815,plain,
% 0.78/1.01 ((~hskp0) | c3_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[814, 809])).
% 0.78/1.01 tff(816,plain,
% 0.78/1.01 (c3_1(a2276)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[815, 802])).
% 0.78/1.01 tff(817,plain,
% 0.78/1.01 (((~hskp0) | c1_1(a2276)) <=> ((~hskp0) | c1_1(a2276))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(818,axiom,((~hskp0) | c1_1(a2276)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.78/1.01 tff(819,plain,
% 0.78/1.01 ((~hskp0) | c1_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[818, 817])).
% 0.78/1.01 tff(820,plain,
% 0.78/1.01 ((~hskp0) | c1_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[819, 817])).
% 0.78/1.01 tff(821,plain,
% 0.78/1.01 ((~hskp0) | c1_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[820, 817])).
% 0.78/1.01 tff(822,plain,
% 0.78/1.01 ((~hskp0) | c1_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[821, 817])).
% 0.78/1.01 tff(823,plain,
% 0.78/1.01 ((~hskp0) | c1_1(a2276)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[822, 817])).
% 0.78/1.01 tff(824,plain,
% 0.78/1.01 (c1_1(a2276)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[823, 802])).
% 0.78/1.01 tff(825,assumption,(~hskp17), introduced(assumption)).
% 0.78/1.01 tff(826,plain,
% 0.78/1.01 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(827,plain,
% 0.78/1.01 ((hskp17 | hskp14 | (~ndr1_0) | c0_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276))) <=> (hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(828,plain,
% 0.78/1.01 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[827])).
% 0.78/1.01 tff(829,plain,
% 0.78/1.01 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[828, 826])).
% 0.78/1.01 tff(830,plain,
% 0.78/1.01 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(831,plain,
% 0.78/1.01 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c0_1(a2276) | (~ndr1_0) | (~c3_1(a2276)) | (~c1_1(a2276))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[830, 829])).
% 0.78/1.01 tff(832,plain,
% 0.78/1.01 ($false),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[831, 160, 825, 78, 824, 816, 808, 801])).
% 0.78/1.01 tff(833,plain,((~hskp0) | hskp17 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/1.01 tff(834,plain,
% 0.78/1.01 (~hskp0),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[833, 791, 78])).
% 0.78/1.01 tff(835,assumption,(hskp4), introduced(assumption)).
% 0.78/1.01 tff(836,plain,
% 0.78/1.01 (~c3_1(a2282)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[172, 835])).
% 0.78/1.01 tff(837,plain,
% 0.78/1.01 (~c0_1(a2282)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[178, 835])).
% 0.78/1.01 tff(838,plain,
% 0.78/1.01 (c2_1(a2282)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[223, 835])).
% 0.78/1.01 tff(839,plain,
% 0.78/1.01 ($false),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[230, 160, 825, 78, 838, 837, 836, 216])).
% 0.78/1.01 tff(840,plain,((~hskp4) | hskp17 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/1.01 tff(841,plain,
% 0.78/1.01 (~hskp4),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[840, 791, 78])).
% 0.78/1.01 tff(842,plain,
% 0.78/1.01 (~hskp12),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[688, 841, 78])).
% 0.78/1.01 tff(843,plain,
% 0.78/1.01 ((hskp12 | hskp6 | hskp0) <=> (hskp12 | hskp6 | hskp0)),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(844,plain,
% 0.78/1.01 (((hskp12 | hskp6) | hskp0) <=> (hskp12 | hskp6 | hskp0)),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(845,plain,
% 0.78/1.01 ((hskp6 | hskp12) <=> (hskp12 | hskp6)),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(846,plain,
% 0.78/1.01 (((hskp6 | hskp12) | hskp0) <=> ((hskp12 | hskp6) | hskp0)),
% 0.78/1.01 inference(monotonicity,[status(thm)],[845])).
% 0.78/1.01 tff(847,plain,
% 0.78/1.01 (((hskp6 | hskp12) | hskp0) <=> (hskp12 | hskp6 | hskp0)),
% 0.78/1.01 inference(transitivity,[status(thm)],[846, 844])).
% 0.78/1.01 tff(848,axiom,((hskp6 | hskp12) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.78/1.01 tff(849,plain,
% 0.78/1.01 (hskp12 | hskp6 | hskp0),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[848, 847])).
% 0.78/1.01 tff(850,plain,
% 0.78/1.01 (hskp12 | hskp6 | hskp0),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[849, 843])).
% 0.78/1.01 tff(851,plain,
% 0.78/1.01 (hskp12 | hskp6 | hskp0),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[850, 843])).
% 0.78/1.01 tff(852,plain,
% 0.78/1.01 (hskp12 | hskp6 | hskp0),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[851, 843])).
% 0.78/1.01 tff(853,plain,
% 0.78/1.01 (hskp12 | hskp6 | hskp0),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[852, 843])).
% 0.78/1.01 tff(854,plain,
% 0.78/1.01 (hskp6),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[853, 842, 834])).
% 0.78/1.01 tff(855,plain,
% 0.78/1.01 (~c3_1(a2285)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[394, 854])).
% 0.78/1.01 tff(856,plain,
% 0.78/1.01 (c0_1(a2285)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[381, 854])).
% 0.78/1.01 tff(857,plain,
% 0.78/1.01 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(858,plain,
% 0.78/1.01 ((hskp4 | hskp2 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285))) <=> (hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(859,plain,
% 0.78/1.01 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[858])).
% 0.78/1.01 tff(860,plain,
% 0.78/1.01 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[859, 857])).
% 0.78/1.01 tff(861,plain,
% 0.78/1.01 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(862,plain,
% 0.78/1.01 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp4 | hskp2 | c3_1(a2285) | (~ndr1_0) | (~c2_1(a2285)) | (~c0_1(a2285))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.78/1.01 tff(863,plain,
% 0.78/1.01 (~c2_1(a2285)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[862, 160, 841, 512, 856, 855, 77])).
% 0.78/1.01 tff(864,plain,
% 0.78/1.01 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | c0_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(865,plain,
% 0.78/1.01 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c0_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(866,plain,
% 0.78/1.01 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | c0_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.78/1.01 tff(867,plain,
% 0.78/1.01 (hskp17 | c0_1(a2280)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[866, 160, 78, 543, 535, 801])).
% 0.78/1.01 tff(868,plain,
% 0.78/1.01 (c0_1(a2280)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[867, 791])).
% 0.78/1.01 tff(869,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(870,plain,
% 0.78/1.01 ((hskp14 | (~ndr1_0) | c2_1(a2280) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285))) <=> (hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(871,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2280) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[870])).
% 0.78/1.01 tff(872,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2280) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[871, 869])).
% 0.78/1.01 tff(873,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2280) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(874,plain,
% 0.78/1.01 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp14 | c3_1(a2285) | c2_1(a2280) | (~ndr1_0) | (~c0_1(a2280)) | (~c1_1(a2280)) | c2_1(a2285) | (~c0_1(a2285))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.78/1.01 tff(875,plain,
% 0.78/1.01 ($false),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[874, 160, 78, 856, 543, 855, 527, 329, 868, 863])).
% 0.78/1.01 tff(876,plain,(hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/1.01 tff(877,plain,
% 0.78/1.01 (((~hskp14) | (~c0_1(a2302))) <=> ((~hskp14) | (~c0_1(a2302)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(878,plain,
% 0.78/1.01 (((~c0_1(a2302)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a2302)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(879,axiom,((~c0_1(a2302)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.78/1.01 tff(880,plain,
% 0.78/1.01 ((~hskp14) | (~c0_1(a2302))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[879, 878])).
% 0.78/1.01 tff(881,plain,
% 0.78/1.01 ((~hskp14) | (~c0_1(a2302))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[880, 877])).
% 0.78/1.01 tff(882,plain,
% 0.78/1.01 (~c0_1(a2302)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[881, 876])).
% 0.78/1.01 tff(883,plain,
% 0.78/1.01 (((~hskp14) | c3_1(a2302)) <=> ((~hskp14) | c3_1(a2302))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(884,axiom,((~hskp14) | c3_1(a2302)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.78/1.01 tff(885,plain,
% 0.78/1.01 ((~hskp14) | c3_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[884, 883])).
% 0.78/1.01 tff(886,plain,
% 0.78/1.01 ((~hskp14) | c3_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[885, 883])).
% 0.78/1.01 tff(887,plain,
% 0.78/1.01 ((~hskp14) | c3_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[886, 883])).
% 0.78/1.01 tff(888,plain,
% 0.78/1.01 ((~hskp14) | c3_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[887, 883])).
% 0.78/1.01 tff(889,plain,
% 0.78/1.01 ((~hskp14) | c3_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[888, 883])).
% 0.78/1.01 tff(890,plain,
% 0.78/1.01 (c3_1(a2302)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[889, 876])).
% 0.78/1.01 tff(891,plain,
% 0.78/1.01 (((~hskp14) | c2_1(a2302)) <=> ((~hskp14) | c2_1(a2302))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(892,axiom,((~hskp14) | c2_1(a2302)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.78/1.01 tff(893,plain,
% 0.78/1.01 ((~hskp14) | c2_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.78/1.01 tff(894,plain,
% 0.78/1.01 ((~hskp14) | c2_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[893, 891])).
% 0.78/1.01 tff(895,plain,
% 0.78/1.01 ((~hskp14) | c2_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[894, 891])).
% 0.78/1.01 tff(896,plain,
% 0.78/1.01 ((~hskp14) | c2_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[895, 891])).
% 0.78/1.01 tff(897,plain,
% 0.78/1.01 ((~hskp14) | c2_1(a2302)),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[896, 891])).
% 0.78/1.01 tff(898,plain,
% 0.78/1.01 (c2_1(a2302)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[897, 876])).
% 0.78/1.01 tff(899,plain,
% 0.78/1.01 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(900,plain,
% 0.78/1.01 ((hskp20 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302))) <=> (hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(901,plain,
% 0.78/1.01 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[900])).
% 0.78/1.01 tff(902,plain,
% 0.78/1.01 (((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.78/1.01 inference(transitivity,[status(thm)],[901, 899])).
% 0.78/1.01 tff(903,plain,
% 0.78/1.01 ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(904,plain,
% 0.78/1.01 ((~![U: $i] : (hskp20 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[903, 902])).
% 0.78/1.01 tff(905,plain,
% 0.78/1.01 (hskp20),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[904, 160, 898, 890, 882, 67])).
% 0.78/1.01 tff(906,plain,
% 0.78/1.01 (~c1_1(a2323)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[112, 905])).
% 0.78/1.01 tff(907,plain,
% 0.78/1.01 (c3_1(a2323)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[120, 905])).
% 0.78/1.01 tff(908,plain,
% 0.78/1.01 (c2_1(a2323)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[128, 905])).
% 0.78/1.01 tff(909,plain,
% 0.78/1.01 (hskp4 | hskp1),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[166, 160, 908, 907, 906, 57])).
% 0.78/1.01 tff(910,plain,
% 0.78/1.01 (hskp4),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[909, 36])).
% 0.78/1.01 tff(911,plain,
% 0.78/1.01 (~c3_1(a2282)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[172, 910])).
% 0.78/1.01 tff(912,plain,
% 0.78/1.01 (c2_1(a2282)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[223, 910])).
% 0.78/1.01 tff(913,plain,
% 0.78/1.01 (~c0_1(a2282)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[178, 910])).
% 0.78/1.01 tff(914,assumption,(hskp9), introduced(assumption)).
% 0.78/1.01 tff(915,plain,
% 0.78/1.01 (((~hskp9) | (~c2_1(a2291))) <=> ((~hskp9) | (~c2_1(a2291)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(916,plain,
% 0.78/1.01 (((~c2_1(a2291)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a2291)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(917,axiom,((~c2_1(a2291)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.78/1.01 tff(918,plain,
% 0.78/1.01 ((~hskp9) | (~c2_1(a2291))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[917, 916])).
% 0.78/1.01 tff(919,plain,
% 0.78/1.01 ((~hskp9) | (~c2_1(a2291))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[918, 915])).
% 0.78/1.01 tff(920,plain,
% 0.78/1.01 (~c2_1(a2291)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[919, 914])).
% 0.78/1.01 tff(921,plain,
% 0.78/1.01 (((~hskp9) | (~c1_1(a2291))) <=> ((~hskp9) | (~c1_1(a2291)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(922,plain,
% 0.78/1.01 (((~c1_1(a2291)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a2291)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(923,axiom,((~c1_1(a2291)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.78/1.01 tff(924,plain,
% 0.78/1.01 ((~hskp9) | (~c1_1(a2291))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.78/1.01 tff(925,plain,
% 0.78/1.01 ((~hskp9) | (~c1_1(a2291))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[924, 921])).
% 0.78/1.01 tff(926,plain,
% 0.78/1.01 (~c1_1(a2291)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[925, 914])).
% 0.78/1.01 tff(927,plain,
% 0.78/1.01 (((~hskp9) | (~c0_1(a2291))) <=> ((~hskp9) | (~c0_1(a2291)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(928,plain,
% 0.78/1.01 (((~c0_1(a2291)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a2291)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(929,axiom,((~c0_1(a2291)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.78/1.01 tff(930,plain,
% 0.78/1.01 ((~hskp9) | (~c0_1(a2291))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.78/1.01 tff(931,plain,
% 0.78/1.01 ((~hskp9) | (~c0_1(a2291))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[930, 927])).
% 0.78/1.01 tff(932,plain,
% 0.78/1.01 (~c0_1(a2291)),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[931, 914])).
% 0.78/1.01 tff(933,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(934,plain,
% 0.78/1.01 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291)) <=> (hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(935,plain,
% 0.78/1.01 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282))))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[934])).
% 0.78/1.02 tff(936,plain,
% 0.78/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.78/1.02 inference(transitivity,[status(thm)],[935, 933])).
% 0.78/1.02 tff(937,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(938,plain,
% 0.78/1.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.78/1.02 tff(939,plain,
% 0.78/1.02 ($false),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[938, 160, 36, 912, 932, 926, 920, 911, 206, 37])).
% 0.78/1.02 tff(940,plain,((~hskp9) | hskp1 | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 0.78/1.02 tff(941,plain,
% 0.78/1.02 (~hskp9),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[940, 37, 36])).
% 0.78/1.02 tff(942,plain,
% 0.78/1.02 (^[U: $i] : refl((hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.78/1.02 inference(bind,[status(th)],[])).
% 0.78/1.02 tff(943,plain,
% 0.78/1.02 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/1.02 inference(quant_intro,[status(thm)],[942])).
% 0.78/1.02 tff(944,plain,
% 0.78/1.02 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(945,plain,
% 0.78/1.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp9) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp9) <=> (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.78/1.02 inference(bind,[status(th)],[])).
% 0.78/1.02 tff(946,plain,
% 0.78/1.02 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp9) <=> ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/1.02 inference(quant_intro,[status(thm)],[945])).
% 0.78/1.02 tff(947,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.78/1.02 tff(948,plain,
% 0.78/1.02 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[947, 946])).
% 0.78/1.02 tff(949,plain,
% 0.78/1.02 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[948, 944])).
% 0.78/1.02 tff(950,plain,(
% 0.78/1.02 ![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/1.02 inference(skolemize,[status(sab)],[949])).
% 0.78/1.02 tff(951,plain,
% 0.78/1.02 (![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[950, 943])).
% 0.78/1.02 tff(952,assumption,(hskp7), introduced(assumption)).
% 0.78/1.02 tff(953,plain,
% 0.78/1.02 (((~hskp7) | (~c2_1(a2286))) <=> ((~hskp7) | (~c2_1(a2286)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(954,plain,
% 0.78/1.02 (((~c2_1(a2286)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a2286)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(955,axiom,((~c2_1(a2286)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.78/1.02 tff(956,plain,
% 0.78/1.02 ((~hskp7) | (~c2_1(a2286))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[955, 954])).
% 0.78/1.02 tff(957,plain,
% 0.78/1.02 ((~hskp7) | (~c2_1(a2286))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[956, 953])).
% 0.78/1.02 tff(958,plain,
% 0.78/1.02 (~c2_1(a2286)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[957, 952])).
% 0.78/1.02 tff(959,plain,
% 0.78/1.02 (((~hskp7) | (~c0_1(a2286))) <=> ((~hskp7) | (~c0_1(a2286)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(960,plain,
% 0.78/1.02 (((~c0_1(a2286)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a2286)))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(961,axiom,((~c0_1(a2286)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.78/1.02 tff(962,plain,
% 0.78/1.02 ((~hskp7) | (~c0_1(a2286))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[961, 960])).
% 0.78/1.02 tff(963,plain,
% 0.78/1.02 ((~hskp7) | (~c0_1(a2286))),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[962, 959])).
% 0.78/1.02 tff(964,plain,
% 0.78/1.02 (~c0_1(a2286)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[963, 952])).
% 0.78/1.02 tff(965,assumption,(~hskp9), introduced(assumption)).
% 0.78/1.02 tff(966,plain,
% 0.78/1.02 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(967,plain,
% 0.78/1.02 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286)) <=> (hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(968,plain,
% 0.78/1.02 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286)))),
% 0.78/1.02 inference(monotonicity,[status(thm)],[967])).
% 0.78/1.02 tff(969,plain,
% 0.78/1.02 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 0.78/1.02 inference(transitivity,[status(thm)],[968, 966])).
% 0.78/1.02 tff(970,plain,
% 0.78/1.02 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))),
% 0.78/1.02 inference(quant_inst,[status(thm)],[])).
% 0.78/1.02 tff(971,plain,
% 0.78/1.02 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286)),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[970, 969])).
% 0.78/1.02 tff(972,plain,
% 0.78/1.02 (c3_1(a2286)),
% 0.78/1.02 inference(unit_resolution,[status(thm)],[971, 160, 35, 965, 964, 958, 951])).
% 0.78/1.02 tff(973,plain,
% 0.78/1.02 (((~hskp7) | c1_1(a2286)) <=> ((~hskp7) | c1_1(a2286))),
% 0.78/1.02 inference(rewrite,[status(thm)],[])).
% 0.78/1.02 tff(974,axiom,((~hskp7) | c1_1(a2286)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.78/1.02 tff(975,plain,
% 0.78/1.02 ((~hskp7) | c1_1(a2286)),
% 0.78/1.02 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.78/1.02 tff(976,plain,
% 0.78/1.02 ((~hskp7) | c1_1(a2286)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[975, 973])).
% 0.85/1.02 tff(977,plain,
% 0.85/1.02 ((~hskp7) | c1_1(a2286)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[976, 973])).
% 0.85/1.02 tff(978,plain,
% 0.85/1.02 ((~hskp7) | c1_1(a2286)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[977, 973])).
% 0.85/1.02 tff(979,plain,
% 0.85/1.02 ((~hskp7) | c1_1(a2286)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[978, 973])).
% 0.85/1.02 tff(980,plain,
% 0.85/1.02 (c1_1(a2286)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[979, 952])).
% 0.85/1.02 tff(981,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(982,plain,
% 0.85/1.02 (((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282))) <=> (c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(983,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[982])).
% 0.85/1.02 tff(984,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[983, 981])).
% 0.85/1.02 tff(985,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(986,plain,
% 0.85/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.85/1.02 tff(987,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[986, 160, 908, 907, 980, 707, 906, 958, 702, 196, 37, 972])).
% 0.85/1.02 tff(988,plain,((~hskp7) | (~c2_1(a2282)) | c0_1(a2282) | c1_1(a2282) | hskp28 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(989,plain,
% 0.85/1.02 (~hskp7),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[988, 941, 913, 37, 35, 912])).
% 0.85/1.02 tff(990,assumption,(hskp16), introduced(assumption)).
% 0.85/1.02 tff(991,plain,
% 0.85/1.02 (((~hskp16) | (~c3_1(a2304))) <=> ((~hskp16) | (~c3_1(a2304)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(992,plain,
% 0.85/1.02 (((~c3_1(a2304)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a2304)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(993,axiom,((~c3_1(a2304)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.85/1.02 tff(994,plain,
% 0.85/1.02 ((~hskp16) | (~c3_1(a2304))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[993, 992])).
% 0.85/1.02 tff(995,plain,
% 0.85/1.02 ((~hskp16) | (~c3_1(a2304))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[994, 991])).
% 0.85/1.02 tff(996,plain,
% 0.85/1.02 (~c3_1(a2304)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[995, 990])).
% 0.85/1.02 tff(997,plain,
% 0.85/1.02 (((~hskp16) | (~c2_1(a2304))) <=> ((~hskp16) | (~c2_1(a2304)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(998,plain,
% 0.85/1.02 (((~c2_1(a2304)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a2304)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(999,axiom,((~c2_1(a2304)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.85/1.02 tff(1000,plain,
% 0.85/1.02 ((~hskp16) | (~c2_1(a2304))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[999, 998])).
% 0.85/1.02 tff(1001,plain,
% 0.85/1.02 ((~hskp16) | (~c2_1(a2304))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1000, 997])).
% 0.85/1.02 tff(1002,plain,
% 0.85/1.02 (~c2_1(a2304)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1001, 990])).
% 0.85/1.02 tff(1003,plain,
% 0.85/1.02 (((~hskp16) | (~c0_1(a2304))) <=> ((~hskp16) | (~c0_1(a2304)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1004,plain,
% 0.85/1.02 (((~c0_1(a2304)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a2304)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1005,axiom,((~c0_1(a2304)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.85/1.02 tff(1006,plain,
% 0.85/1.02 ((~hskp16) | (~c0_1(a2304))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.85/1.02 tff(1007,plain,
% 0.85/1.02 ((~hskp16) | (~c0_1(a2304))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1006, 1003])).
% 0.85/1.02 tff(1008,plain,
% 0.85/1.02 (~c0_1(a2304)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1007, 990])).
% 0.85/1.02 tff(1009,plain,
% 0.85/1.02 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1010,plain,
% 0.85/1.02 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304)) <=> (hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1011,plain,
% 0.85/1.02 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0)))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[1010])).
% 0.85/1.02 tff(1012,plain,
% 0.85/1.02 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 0.85/1.02 inference(transitivity,[status(thm)],[1011, 1009])).
% 0.85/1.02 tff(1013,plain,
% 0.85/1.02 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(1014,plain,
% 0.85/1.02 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.85/1.02 tff(1015,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1014, 160, 35, 965, 1008, 1002, 996, 951])).
% 0.85/1.02 tff(1016,plain,((~hskp16) | hskp28 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(1017,plain,
% 0.85/1.02 (~hskp16),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1016, 941, 35])).
% 0.85/1.02 tff(1018,plain,
% 0.85/1.02 ((hskp28 | hskp26 | hskp16) <=> (hskp28 | hskp26 | hskp16)),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1019,plain,
% 0.85/1.02 (((hskp28 | hskp26) | hskp16) <=> (hskp28 | hskp26 | hskp16)),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1020,plain,
% 0.85/1.02 ((hskp28 | hskp26) <=> (hskp28 | hskp26)),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1021,plain,
% 0.85/1.02 (((hskp28 | hskp26) | hskp16) <=> ((hskp28 | hskp26) | hskp16)),
% 0.85/1.02 inference(monotonicity,[status(thm)],[1020])).
% 0.85/1.02 tff(1022,plain,
% 0.85/1.02 (((hskp28 | hskp26) | hskp16) <=> (hskp28 | hskp26 | hskp16)),
% 0.85/1.02 inference(transitivity,[status(thm)],[1021, 1019])).
% 0.85/1.02 tff(1023,axiom,((hskp28 | hskp26) | hskp16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.85/1.02 tff(1024,plain,
% 0.85/1.02 (hskp28 | hskp26 | hskp16),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.85/1.02 tff(1025,plain,
% 0.85/1.02 (hskp28 | hskp26 | hskp16),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1024, 1018])).
% 0.85/1.02 tff(1026,plain,
% 0.85/1.02 (hskp28 | hskp26 | hskp16),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1025, 1018])).
% 0.85/1.02 tff(1027,plain,
% 0.85/1.02 (hskp28 | hskp26 | hskp16),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1026, 1018])).
% 0.85/1.02 tff(1028,plain,
% 0.85/1.02 (hskp28 | hskp26 | hskp16),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1027, 1018])).
% 0.85/1.02 tff(1029,plain,
% 0.85/1.02 (hskp26),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1028, 1017, 35])).
% 0.85/1.02 tff(1030,plain,
% 0.85/1.02 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(1031,plain,
% 0.85/1.02 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[1030])).
% 0.85/1.02 tff(1032,plain,
% 0.85/1.02 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1033,plain,
% 0.85/1.02 (^[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) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(1034,plain,
% 0.85/1.02 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[1033])).
% 0.85/1.02 tff(1035,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.85/1.02 tff(1036,plain,
% 0.85/1.02 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.85/1.02 tff(1037,plain,
% 0.85/1.02 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1036, 1032])).
% 0.85/1.02 tff(1038,plain,(
% 0.85/1.02 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.85/1.02 inference(skolemize,[status(sab)],[1037])).
% 0.85/1.02 tff(1039,plain,
% 0.85/1.02 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1038, 1031])).
% 0.85/1.02 tff(1040,assumption,(hskp26), introduced(assumption)).
% 0.85/1.02 tff(1041,plain,
% 0.85/1.02 (((~hskp26) | (~c1_1(a2345))) <=> ((~hskp26) | (~c1_1(a2345)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1042,plain,
% 0.85/1.02 (((~c1_1(a2345)) | (~hskp26)) <=> ((~hskp26) | (~c1_1(a2345)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1043,axiom,((~c1_1(a2345)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.85/1.02 tff(1044,plain,
% 0.85/1.02 ((~hskp26) | (~c1_1(a2345))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 0.85/1.02 tff(1045,plain,
% 0.85/1.02 ((~hskp26) | (~c1_1(a2345))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1044, 1041])).
% 0.85/1.02 tff(1046,plain,
% 0.85/1.02 (~c1_1(a2345)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1045, 1040])).
% 0.85/1.02 tff(1047,plain,
% 0.85/1.02 (((~hskp26) | (~c0_1(a2345))) <=> ((~hskp26) | (~c0_1(a2345)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1048,plain,
% 0.85/1.02 (((~c0_1(a2345)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a2345)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1049,axiom,((~c0_1(a2345)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.85/1.02 tff(1050,plain,
% 0.85/1.02 ((~hskp26) | (~c0_1(a2345))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 0.85/1.02 tff(1051,plain,
% 0.85/1.02 ((~hskp26) | (~c0_1(a2345))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1050, 1047])).
% 0.85/1.02 tff(1052,plain,
% 0.85/1.02 (~c0_1(a2345)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1051, 1040])).
% 0.85/1.02 tff(1053,plain,
% 0.85/1.02 (((~hskp26) | c3_1(a2345)) <=> ((~hskp26) | c3_1(a2345))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1054,axiom,((~hskp26) | c3_1(a2345)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.85/1.02 tff(1055,plain,
% 0.85/1.02 ((~hskp26) | c3_1(a2345)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 0.85/1.02 tff(1056,plain,
% 0.85/1.02 ((~hskp26) | c3_1(a2345)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1055, 1053])).
% 0.85/1.02 tff(1057,plain,
% 0.85/1.02 ((~hskp26) | c3_1(a2345)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1056, 1053])).
% 0.85/1.02 tff(1058,plain,
% 0.85/1.02 ((~hskp26) | c3_1(a2345)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1057, 1053])).
% 0.85/1.02 tff(1059,plain,
% 0.85/1.02 ((~hskp26) | c3_1(a2345)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1058, 1053])).
% 0.85/1.02 tff(1060,plain,
% 0.85/1.02 (c3_1(a2345)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1059, 1040])).
% 0.85/1.02 tff(1061,assumption,(~hskp6), introduced(assumption)).
% 0.85/1.02 tff(1062,assumption,(~hskp7), introduced(assumption)).
% 0.85/1.02 tff(1063,plain,
% 0.85/1.02 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1064,plain,
% 0.85/1.02 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a2345) | c0_1(a2345) | (~c3_1(a2345))) <=> (hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1065,plain,
% 0.85/1.02 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2345) | c0_1(a2345) | (~c3_1(a2345)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[1064])).
% 0.85/1.02 tff(1066,plain,
% 0.85/1.02 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2345) | c0_1(a2345) | (~c3_1(a2345)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[1065, 1063])).
% 0.85/1.02 tff(1067,plain,
% 0.85/1.02 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2345) | c0_1(a2345) | (~c3_1(a2345)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(1068,plain,
% 0.85/1.02 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2345) | c1_1(a2345) | (~ndr1_0) | (~c3_1(a2345))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 0.85/1.02 tff(1069,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1068, 160, 1062, 1061, 1060, 1052, 1046, 1039])).
% 0.85/1.02 tff(1070,plain,((~hskp26) | hskp7 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(1071,plain,
% 0.85/1.02 (hskp6),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1070, 1029, 989])).
% 0.85/1.02 tff(1072,plain,
% 0.85/1.02 (~c3_1(a2285)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[394, 1071])).
% 0.85/1.02 tff(1073,plain,
% 0.85/1.02 (c1_1(a2285)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[373, 1071])).
% 0.85/1.02 tff(1074,plain,
% 0.85/1.02 (c0_1(a2285)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[381, 1071])).
% 0.85/1.02 tff(1075,assumption,(hskp23), introduced(assumption)).
% 0.85/1.02 tff(1076,plain,
% 0.85/1.02 (~c2_1(a2327)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[278, 1075])).
% 0.85/1.02 tff(1077,plain,
% 0.85/1.02 (c3_1(a2327)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[286, 1075])).
% 0.85/1.02 tff(1078,plain,
% 0.85/1.02 (~c1_1(a2327)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[293, 160, 1077, 908, 907, 912, 1076, 906, 913, 196, 37])).
% 0.85/1.02 tff(1079,plain,
% 0.85/1.02 (~c0_1(a2327)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[299, 1075])).
% 0.85/1.02 tff(1080,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[306, 160, 36, 912, 1079, 1076, 911, 206, 37, 1078])).
% 0.85/1.02 tff(1081,plain,((~hskp23) | hskp1 | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(1082,plain,
% 0.85/1.02 (~hskp23),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1081, 37, 36])).
% 0.85/1.02 tff(1083,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1084,plain,
% 0.85/1.02 ((hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1085,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[1084])).
% 0.85/1.02 tff(1086,plain,
% 0.85/1.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[1085, 1083])).
% 0.85/1.02 tff(1087,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(1088,plain,
% 0.85/1.02 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2285) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c0_1(a2285))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 0.85/1.02 tff(1089,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1088, 160, 1082, 1074, 1073, 912, 1072, 911, 47, 37])).
% 0.85/1.02 tff(1090,plain,(c1_1(a2282) | hskp28 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(1091,plain,
% 0.85/1.02 (c1_1(a2282)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1090, 36, 35])).
% 0.85/1.02 tff(1092,assumption,(c1_1(a2282)), introduced(assumption)).
% 0.85/1.02 tff(1093,assumption,(~c3_1(a2282)), introduced(assumption)).
% 0.85/1.02 tff(1094,assumption,(hskp10), introduced(assumption)).
% 0.85/1.02 tff(1095,plain,
% 0.85/1.02 (((~hskp10) | (~c3_1(a2293))) <=> ((~hskp10) | (~c3_1(a2293)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1096,plain,
% 0.85/1.02 (((~c3_1(a2293)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a2293)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1097,axiom,((~c3_1(a2293)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.85/1.02 tff(1098,plain,
% 0.85/1.02 ((~hskp10) | (~c3_1(a2293))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 0.85/1.02 tff(1099,plain,
% 0.85/1.02 ((~hskp10) | (~c3_1(a2293))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1098, 1095])).
% 0.85/1.02 tff(1100,plain,
% 0.85/1.02 (~c3_1(a2293)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1099, 1094])).
% 0.85/1.02 tff(1101,plain,
% 0.85/1.02 (((~hskp10) | c2_1(a2293)) <=> ((~hskp10) | c2_1(a2293))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1102,axiom,((~hskp10) | c2_1(a2293)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.85/1.02 tff(1103,plain,
% 0.85/1.02 ((~hskp10) | c2_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.85/1.02 tff(1104,plain,
% 0.85/1.02 ((~hskp10) | c2_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1103, 1101])).
% 0.85/1.02 tff(1105,plain,
% 0.85/1.02 ((~hskp10) | c2_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1104, 1101])).
% 0.85/1.02 tff(1106,plain,
% 0.85/1.02 ((~hskp10) | c2_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1105, 1101])).
% 0.85/1.02 tff(1107,plain,
% 0.85/1.02 ((~hskp10) | c2_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1106, 1101])).
% 0.85/1.02 tff(1108,plain,
% 0.85/1.02 (c2_1(a2293)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1107, 1094])).
% 0.85/1.02 tff(1109,plain,
% 0.85/1.02 (((~hskp10) | c0_1(a2293)) <=> ((~hskp10) | c0_1(a2293))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1110,axiom,((~hskp10) | c0_1(a2293)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.85/1.02 tff(1111,plain,
% 0.85/1.02 ((~hskp10) | c0_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.85/1.02 tff(1112,plain,
% 0.85/1.02 ((~hskp10) | c0_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1111, 1109])).
% 0.85/1.02 tff(1113,plain,
% 0.85/1.02 ((~hskp10) | c0_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1112, 1109])).
% 0.85/1.02 tff(1114,plain,
% 0.85/1.02 ((~hskp10) | c0_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1113, 1109])).
% 0.85/1.02 tff(1115,plain,
% 0.85/1.02 ((~hskp10) | c0_1(a2293)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[1114, 1109])).
% 0.85/1.02 tff(1116,plain,
% 0.85/1.02 (c0_1(a2293)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1115, 1094])).
% 0.85/1.02 tff(1117,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1118,plain,
% 0.85/1.02 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2293) | (~c0_1(a2293)) | (~c2_1(a2293)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> (c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(1119,plain,
% 0.85/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2293) | (~c0_1(a2293)) | (~c2_1(a2293)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1118])).
% 0.85/1.03 tff(1120,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2293) | (~c0_1(a2293)) | (~c2_1(a2293)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1119, 1117])).
% 0.85/1.03 tff(1121,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2293) | (~c0_1(a2293)) | (~c2_1(a2293)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1122,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2293) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2293)) | (~c0_1(a2293))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.85/1.03 tff(1123,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1122, 160, 1116, 1108, 707, 1100, 702, 1093, 675, 1092])).
% 0.85/1.03 tff(1124,plain,((~hskp10) | (~c2_1(a2282)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(1125,plain,
% 0.85/1.03 (~hskp10),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1124, 1091, 913, 911, 912])).
% 0.85/1.03 tff(1126,plain,
% 0.85/1.03 (c1_1(a2306) | c0_1(a2306)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[249, 160, 36, 912, 364, 911, 206, 37])).
% 0.85/1.03 tff(1127,plain,
% 0.85/1.03 (c0_1(a2306)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1126, 365])).
% 0.85/1.03 tff(1128,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[272, 160, 1082, 365, 364, 363, 260, 1127])).
% 0.85/1.03 tff(1129,plain,(c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | hskp1 | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(1130,plain,
% 0.85/1.03 (c1_1(a2306)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1129, 37, 363, 36, 364])).
% 0.85/1.03 tff(1131,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1132,plain,
% 0.85/1.03 ((hskp23 | (~ndr1_0) | c3_1(a2306) | (~c0_1(a2306)) | (~c1_1(a2306)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1133,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2306) | (~c0_1(a2306)) | (~c1_1(a2306)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1132])).
% 0.85/1.03 tff(1134,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2306) | (~c0_1(a2306)) | (~c1_1(a2306)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1133, 1131])).
% 0.85/1.03 tff(1135,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2306) | (~c0_1(a2306)) | (~c1_1(a2306)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1136,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | (~c1_1(a2306)) | c3_1(a2306) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c0_1(a2306))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.85/1.03 tff(1137,plain,
% 0.85/1.03 (hskp23 | (~c1_1(a2306)) | (~c0_1(a2306))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1136, 160, 912, 363, 911, 47, 37])).
% 0.85/1.03 tff(1138,plain,
% 0.85/1.03 (~c0_1(a2306)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1137, 1130, 1082])).
% 0.85/1.03 tff(1139,plain,
% 0.85/1.03 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1140,plain,
% 0.85/1.03 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306)) <=> (hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1141,plain,
% 0.85/1.03 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1140])).
% 0.85/1.03 tff(1142,plain,
% 0.85/1.03 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1141, 1139])).
% 0.85/1.03 tff(1143,plain,
% 0.85/1.03 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1144,plain,
% 0.85/1.03 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 0.85/1.03 tff(1145,plain,
% 0.85/1.03 (hskp9 | c2_1(a2306) | c0_1(a2306)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1144, 160, 35, 363, 951])).
% 0.85/1.03 tff(1146,plain,
% 0.85/1.03 (hskp9),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1145, 1138, 364])).
% 0.85/1.03 tff(1147,plain,
% 0.85/1.03 (~c2_1(a2291)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[919, 1146])).
% 0.85/1.03 tff(1148,plain,
% 0.85/1.03 (~c1_1(a2291)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[925, 1146])).
% 0.85/1.03 tff(1149,plain,
% 0.85/1.03 (~c0_1(a2291)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[931, 1146])).
% 0.85/1.03 tff(1150,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[938, 160, 36, 912, 1149, 1148, 1147, 911, 206, 37])).
% 0.85/1.03 tff(1151,plain,(c1_1(a2282) | hskp1 | c2_1(a2306) | hskp28 | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(1152,plain,
% 0.85/1.03 (c1_1(a2282)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1151, 364, 36, 35, 363])).
% 0.85/1.03 tff(1153,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(1154,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[1153])).
% 0.85/1.03 tff(1155,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1156,plain,
% 0.85/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(1157,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[1156])).
% 0.85/1.03 tff(1158,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 0.85/1.03 tff(1159,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 0.85/1.03 tff(1160,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1159, 1155])).
% 0.85/1.03 tff(1161,plain,(
% 0.85/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.85/1.03 inference(skolemize,[status(sab)],[1160])).
% 0.85/1.03 tff(1162,plain,
% 0.85/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1161, 1154])).
% 0.85/1.03 tff(1163,plain,
% 0.85/1.03 (~hskp10),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1124, 1092, 702, 1093, 707])).
% 0.85/1.03 tff(1164,assumption,(~hskp10), introduced(assumption)).
% 0.85/1.03 tff(1165,assumption,(~hskp23), introduced(assumption)).
% 0.85/1.03 tff(1166,plain,
% 0.85/1.03 (hskp23 | (~c0_1(a2306))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[272, 160, 365, 364, 363, 260])).
% 0.85/1.03 tff(1167,plain,
% 0.85/1.03 (~c0_1(a2306)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1166, 1165])).
% 0.85/1.03 tff(1168,plain,
% 0.85/1.03 (^[U: $i] : refl((hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(1169,plain,
% 0.85/1.03 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[1168])).
% 0.85/1.03 tff(1170,plain,
% 0.85/1.03 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1171,plain,
% 0.85/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp10) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10) <=> (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp10) <=> (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(1172,plain,
% 0.85/1.03 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp10) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[1171])).
% 0.85/1.03 tff(1173,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.85/1.03 tff(1174,plain,
% 0.85/1.03 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.85/1.03 tff(1175,plain,
% 0.85/1.03 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1174, 1170])).
% 0.85/1.03 tff(1176,plain,(
% 0.85/1.03 ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.85/1.03 inference(skolemize,[status(sab)],[1175])).
% 0.85/1.03 tff(1177,plain,
% 0.85/1.03 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1176, 1169])).
% 0.85/1.03 tff(1178,plain,
% 0.85/1.03 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1179,plain,
% 0.85/1.03 ((hskp10 | hskp6 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306)) <=> (hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1180,plain,
% 0.85/1.03 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1179])).
% 0.85/1.03 tff(1181,plain,
% 0.85/1.03 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1180, 1178])).
% 0.85/1.03 tff(1182,plain,
% 0.85/1.03 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2306) | c0_1(a2306) | c3_1(a2306))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1183,plain,
% 0.85/1.03 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.85/1.03 tff(1184,plain,
% 0.85/1.03 (hskp10 | hskp6 | c2_1(a2306) | c0_1(a2306)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1183, 160, 363, 1177])).
% 0.85/1.03 tff(1185,plain,
% 0.85/1.03 (hskp6),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1184, 1167, 364, 1164])).
% 0.85/1.03 tff(1186,plain,
% 0.85/1.03 (~c3_1(a2285)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[394, 1185])).
% 0.85/1.03 tff(1187,plain,
% 0.85/1.03 (c1_1(a2285)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[373, 1185])).
% 0.85/1.03 tff(1188,plain,
% 0.85/1.03 (c0_1(a2285)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[381, 1185])).
% 0.85/1.03 tff(1189,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1190,plain,
% 0.85/1.03 (((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> (c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1191,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1190])).
% 0.85/1.03 tff(1192,plain,
% 0.85/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1191, 1189])).
% 0.85/1.03 tff(1193,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1194,plain,
% 0.85/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 0.85/1.03 tff(1195,plain,
% 0.85/1.03 (~c2_1(a2285)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1194, 160, 1188, 1187, 707, 1186, 702, 675, 1092])).
% 0.85/1.03 tff(1196,assumption,(hskp13), introduced(assumption)).
% 0.85/1.03 tff(1197,plain,
% 0.85/1.03 (((~hskp13) | (~c3_1(a2299))) <=> ((~hskp13) | (~c3_1(a2299)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1198,plain,
% 0.85/1.03 (((~c3_1(a2299)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a2299)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1199,axiom,((~c3_1(a2299)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.85/1.03 tff(1200,plain,
% 0.85/1.03 ((~hskp13) | (~c3_1(a2299))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 0.85/1.03 tff(1201,plain,
% 0.85/1.03 ((~hskp13) | (~c3_1(a2299))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1200, 1197])).
% 0.85/1.03 tff(1202,plain,
% 0.85/1.03 (~c3_1(a2299)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1201, 1196])).
% 0.85/1.03 tff(1203,plain,
% 0.85/1.03 (((~hskp13) | c2_1(a2299)) <=> ((~hskp13) | c2_1(a2299))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1204,axiom,((~hskp13) | c2_1(a2299)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.85/1.03 tff(1205,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a2299)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.85/1.03 tff(1206,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a2299)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1205, 1203])).
% 0.85/1.03 tff(1207,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a2299)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1206, 1203])).
% 0.85/1.03 tff(1208,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a2299)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1207, 1203])).
% 0.85/1.03 tff(1209,plain,
% 0.85/1.03 ((~hskp13) | c2_1(a2299)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1208, 1203])).
% 0.85/1.03 tff(1210,plain,
% 0.85/1.03 (c2_1(a2299)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1209, 1196])).
% 0.85/1.03 tff(1211,plain,
% 0.85/1.03 (((~hskp13) | (~c1_1(a2299))) <=> ((~hskp13) | (~c1_1(a2299)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1212,plain,
% 0.85/1.03 (((~c1_1(a2299)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a2299)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1213,axiom,((~c1_1(a2299)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.85/1.03 tff(1214,plain,
% 0.85/1.03 ((~hskp13) | (~c1_1(a2299))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 0.85/1.03 tff(1215,plain,
% 0.85/1.03 ((~hskp13) | (~c1_1(a2299))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1214, 1211])).
% 0.85/1.03 tff(1216,plain,
% 0.85/1.03 (~c1_1(a2299)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1215, 1196])).
% 0.85/1.03 tff(1217,assumption,(~c3_1(a2299)), introduced(assumption)).
% 0.85/1.03 tff(1218,assumption,(~c1_1(a2299)), introduced(assumption)).
% 0.85/1.03 tff(1219,assumption,(c2_1(a2299)), introduced(assumption)).
% 0.85/1.03 tff(1220,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1221,plain,
% 0.85/1.03 ((hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299))) <=> (hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(1222,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[1221])).
% 0.85/1.03 tff(1223,plain,
% 0.85/1.03 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[1222, 1220])).
% 0.85/1.03 tff(1224,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(1225,plain,
% 0.85/1.03 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2299) | c3_1(a2299) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2299))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.85/1.03 tff(1226,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1225, 160, 1165, 1219, 382, 374, 1218, 1217, 395, 47])).
% 0.85/1.03 tff(1227,plain,((~hskp6) | hskp23 | (~c2_1(a2299)) | c1_1(a2299) | c3_1(a2299)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(1228,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1227, 1216, 1210, 366, 1165, 1202])).
% 0.85/1.03 tff(1229,plain,((~hskp13) | (~hskp6) | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(1230,plain,
% 0.85/1.03 (~hskp13),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[1229, 1185, 1165])).
% 0.85/1.03 tff(1231,plain,
% 0.85/1.03 (^[U: $i] : refl((hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(1232,plain,
% 0.85/1.03 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[1231])).
% 0.85/1.04 tff(1233,plain,
% 0.85/1.04 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1234,plain,
% 0.85/1.04 (^[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)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp13) <=> ((hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13))), rewrite(((hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(1235,plain,
% 0.85/1.04 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp13) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[1234])).
% 0.85/1.04 tff(1236,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.85/1.04 tff(1237,plain,
% 0.85/1.04 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 0.85/1.04 tff(1238,plain,
% 0.85/1.04 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1237, 1233])).
% 0.85/1.04 tff(1239,plain,(
% 0.85/1.04 ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(skolemize,[status(sab)],[1238])).
% 0.85/1.04 tff(1240,plain,
% 0.85/1.04 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1239, 1232])).
% 0.85/1.04 tff(1241,plain,
% 0.85/1.04 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1242,plain,
% 0.85/1.04 ((hskp13 | hskp12 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302))) <=> (hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1243,plain,
% 0.85/1.04 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1242])).
% 0.85/1.04 tff(1244,plain,
% 0.85/1.04 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1243, 1241])).
% 0.85/1.04 tff(1245,plain,
% 0.85/1.04 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c0_1(a2302) | (~c3_1(a2302)) | (~c2_1(a2302)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1246,plain,
% 0.85/1.04 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.85/1.04 tff(1247,plain,
% 0.85/1.04 (hskp13 | hskp12),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1246, 160, 898, 890, 882, 1240])).
% 0.85/1.04 tff(1248,plain,
% 0.85/1.04 (hskp12),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1247, 1230])).
% 0.85/1.04 tff(1249,plain,
% 0.85/1.04 (~c3_1(a2295)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[644, 1248])).
% 0.85/1.04 tff(1250,plain,
% 0.85/1.04 (((~hskp12) | (~c1_1(a2295))) <=> ((~hskp12) | (~c1_1(a2295)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1251,plain,
% 0.85/1.04 (((~c1_1(a2295)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a2295)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1252,axiom,((~c1_1(a2295)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.85/1.04 tff(1253,plain,
% 0.85/1.04 ((~hskp12) | (~c1_1(a2295))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 0.85/1.04 tff(1254,plain,
% 0.85/1.04 ((~hskp12) | (~c1_1(a2295))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1253, 1250])).
% 0.85/1.04 tff(1255,plain,
% 0.85/1.04 (~c1_1(a2295)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1254, 1248])).
% 0.85/1.04 tff(1256,plain,
% 0.85/1.04 (c0_1(a2295)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[652, 1248])).
% 0.85/1.04 tff(1257,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1258,plain,
% 0.85/1.04 ((hskp23 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1259,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1258])).
% 0.85/1.04 tff(1260,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1259, 1257])).
% 0.85/1.04 tff(1261,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1262,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c3_1(a2285) | (~ndr1_0) | c2_1(a2285) | (~c0_1(a2285)) | (~c0_1(a2295))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 0.85/1.04 tff(1263,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1262, 160, 1165, 1256, 1188, 1255, 1249, 1186, 260, 1195])).
% 0.85/1.04 tff(1264,plain,(hskp23 | (~c2_1(a2282)) | c0_1(a2282) | (~c1_1(a2282)) | c2_1(a2306) | hskp10 | c3_1(a2306) | c1_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(1265,plain,
% 0.85/1.04 (hskp23),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1264, 365, 702, 1092, 364, 1163, 363, 707])).
% 0.85/1.04 tff(1266,plain,
% 0.85/1.04 (~c2_1(a2327)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[278, 1265])).
% 0.85/1.04 tff(1267,plain,
% 0.85/1.04 (~c0_1(a2327)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[299, 1265])).
% 0.85/1.04 tff(1268,plain,
% 0.85/1.04 (c3_1(a2327)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[286, 1265])).
% 0.85/1.04 tff(1269,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1270,plain,
% 0.85/1.04 (((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2306) | c2_1(a2306) | c0_1(a2306)) <=> (c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1271,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2306) | c2_1(a2306) | c0_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1270])).
% 0.85/1.04 tff(1272,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2306) | c2_1(a2306) | c0_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1271, 1269])).
% 0.85/1.04 tff(1273,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2306) | c2_1(a2306) | c0_1(a2306))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1274,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2306) | (~c3_1(a2327))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.85/1.04 tff(1275,plain,
% 0.85/1.04 (c0_1(a2306)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1274, 160, 1268, 707, 1267, 1266, 364, 363, 702, 1162, 1092])).
% 0.85/1.04 tff(1276,plain,
% 0.85/1.04 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(1277,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[1276])).
% 0.85/1.04 tff(1278,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1279,plain,
% 0.85/1.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(1280,plain,
% 0.85/1.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[1279])).
% 0.85/1.04 tff(1281,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 0.85/1.04 tff(1282,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.85/1.04 tff(1283,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1282, 1278])).
% 0.85/1.04 tff(1284,plain,(
% 0.85/1.04 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.04 inference(skolemize,[status(sab)],[1283])).
% 0.85/1.04 tff(1285,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1284, 1277])).
% 0.85/1.04 tff(1286,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1287,plain,
% 0.85/1.04 ((hskp8 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1288,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1287])).
% 0.85/1.04 tff(1289,plain,
% 0.85/1.04 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1288, 1286])).
% 0.85/1.04 tff(1290,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1291,plain,
% 0.85/1.04 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c0_1(a2306))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 0.85/1.04 tff(1292,plain,
% 0.85/1.04 (hskp8 | (~c0_1(a2306))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1291, 160, 898, 890, 365, 363, 882, 1285])).
% 0.85/1.04 tff(1293,plain,
% 0.85/1.04 (hskp8),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1292, 1275])).
% 0.85/1.04 tff(1294,plain,
% 0.85/1.04 (((~hskp8) | c0_1(a2287)) <=> ((~hskp8) | c0_1(a2287))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1295,axiom,((~hskp8) | c0_1(a2287)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.85/1.04 tff(1296,plain,
% 0.85/1.04 ((~hskp8) | c0_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 0.85/1.04 tff(1297,plain,
% 0.85/1.04 ((~hskp8) | c0_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1296, 1294])).
% 0.85/1.04 tff(1298,plain,
% 0.85/1.04 ((~hskp8) | c0_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1297, 1294])).
% 0.85/1.04 tff(1299,plain,
% 0.85/1.04 ((~hskp8) | c0_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1298, 1294])).
% 0.85/1.04 tff(1300,plain,
% 0.85/1.04 ((~hskp8) | c0_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1299, 1294])).
% 0.85/1.04 tff(1301,plain,
% 0.85/1.04 (c0_1(a2287)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1300, 1293])).
% 0.85/1.04 tff(1302,plain,
% 0.85/1.04 (((~hskp8) | c2_1(a2287)) <=> ((~hskp8) | c2_1(a2287))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1303,axiom,((~hskp8) | c2_1(a2287)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.85/1.04 tff(1304,plain,
% 0.85/1.04 ((~hskp8) | c2_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 0.85/1.04 tff(1305,plain,
% 0.85/1.04 ((~hskp8) | c2_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1304, 1302])).
% 0.85/1.04 tff(1306,plain,
% 0.85/1.04 ((~hskp8) | c2_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1305, 1302])).
% 0.85/1.04 tff(1307,plain,
% 0.85/1.04 ((~hskp8) | c2_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1306, 1302])).
% 0.85/1.04 tff(1308,plain,
% 0.85/1.04 ((~hskp8) | c2_1(a2287)),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1307, 1302])).
% 0.85/1.04 tff(1309,plain,
% 0.85/1.04 (c2_1(a2287)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1308, 1293])).
% 0.85/1.04 tff(1310,assumption,(~c3_1(a2287)), introduced(assumption)).
% 0.85/1.04 tff(1311,assumption,(c2_1(a2287)), introduced(assumption)).
% 0.85/1.04 tff(1312,assumption,(c0_1(a2287)), introduced(assumption)).
% 0.85/1.04 tff(1313,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1314,plain,
% 0.85/1.04 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> (c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1315,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1314])).
% 0.85/1.04 tff(1316,plain,
% 0.85/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1315, 1313])).
% 0.85/1.04 tff(1317,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1318,plain,
% 0.85/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 0.85/1.04 tff(1319,plain,
% 0.85/1.04 ($false),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1318, 160, 1312, 1311, 707, 702, 1093, 675, 1092, 1310])).
% 0.85/1.04 tff(1320,plain,(c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | (~c2_1(a2282)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.04 tff(1321,plain,
% 0.85/1.04 (c3_1(a2287)),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[1320, 1309, 1092, 707, 702, 1093, 1301])).
% 0.85/1.04 tff(1322,plain,
% 0.85/1.04 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(1323,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[1322])).
% 0.85/1.04 tff(1324,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1325,plain,
% 0.85/1.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_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)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.85/1.04 inference(bind,[status(th)],[])).
% 0.85/1.04 tff(1326,plain,
% 0.85/1.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.85/1.04 inference(quant_intro,[status(thm)],[1325])).
% 0.85/1.04 tff(1327,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 0.85/1.04 tff(1328,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 0.85/1.04 tff(1329,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1328, 1324])).
% 0.85/1.04 tff(1330,plain,(
% 0.85/1.04 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.85/1.04 inference(skolemize,[status(sab)],[1329])).
% 0.85/1.04 tff(1331,plain,
% 0.85/1.04 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[1330, 1323])).
% 0.85/1.04 tff(1332,assumption,(~c2_1(a2327)), introduced(assumption)).
% 0.85/1.04 tff(1333,assumption,(c3_1(a2327)), introduced(assumption)).
% 0.85/1.04 tff(1334,plain,
% 0.85/1.04 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1335,plain,
% 0.85/1.04 ((hskp10 | hskp6 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304)) <=> (hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(1336,plain,
% 0.85/1.04 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0)))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[1335])).
% 0.85/1.04 tff(1337,plain,
% 0.85/1.04 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0))),
% 0.85/1.04 inference(transitivity,[status(thm)],[1336, 1334])).
% 0.85/1.04 tff(1338,plain,
% 0.85/1.04 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2304) | c0_1(a2304) | c3_1(a2304))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(1339,plain,
% 0.85/1.04 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 0.85/1.05 tff(1340,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1339, 160, 1164, 1061, 1008, 1002, 996, 1177])).
% 0.85/1.05 tff(1341,plain,((~hskp16) | hskp10 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(1342,plain,
% 0.85/1.05 (~hskp16),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1341, 1061, 1164])).
% 0.85/1.05 tff(1343,plain,
% 0.85/1.05 (hskp26),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1028, 1342, 35])).
% 0.85/1.05 tff(1344,assumption,(c1_1(a2327)), introduced(assumption)).
% 0.85/1.05 tff(1345,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1346,plain,
% 0.85/1.05 (((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345))) <=> (c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1347,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1346])).
% 0.85/1.05 tff(1348,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1347, 1345])).
% 0.85/1.05 tff(1349,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1350,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | (~c2_1(a2345)) | (~c3_1(a2345))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 0.85/1.05 tff(1351,plain,
% 0.85/1.05 (~c2_1(a2345)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1350, 160, 1060, 1333, 1052, 1046, 1332, 196, 1344])).
% 0.85/1.05 tff(1352,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1353,plain,
% 0.85/1.05 ((hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345)) <=> (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1354,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1353])).
% 0.85/1.05 tff(1355,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1354, 1352])).
% 0.85/1.05 tff(1356,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1357,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2345)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 0.85/1.05 tff(1358,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1357, 160, 35, 1333, 1052, 1046, 1332, 421, 1344, 1351])).
% 0.85/1.05 tff(1359,plain,((~hskp26) | hskp28 | (~c3_1(a2327)) | c2_1(a2327) | (~c1_1(a2327))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(1360,plain,
% 0.85/1.05 (~c1_1(a2327)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1359, 1343, 1333, 1332, 35])).
% 0.85/1.05 tff(1361,assumption,(~c0_1(a2327)), introduced(assumption)).
% 0.85/1.05 tff(1362,plain,
% 0.85/1.05 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1363,plain,
% 0.85/1.05 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327))) <=> (hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1364,plain,
% 0.85/1.05 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1363])).
% 0.85/1.05 tff(1365,plain,
% 0.85/1.05 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1364, 1362])).
% 0.85/1.05 tff(1366,plain,
% 0.85/1.05 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1367,plain,
% 0.85/1.05 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.85/1.05 tff(1368,plain,
% 0.85/1.05 (hskp7 | hskp6 | c1_1(a2327)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1367, 160, 1333, 1361, 1039])).
% 0.85/1.05 tff(1369,plain,
% 0.85/1.05 (hskp7),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1368, 1360, 1061])).
% 0.85/1.05 tff(1370,plain,
% 0.85/1.05 (~c2_1(a2286)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[957, 1369])).
% 0.85/1.05 tff(1371,plain,
% 0.85/1.05 (c1_1(a2286)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[979, 1369])).
% 0.85/1.05 tff(1372,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1373,plain,
% 0.85/1.05 ((hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1374,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1373])).
% 0.85/1.05 tff(1375,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1374, 1372])).
% 0.85/1.05 tff(1376,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1377,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2327)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 0.85/1.05 tff(1378,plain,
% 0.85/1.05 (~c3_1(a2286)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1377, 160, 35, 1371, 1361, 1332, 1370, 421, 1360])).
% 0.85/1.05 tff(1379,plain,
% 0.85/1.05 (~c0_1(a2286)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[963, 1369])).
% 0.85/1.05 tff(1380,plain,
% 0.85/1.05 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1381,plain,
% 0.85/1.05 ((hskp10 | hskp6 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286)) <=> (hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1382,plain,
% 0.85/1.05 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1381])).
% 0.85/1.05 tff(1383,plain,
% 0.85/1.05 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1382, 1380])).
% 0.85/1.05 tff(1384,plain,
% 0.85/1.05 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2286) | c0_1(a2286) | c3_1(a2286))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1385,plain,
% 0.85/1.05 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 0.85/1.05 tff(1386,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1385, 160, 1164, 1061, 1379, 1370, 1177, 1378])).
% 0.85/1.05 tff(1387,plain,(hskp6 | hskp10 | hskp28 | c0_1(a2327) | c2_1(a2327) | (~c3_1(a2327))), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(1388,plain,
% 0.85/1.05 (hskp6),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1387, 1267, 35, 1163, 1266, 1268])).
% 0.85/1.05 tff(1389,plain,
% 0.85/1.05 (~c3_1(a2285)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[394, 1388])).
% 0.85/1.05 tff(1390,plain,
% 0.85/1.05 (c1_1(a2285)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[373, 1388])).
% 0.85/1.05 tff(1391,plain,
% 0.85/1.05 (c0_1(a2285)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[381, 1388])).
% 0.85/1.05 tff(1392,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1393,plain,
% 0.85/1.05 ((hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285))) <=> (hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1394,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1393])).
% 0.85/1.05 tff(1395,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1394, 1392])).
% 0.85/1.05 tff(1396,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1397,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 0.85/1.05 tff(1398,plain,
% 0.85/1.05 (hskp3),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1397, 160, 1301, 1309, 1391, 1390, 1389, 1331, 1321])).
% 0.85/1.05 tff(1399,plain,
% 0.85/1.05 (~c2_1(a2280)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[526, 1398])).
% 0.85/1.05 tff(1400,plain,
% 0.85/1.05 (c3_1(a2280)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[534, 1398])).
% 0.85/1.05 tff(1401,plain,
% 0.85/1.05 (c1_1(a2280)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[542, 1398])).
% 0.85/1.05 tff(1402,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1403,plain,
% 0.85/1.05 (((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302))) <=> (c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1404,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1403])).
% 0.85/1.05 tff(1405,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1404, 1402])).
% 0.85/1.05 tff(1406,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1407,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 0.85/1.05 tff(1408,plain,
% 0.85/1.05 (c1_1(a2302)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1407, 160, 908, 907, 898, 1401, 1400, 906, 882, 1399, 196])).
% 0.85/1.05 tff(1409,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1410,plain,
% 0.85/1.05 ((hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1411,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1410])).
% 0.85/1.05 tff(1412,plain,
% 0.85/1.05 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1411, 1409])).
% 0.85/1.05 tff(1413,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1414,plain,
% 0.85/1.05 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2327)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 0.85/1.05 tff(1415,plain,
% 0.85/1.05 (c1_1(a2327)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1414, 160, 35, 1401, 1400, 1267, 1266, 1399, 421])).
% 0.85/1.05 tff(1416,plain,
% 0.85/1.05 (~hskp26),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1359, 1415, 1268, 1266, 35])).
% 0.85/1.05 tff(1417,plain,
% 0.85/1.05 (hskp16),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1028, 1416, 35])).
% 0.85/1.05 tff(1418,plain,
% 0.85/1.05 (~c3_1(a2304)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[995, 1417])).
% 0.85/1.05 tff(1419,plain,
% 0.85/1.05 (~c2_1(a2304)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1001, 1417])).
% 0.85/1.05 tff(1420,plain,
% 0.85/1.05 (~c0_1(a2304)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1007, 1417])).
% 0.85/1.05 tff(1421,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1422,plain,
% 0.85/1.05 (((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1423,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[1422])).
% 0.85/1.05 tff(1424,plain,
% 0.85/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 0.85/1.05 inference(transitivity,[status(thm)],[1423, 1421])).
% 0.85/1.05 tff(1425,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(1426,plain,
% 0.85/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 0.85/1.05 tff(1427,plain,
% 0.85/1.05 ($false),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1426, 160, 1268, 898, 1267, 1266, 1420, 1419, 1418, 882, 1162, 1408])).
% 0.85/1.05 tff(1428,plain,(c1_1(a2306) | hskp28 | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2282) | c3_1(a2282) | c3_1(a2306) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.05 tff(1429,plain,
% 0.85/1.05 (c1_1(a2306)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[1428, 1152, 35, 912, 913, 911, 363, 364])).
% 0.85/1.05 tff(1430,plain,
% 0.85/1.05 (~hskp17),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[242, 1429])).
% 0.85/1.05 tff(1431,plain,
% 0.85/1.05 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(1432,plain,
% 0.85/1.05 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[1431])).
% 0.85/1.05 tff(1433,plain,
% 0.85/1.05 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(1434,plain,
% 0.85/1.05 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1435,plain,
% 0.85/1.06 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1434])).
% 0.85/1.06 tff(1436,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.85/1.06 tff(1437,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 0.85/1.06 tff(1438,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1437, 1433])).
% 0.85/1.06 tff(1439,plain,(
% 0.85/1.06 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.85/1.06 inference(skolemize,[status(sab)],[1438])).
% 0.85/1.06 tff(1440,plain,
% 0.85/1.06 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1439, 1432])).
% 0.85/1.06 tff(1441,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1442,plain,
% 0.85/1.06 ((hskp17 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1443,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1442])).
% 0.85/1.06 tff(1444,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1443, 1441])).
% 0.85/1.06 tff(1445,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1446,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 0.85/1.06 tff(1447,plain,
% 0.85/1.06 (hskp17 | (~c1_1(a2306)) | (~c1_1(a2282))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1446, 160, 912, 364, 363, 913, 1440])).
% 0.85/1.06 tff(1448,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1447, 1430, 1429, 1152])).
% 0.85/1.06 tff(1449,plain,(c2_1(a2306) | c3_1(a2306) | hskp28 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1450,plain,
% 0.85/1.06 (c2_1(a2306)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1449, 363, 35, 36])).
% 0.85/1.06 tff(1451,assumption,(c2_1(a2306)), introduced(assumption)).
% 0.85/1.06 tff(1452,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1453,plain,
% 0.85/1.06 ((hskp1 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291)) <=> (hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1454,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0)))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1453])).
% 0.85/1.06 tff(1455,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1454, 1452])).
% 0.85/1.06 tff(1456,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1457,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 0.85/1.06 tff(1458,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1457, 160, 36, 365, 1451, 363, 932, 926, 920, 206])).
% 0.85/1.06 tff(1459,plain,((~hskp9) | hskp1 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1460,plain,
% 0.85/1.06 (~hskp9),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1459, 365, 36, 1450, 363])).
% 0.85/1.06 tff(1461,plain,
% 0.85/1.06 (~hskp7),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[988, 1460, 913, 37, 35, 912])).
% 0.85/1.06 tff(1462,plain,
% 0.85/1.06 (hskp10),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1341, 990, 1061])).
% 0.85/1.06 tff(1463,plain,
% 0.85/1.06 (~c3_1(a2293)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1099, 1462])).
% 0.85/1.06 tff(1464,plain,
% 0.85/1.06 (c0_1(a2293)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1115, 1462])).
% 0.85/1.06 tff(1465,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1466,plain,
% 0.85/1.06 ((hskp23 | (~ndr1_0) | c3_1(a2293) | (~c0_1(a2293)) | (~c1_1(a2293)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306))) <=> (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1467,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2293) | (~c0_1(a2293)) | (~c1_1(a2293)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1466])).
% 0.85/1.06 tff(1468,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2293) | (~c0_1(a2293)) | (~c1_1(a2293)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1467, 1465])).
% 0.85/1.06 tff(1469,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2293) | (~c0_1(a2293)) | (~c1_1(a2293)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1470,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2293) | (~ndr1_0) | (~c1_1(a2293)) | (~c0_1(a2293))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 0.85/1.06 tff(1471,plain,
% 0.85/1.06 (~c1_1(a2293)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1470, 160, 1165, 1464, 365, 1450, 363, 1463, 47])).
% 0.85/1.06 tff(1472,plain,
% 0.85/1.06 (hskp9),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1014, 160, 35, 1008, 1002, 996, 951])).
% 0.85/1.06 tff(1473,plain,
% 0.85/1.06 (~c2_1(a2291)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[919, 1472])).
% 0.85/1.06 tff(1474,plain,
% 0.85/1.06 (~c1_1(a2291)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[925, 1472])).
% 0.85/1.06 tff(1475,plain,
% 0.85/1.06 (~c0_1(a2291)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[931, 1472])).
% 0.85/1.06 tff(1476,plain,
% 0.85/1.06 (c2_1(a2293)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1107, 1462])).
% 0.85/1.06 tff(1477,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1478,plain,
% 0.85/1.06 ((hskp1 | (~ndr1_0) | c1_1(a2293) | c3_1(a2293) | (~c2_1(a2293)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291)) <=> (hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1479,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2293) | c3_1(a2293) | (~c2_1(a2293)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1478])).
% 0.85/1.06 tff(1480,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2293) | c3_1(a2293) | (~c2_1(a2293)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1479, 1477])).
% 0.85/1.06 tff(1481,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2293) | c3_1(a2293) | (~c2_1(a2293)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1482,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a2293) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | c1_1(a2293) | (~c2_1(a2293))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 0.85/1.06 tff(1483,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1482, 160, 36, 1476, 1463, 1475, 1474, 1473, 206, 1471])).
% 0.85/1.06 tff(1484,plain,((~hskp16) | hskp1 | hskp23 | c1_1(a2306) | c3_1(a2306) | hskp28 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1485,plain,
% 0.85/1.06 (~hskp16),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1484, 1061, 1165, 365, 363, 35, 36])).
% 0.85/1.06 tff(1486,plain,
% 0.85/1.06 (hskp26),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1028, 1485, 35])).
% 0.85/1.06 tff(1487,plain,
% 0.85/1.06 (~c1_1(a2345)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1045, 1486])).
% 0.85/1.06 tff(1488,plain,
% 0.85/1.06 (~c0_1(a2345)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1051, 1486])).
% 0.85/1.06 tff(1489,plain,
% 0.85/1.06 (c3_1(a2345)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1059, 1486])).
% 0.85/1.06 tff(1490,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1068, 160, 1062, 1061, 1489, 1488, 1487, 1039])).
% 0.85/1.06 tff(1491,plain,(hskp6 | hskp7 | hskp28 | hskp23 | c1_1(a2306) | c3_1(a2306) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1492,plain,
% 0.85/1.06 (hskp6),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1491, 1461, 35, 1082, 365, 363, 36])).
% 0.85/1.06 tff(1493,plain,
% 0.85/1.06 (~c3_1(a2285)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[394, 1492])).
% 0.85/1.06 tff(1494,plain,
% 0.85/1.06 (c1_1(a2285)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[373, 1492])).
% 0.85/1.06 tff(1495,plain,
% 0.85/1.06 (c0_1(a2285)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[381, 1492])).
% 0.85/1.06 tff(1496,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1497,plain,
% 0.85/1.06 ((hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306))) <=> (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1498,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1497])).
% 0.85/1.06 tff(1499,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1498, 1496])).
% 0.85/1.06 tff(1500,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2285) | (~c0_1(a2285)) | (~c1_1(a2285)) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1501,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c0_1(a2285))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 0.85/1.06 tff(1502,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1501, 160, 1082, 1495, 1494, 365, 1450, 363, 1493, 47])).
% 0.85/1.06 tff(1503,plain,(c1_1(a2306) | c3_1(a2306) | hskp28 | hskp1 | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1504,plain,
% 0.85/1.06 (c1_1(a2306)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1503, 37, 35, 36, 363])).
% 0.85/1.06 tff(1505,plain,
% 0.85/1.06 ((~c1_1(a2306)) | (~c0_1(a2306))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1136, 160, 1082, 912, 363, 911, 47, 37])).
% 0.85/1.06 tff(1506,plain,
% 0.85/1.06 (~c0_1(a2306)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1505, 1504])).
% 0.85/1.06 tff(1507,assumption,(c1_1(a2306)), introduced(assumption)).
% 0.85/1.06 tff(1508,plain,
% 0.85/1.06 (~hskp17),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[236, 1451])).
% 0.85/1.06 tff(1509,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1510,plain,
% 0.85/1.06 ((hskp17 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306))) <=> (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1511,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306)))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1510])).
% 0.85/1.06 tff(1512,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1511, 1509])).
% 0.85/1.06 tff(1513,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1514,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c1_1(a2304)) | c0_1(a2306)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 0.85/1.06 tff(1515,plain,
% 0.85/1.06 (~c1_1(a2304)),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1514, 160, 1508, 1507, 1451, 1002, 996, 1440, 576])).
% 0.85/1.06 tff(1516,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1517,plain,
% 0.85/1.06 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304)) <=> (hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1518,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304)))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[1517])).
% 0.85/1.06 tff(1519,plain,
% 0.85/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304))),
% 0.85/1.06 inference(transitivity,[status(thm)],[1518, 1516])).
% 0.85/1.06 tff(1520,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(1521,plain,
% 0.85/1.06 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2304) | c2_1(a2304) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | c1_1(a2304)),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 0.85/1.06 tff(1522,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1521, 160, 36, 912, 1008, 1002, 911, 206, 37, 1515])).
% 0.85/1.06 tff(1523,plain,((~hskp16) | hskp1 | c1_1(a2282) | (~c1_1(a2306)) | (~c2_1(a2306)) | c0_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.06 tff(1524,plain,
% 0.85/1.06 (~hskp16),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[1523, 37, 36, 1504, 1450, 1506])).
% 0.85/1.06 tff(1525,assumption,(~hskp16), introduced(assumption)).
% 0.85/1.06 tff(1526,plain,
% 0.85/1.06 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1527,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1526])).
% 0.85/1.06 tff(1528,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1529,plain,
% 0.85/1.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp16))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.85/1.06 inference(bind,[status(th)],[])).
% 0.85/1.06 tff(1530,plain,
% 0.85/1.06 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.85/1.06 inference(quant_intro,[status(thm)],[1529])).
% 0.85/1.06 tff(1531,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 0.85/1.06 tff(1532,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 0.85/1.06 tff(1533,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1532, 1528])).
% 0.85/1.06 tff(1534,plain,(
% 0.85/1.06 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.85/1.06 inference(skolemize,[status(sab)],[1533])).
% 0.85/1.06 tff(1535,plain,
% 0.85/1.06 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[1534, 1527])).
% 0.85/1.06 tff(1536,plain,
% 0.85/1.06 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(1537,plain,
% 0.85/1.06 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a2306) | c3_1(a2306) | (~c1_1(a2306))) <=> (hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1538,plain,
% 0.85/1.07 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2306) | c3_1(a2306) | (~c1_1(a2306)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1537])).
% 0.85/1.07 tff(1539,plain,
% 0.85/1.07 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2306) | c3_1(a2306) | (~c1_1(a2306)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1538, 1536])).
% 0.85/1.07 tff(1540,plain,
% 0.85/1.07 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2306) | c3_1(a2306) | (~c1_1(a2306)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1541,plain,
% 0.85/1.07 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | (~c1_1(a2306)) | c3_1(a2306) | (~ndr1_0) | c0_1(a2306)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 0.85/1.07 tff(1542,plain,
% 0.85/1.07 (hskp16 | hskp15 | (~c1_1(a2306)) | c0_1(a2306)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1541, 160, 363, 1535])).
% 0.85/1.07 tff(1543,plain,
% 0.85/1.07 (hskp15),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1542, 1525, 1507, 576])).
% 0.85/1.07 tff(1544,plain,
% 0.85/1.07 (((~hskp15) | (~c3_1(a2303))) <=> ((~hskp15) | (~c3_1(a2303)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1545,plain,
% 0.85/1.07 (((~c3_1(a2303)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a2303)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1546,axiom,((~c3_1(a2303)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.85/1.07 tff(1547,plain,
% 0.85/1.07 ((~hskp15) | (~c3_1(a2303))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1546, 1545])).
% 0.85/1.07 tff(1548,plain,
% 0.85/1.07 ((~hskp15) | (~c3_1(a2303))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1547, 1544])).
% 0.85/1.07 tff(1549,plain,
% 0.85/1.07 (~c3_1(a2303)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1548, 1543])).
% 0.85/1.07 tff(1550,plain,
% 0.85/1.07 (((~hskp15) | c2_1(a2303)) <=> ((~hskp15) | c2_1(a2303))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1551,axiom,((~hskp15) | c2_1(a2303)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.85/1.07 tff(1552,plain,
% 0.85/1.07 ((~hskp15) | c2_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 0.85/1.07 tff(1553,plain,
% 0.85/1.07 ((~hskp15) | c2_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1552, 1550])).
% 0.85/1.07 tff(1554,plain,
% 0.85/1.07 ((~hskp15) | c2_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1553, 1550])).
% 0.85/1.07 tff(1555,plain,
% 0.85/1.07 ((~hskp15) | c2_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1554, 1550])).
% 0.85/1.07 tff(1556,plain,
% 0.85/1.07 ((~hskp15) | c2_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1555, 1550])).
% 0.85/1.07 tff(1557,plain,
% 0.85/1.07 (c2_1(a2303)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1556, 1543])).
% 0.85/1.07 tff(1558,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1559,plain,
% 0.85/1.07 (((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2306) | (~c2_1(a2306)) | (~c1_1(a2306))) <=> ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1560,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2306) | (~c2_1(a2306)) | (~c1_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1559])).
% 0.85/1.07 tff(1561,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2306) | (~c2_1(a2306)) | (~c1_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1560, 1558])).
% 0.85/1.07 tff(1562,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2306) | (~c2_1(a2306)) | (~c1_1(a2306)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1563,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | (~ndr1_0) | (~c2_1(a2303)) | (~c0_1(a2303)) | c0_1(a2306)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 0.85/1.07 tff(1564,plain,
% 0.85/1.07 (~c0_1(a2303)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1563, 160, 1557, 1507, 1451, 363, 1549, 675, 576])).
% 0.85/1.07 tff(1565,plain,
% 0.85/1.07 (hskp26),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1028, 1525, 35])).
% 0.85/1.07 tff(1566,plain,
% 0.85/1.07 (~c1_1(a2345)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1045, 1565])).
% 0.85/1.07 tff(1567,plain,
% 0.85/1.07 (~c0_1(a2345)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1051, 1565])).
% 0.85/1.07 tff(1568,plain,
% 0.85/1.07 (c3_1(a2345)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1059, 1565])).
% 0.85/1.07 tff(1569,plain,
% 0.85/1.07 (hskp7),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1068, 160, 1061, 1568, 1567, 1566, 1039])).
% 0.85/1.07 tff(1570,plain,
% 0.85/1.07 (~c2_1(a2286)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[957, 1569])).
% 0.85/1.07 tff(1571,plain,
% 0.85/1.07 (c1_1(a2286)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[979, 1569])).
% 0.85/1.07 tff(1572,plain,
% 0.85/1.07 (((~hskp15) | c1_1(a2303)) <=> ((~hskp15) | c1_1(a2303))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1573,axiom,((~hskp15) | c1_1(a2303)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.85/1.07 tff(1574,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 0.85/1.07 tff(1575,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1574, 1572])).
% 0.85/1.07 tff(1576,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1575, 1572])).
% 0.85/1.07 tff(1577,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1576, 1572])).
% 0.85/1.07 tff(1578,plain,
% 0.85/1.07 ((~hskp15) | c1_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1577, 1572])).
% 0.85/1.07 tff(1579,plain,
% 0.85/1.07 (c1_1(a2303)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1578, 1543])).
% 0.85/1.07 tff(1580,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1581,plain,
% 0.85/1.07 ((hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303))) <=> (hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1582,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303)))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1581])).
% 0.85/1.07 tff(1583,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1582, 1580])).
% 0.85/1.07 tff(1584,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1585,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c1_1(a2303)) | (~c2_1(a2303)) | c0_1(a2303)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 0.85/1.07 tff(1586,plain,
% 0.85/1.07 (c3_1(a2286)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1585, 160, 1508, 1579, 1557, 1571, 1570, 1440, 1564])).
% 0.85/1.07 tff(1587,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[986, 160, 908, 907, 1571, 707, 906, 1570, 702, 196, 37, 1586])).
% 0.85/1.07 tff(1588,plain,(hskp16 | (~c2_1(a2282)) | c0_1(a2282) | c1_1(a2282) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2306) | hskp6 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1589,plain,
% 0.85/1.07 (hskp6),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1588, 1524, 913, 37, 1504, 1450, 363, 1506, 912, 35])).
% 0.85/1.07 tff(1590,plain,
% 0.85/1.07 (~c3_1(a2285)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[394, 1589])).
% 0.85/1.07 tff(1591,plain,
% 0.85/1.07 (c1_1(a2285)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[373, 1589])).
% 0.85/1.07 tff(1592,plain,
% 0.85/1.07 (c0_1(a2285)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[381, 1589])).
% 0.85/1.07 tff(1593,plain,
% 0.85/1.07 ($false),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1088, 160, 1082, 1592, 1591, 912, 1590, 911, 47, 37])).
% 0.85/1.07 tff(1594,plain,(c1_1(a2282) | c3_1(a2306) | hskp28 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.85/1.07 tff(1595,plain,
% 0.85/1.07 (c1_1(a2282)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1594, 363, 35, 36])).
% 0.85/1.07 tff(1596,plain,
% 0.85/1.07 (~hskp10),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1124, 1595, 913, 911, 912])).
% 0.85/1.07 tff(1597,plain,
% 0.85/1.07 (^[U: $i] : refl((hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1598,plain,
% 0.85/1.07 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1597])).
% 0.85/1.07 tff(1599,plain,
% 0.85/1.07 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1600,plain,
% 0.85/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp9) <=> ((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp9))), rewrite(((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1601,plain,
% 0.85/1.07 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp9) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1600])).
% 0.85/1.07 tff(1602,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.85/1.07 tff(1603,plain,
% 0.85/1.07 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 0.85/1.07 tff(1604,plain,
% 0.85/1.07 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1603, 1599])).
% 0.85/1.07 tff(1605,plain,(
% 0.85/1.07 ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.07 inference(skolemize,[status(sab)],[1604])).
% 0.85/1.07 tff(1606,plain,
% 0.85/1.07 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1605, 1598])).
% 0.85/1.07 tff(1607,plain,
% 0.85/1.07 (^[V: $i, U: $i] : refl((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1608,plain,
% 0.85/1.07 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1607])).
% 0.85/1.07 tff(1609,plain,
% 0.85/1.07 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1610,plain,
% 0.85/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.85/1.07 inference(bind,[status(th)],[])).
% 0.85/1.07 tff(1611,plain,
% 0.85/1.07 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp30) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.07 inference(quant_intro,[status(thm)],[1610])).
% 0.85/1.07 tff(1612,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 0.85/1.07 tff(1613,plain,
% 0.85/1.07 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 0.85/1.07 tff(1614,plain,
% 0.85/1.07 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1613, 1609])).
% 0.85/1.07 tff(1615,plain,(
% 0.85/1.07 ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.07 inference(skolemize,[status(sab)],[1614])).
% 0.85/1.07 tff(1616,plain,
% 0.85/1.07 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1615, 1608])).
% 0.85/1.07 tff(1617,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1618,plain,
% 0.85/1.07 ((hskp30 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1619,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1618])).
% 0.85/1.07 tff(1620,plain,
% 0.85/1.07 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1619, 1617])).
% 0.85/1.07 tff(1621,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c2_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1622,plain,
% 0.85/1.07 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c1_1(a2306) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 0.85/1.07 tff(1623,plain,
% 0.85/1.07 (hskp30),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1622, 160, 898, 890, 365, 1450, 363, 882, 1616])).
% 0.85/1.07 tff(1624,plain,
% 0.85/1.07 (c3_1(a2315)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[726, 1623])).
% 0.85/1.07 tff(1625,plain,
% 0.85/1.07 (c2_1(a2315)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[734, 1623])).
% 0.85/1.07 tff(1626,plain,
% 0.85/1.07 (c1_1(a2315)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[751, 1623])).
% 0.85/1.07 tff(1627,plain,
% 0.85/1.07 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1628,plain,
% 0.85/1.07 ((hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315))) <=> (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1629,plain,
% 0.85/1.07 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1628])).
% 0.85/1.07 tff(1630,plain,
% 0.85/1.07 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1629, 1627])).
% 0.85/1.07 tff(1631,plain,
% 0.85/1.07 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1632,plain,
% 0.85/1.07 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp9 | (~ndr1_0) | (~c3_1(a2315)) | (~c2_1(a2315)) | (~c1_1(a2315))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 0.85/1.07 tff(1633,plain,
% 0.85/1.07 (hskp27),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1632, 160, 1460, 1626, 1625, 1624, 1606])).
% 0.85/1.07 tff(1634,plain,
% 0.85/1.07 (((~hskp27) | (~c0_1(a2367))) <=> ((~hskp27) | (~c0_1(a2367)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1635,plain,
% 0.85/1.07 (((~c0_1(a2367)) | (~hskp27)) <=> ((~hskp27) | (~c0_1(a2367)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1636,axiom,((~c0_1(a2367)) | (~hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.85/1.07 tff(1637,plain,
% 0.85/1.07 ((~hskp27) | (~c0_1(a2367))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1636, 1635])).
% 0.85/1.07 tff(1638,plain,
% 0.85/1.07 ((~hskp27) | (~c0_1(a2367))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1637, 1634])).
% 0.85/1.07 tff(1639,plain,
% 0.85/1.07 (~c0_1(a2367)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1638, 1633])).
% 0.85/1.07 tff(1640,plain,
% 0.85/1.07 (((~hskp27) | c2_1(a2367)) <=> ((~hskp27) | c2_1(a2367))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1641,axiom,((~hskp27) | c2_1(a2367)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.85/1.07 tff(1642,plain,
% 0.85/1.07 ((~hskp27) | c2_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 0.85/1.07 tff(1643,plain,
% 0.85/1.07 ((~hskp27) | c2_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1642, 1640])).
% 0.85/1.07 tff(1644,plain,
% 0.85/1.07 ((~hskp27) | c2_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1643, 1640])).
% 0.85/1.07 tff(1645,plain,
% 0.85/1.07 ((~hskp27) | c2_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1644, 1640])).
% 0.85/1.07 tff(1646,plain,
% 0.85/1.07 ((~hskp27) | c2_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1645, 1640])).
% 0.85/1.07 tff(1647,plain,
% 0.85/1.07 (c2_1(a2367)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1646, 1633])).
% 0.85/1.07 tff(1648,plain,
% 0.85/1.07 (((~hskp27) | c1_1(a2367)) <=> ((~hskp27) | c1_1(a2367))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1649,axiom,((~hskp27) | c1_1(a2367)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.85/1.07 tff(1650,plain,
% 0.85/1.07 ((~hskp27) | c1_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 0.85/1.07 tff(1651,plain,
% 0.85/1.07 ((~hskp27) | c1_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1650, 1648])).
% 0.85/1.07 tff(1652,plain,
% 0.85/1.07 ((~hskp27) | c1_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1651, 1648])).
% 0.85/1.07 tff(1653,plain,
% 0.85/1.07 ((~hskp27) | c1_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1652, 1648])).
% 0.85/1.07 tff(1654,plain,
% 0.85/1.07 ((~hskp27) | c1_1(a2367)),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1653, 1648])).
% 0.85/1.07 tff(1655,plain,
% 0.85/1.07 (c1_1(a2367)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1654, 1633])).
% 0.85/1.07 tff(1656,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1657,plain,
% 0.85/1.07 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2306) | (~c0_1(a2306)) | (~c2_1(a2306)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> ((~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1658,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2306) | (~c0_1(a2306)) | (~c2_1(a2306)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1657])).
% 0.85/1.07 tff(1659,plain,
% 0.85/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2306) | (~c0_1(a2306)) | (~c2_1(a2306)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1658, 1656])).
% 0.85/1.07 tff(1660,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2306) | (~c0_1(a2306)) | (~c2_1(a2306)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1661,plain,
% 0.85/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c0_1(a2306))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 0.85/1.07 tff(1662,plain,
% 0.85/1.07 ((~c2_1(a2306)) | (~c1_1(a2282)) | (~c0_1(a2306))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1661, 160, 912, 363, 913, 911, 675])).
% 0.85/1.07 tff(1663,plain,
% 0.85/1.07 (~c0_1(a2306)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1662, 1595, 1450])).
% 0.85/1.07 tff(1664,plain,
% 0.85/1.07 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1665,plain,
% 0.85/1.07 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))) <=> (hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 0.85/1.07 inference(rewrite,[status(thm)],[])).
% 0.85/1.07 tff(1666,plain,
% 0.85/1.07 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282))))),
% 0.85/1.07 inference(monotonicity,[status(thm)],[1665])).
% 0.85/1.07 tff(1667,plain,
% 0.85/1.07 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)))),
% 0.85/1.07 inference(transitivity,[status(thm)],[1666, 1664])).
% 0.85/1.07 tff(1668,plain,
% 0.85/1.07 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))),
% 0.85/1.07 inference(quant_inst,[status(thm)],[])).
% 0.85/1.07 tff(1669,plain,
% 0.85/1.07 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp16 | hskp15 | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282))),
% 0.85/1.07 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 0.85/1.07 tff(1670,plain,
% 0.85/1.07 (hskp16 | hskp15 | (~c1_1(a2282))),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1669, 160, 702, 1093, 1535])).
% 0.85/1.07 tff(1671,plain,
% 0.85/1.07 (hskp15),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1670, 1342, 1092])).
% 0.85/1.07 tff(1672,plain,
% 0.85/1.07 (~c3_1(a2303)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1548, 1671])).
% 0.85/1.07 tff(1673,assumption,(~c0_1(a2367)), introduced(assumption)).
% 0.85/1.07 tff(1674,plain,
% 0.85/1.07 (c2_1(a2303)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1556, 1671])).
% 0.85/1.07 tff(1675,plain,
% 0.85/1.07 (c1_1(a2303)),
% 0.85/1.07 inference(unit_resolution,[status(thm)],[1578, 1671])).
% 0.85/1.07 tff(1676,assumption,(c2_1(a2367)), introduced(assumption)).
% 0.85/1.07 tff(1677,assumption,(c1_1(a2367)), introduced(assumption)).
% 0.85/1.08 tff(1678,plain,
% 0.85/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1679,plain,
% 0.85/1.08 (((~ndr1_0) | c3_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367))) <=> (c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1680,plain,
% 0.85/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1679])).
% 0.85/1.08 tff(1681,plain,
% 0.85/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1680, 1678])).
% 0.85/1.08 tff(1682,plain,
% 0.85/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2303) | (~c1_1(a2303)) | (~c2_1(a2303)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1683,plain,
% 0.85/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2303) | (~ndr1_0) | (~c1_1(a2303)) | (~c2_1(a2303)) | (~c0_1(a2303)) | (~c2_1(a2367)) | (~c1_1(a2367))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 0.85/1.08 tff(1684,plain,
% 0.85/1.08 (~c0_1(a2303)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1683, 160, 1677, 1676, 1675, 1674, 1673, 1672, 675])).
% 0.85/1.08 tff(1685,plain,
% 0.85/1.08 (~c1_1(a2345)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1045, 1343])).
% 0.85/1.08 tff(1686,plain,
% 0.85/1.08 (~c0_1(a2345)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1051, 1343])).
% 0.85/1.08 tff(1687,plain,
% 0.85/1.08 (c3_1(a2345)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1059, 1343])).
% 0.85/1.08 tff(1688,plain,
% 0.85/1.08 (hskp7),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1068, 160, 1061, 1687, 1686, 1685, 1039])).
% 0.85/1.08 tff(1689,plain,
% 0.85/1.08 (~c2_1(a2286)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[957, 1688])).
% 0.85/1.08 tff(1690,plain,
% 0.85/1.08 (c1_1(a2286)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[979, 1688])).
% 0.85/1.08 tff(1691,plain,
% 0.85/1.08 (c3_1(a2286)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1585, 160, 1508, 1675, 1674, 1690, 1689, 1440, 1684])).
% 0.85/1.08 tff(1692,plain,
% 0.85/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1693,plain,
% 0.85/1.08 (((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306))) <=> (c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1694,plain,
% 0.85/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1693])).
% 0.85/1.08 tff(1695,plain,
% 0.85/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1694, 1692])).
% 0.85/1.08 tff(1696,plain,
% 0.85/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1697,plain,
% 0.85/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c1_1(a2306) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2306) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 0.85/1.08 tff(1698,plain,
% 0.85/1.08 ($false),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1697, 160, 908, 907, 1690, 906, 365, 1451, 1689, 196, 576, 1691])).
% 0.85/1.08 tff(1699,plain,(hskp6 | c1_1(a2306) | (~c2_1(a2306)) | c0_1(a2306) | (~c1_1(a2367)) | (~c2_1(a2367)) | c0_1(a2367) | (~c1_1(a2282)) | c0_1(a2282) | c3_1(a2282) | hskp28 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.85/1.08 tff(1700,plain,
% 0.85/1.08 (hskp6),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1699, 365, 1450, 1663, 1655, 1647, 1639, 1595, 913, 911, 35, 1596])).
% 0.85/1.08 tff(1701,plain,
% 0.85/1.08 (~c3_1(a2285)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[394, 1700])).
% 0.85/1.08 tff(1702,plain,
% 0.85/1.08 (c1_1(a2285)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[373, 1700])).
% 0.85/1.08 tff(1703,plain,
% 0.85/1.08 (c0_1(a2285)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[381, 1700])).
% 0.85/1.08 tff(1704,plain,
% 0.85/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1705,plain,
% 0.85/1.08 (((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367))) <=> (c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1706,plain,
% 0.85/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367))))),
% 0.85/1.08 inference(monotonicity,[status(thm)],[1705])).
% 0.85/1.08 tff(1707,plain,
% 0.85/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(transitivity,[status(thm)],[1706, 1704])).
% 0.85/1.08 tff(1708,plain,
% 0.85/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2285) | (~c1_1(a2285)) | (~c2_1(a2285)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2367) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(quant_inst,[status(thm)],[])).
% 0.85/1.08 tff(1709,plain,
% 0.85/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | (~c2_1(a2285)) | (~c0_1(a2285)) | (~c2_1(a2367)) | (~c1_1(a2367))),
% 0.85/1.08 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 0.85/1.08 tff(1710,plain,
% 0.85/1.08 (~c2_1(a2285)),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[1709, 160, 1655, 1647, 1703, 1702, 1639, 1701, 675])).
% 0.85/1.08 tff(1711,plain,
% 0.85/1.08 (~hskp17),
% 0.85/1.08 inference(unit_resolution,[status(thm)],[236, 1450])).
% 0.85/1.08 tff(1712,plain,
% 0.85/1.08 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1713,plain,
% 0.85/1.08 ((hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2367) | (~c1_1(a2367)) | (~c2_1(a2367))) <=> (hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.85/1.08 inference(rewrite,[status(thm)],[])).
% 0.85/1.08 tff(1714,plain,
% 0.85/1.08 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2367) | (~c1_1(a2367)) | (~c2_1(a2367)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1713])).
% 0.91/1.08 tff(1715,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2367) | (~c1_1(a2367)) | (~c2_1(a2367)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[1714, 1712])).
% 0.91/1.08 tff(1716,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2367) | (~c1_1(a2367)) | (~c2_1(a2367)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(1717,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2367) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2367)) | (~c1_1(a2367))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 0.91/1.08 tff(1718,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1717, 160, 1711, 1655, 1647, 1702, 1639, 1701, 1440, 1710])).
% 0.91/1.08 tff(1719,plain,(c1_1(a2306) | hskp28 | c3_1(a2306) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(1720,plain,
% 0.91/1.08 (c1_1(a2306)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1719, 363, 35, 36])).
% 0.91/1.08 tff(1721,plain,
% 0.91/1.08 (~hskp16),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1341, 1061, 1163])).
% 0.91/1.08 tff(1722,plain,
% 0.91/1.08 (hskp15),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1670, 1721, 1092])).
% 0.91/1.08 tff(1723,plain,
% 0.91/1.08 (~c3_1(a2303)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1548, 1722])).
% 0.91/1.08 tff(1724,plain,
% 0.91/1.08 (c2_1(a2303)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1556, 1722])).
% 0.91/1.08 tff(1725,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1726,plain,
% 0.91/1.08 (((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1727,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1726])).
% 0.91/1.08 tff(1728,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[1727, 1725])).
% 0.91/1.08 tff(1729,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2303) | (~c0_1(a2303)) | (~c2_1(a2303)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(1730,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2303) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2303)) | (~c0_1(a2303))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 0.91/1.08 tff(1731,plain,
% 0.91/1.08 (~c0_1(a2303)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1730, 160, 1724, 707, 1507, 1451, 363, 1723, 702, 675, 1092])).
% 0.91/1.08 tff(1732,plain,
% 0.91/1.08 (hskp26),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1028, 1721, 35])).
% 0.91/1.08 tff(1733,plain,
% 0.91/1.08 (~c1_1(a2345)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1045, 1732])).
% 0.91/1.08 tff(1734,plain,
% 0.91/1.08 (~c0_1(a2345)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1051, 1732])).
% 0.91/1.08 tff(1735,plain,
% 0.91/1.08 (c3_1(a2345)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1059, 1732])).
% 0.91/1.08 tff(1736,plain,
% 0.91/1.08 (hskp7),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1068, 160, 1061, 1735, 1734, 1733, 1039])).
% 0.91/1.08 tff(1737,plain,
% 0.91/1.08 (~c2_1(a2286)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[957, 1736])).
% 0.91/1.08 tff(1738,plain,
% 0.91/1.08 (c1_1(a2286)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[979, 1736])).
% 0.91/1.08 tff(1739,plain,
% 0.91/1.08 (c1_1(a2303)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1578, 1722])).
% 0.91/1.08 tff(1740,plain,
% 0.91/1.08 (c3_1(a2286)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1585, 160, 1508, 1739, 1724, 1738, 1737, 1440, 1731])).
% 0.91/1.08 tff(1741,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1742,plain,
% 0.91/1.08 (((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345))) <=> (c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1743,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1742])).
% 0.91/1.08 tff(1744,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[1743, 1741])).
% 0.91/1.08 tff(1745,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2345) | (~c2_1(a2345)) | (~c3_1(a2345)) | c0_1(a2345) | c1_1(a2345) | (~c2_1(a2345)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(1746,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2345)) | (~c3_1(a2345))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 0.91/1.08 tff(1747,plain,
% 0.91/1.08 (~c2_1(a2345)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1746, 160, 1735, 1738, 1734, 1733, 1737, 196, 1740])).
% 0.91/1.08 tff(1748,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1749,plain,
% 0.91/1.08 ((hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345)) <=> (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(1750,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1749])).
% 0.91/1.08 tff(1751,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345))),
% 0.91/1.08 inference(transitivity,[status(thm)],[1750, 1748])).
% 0.91/1.08 tff(1752,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345) | c1_1(a2345) | c0_1(a2345))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(1753,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2345) | c1_1(a2345) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2345)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 0.91/1.08 tff(1754,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1753, 160, 35, 1738, 1734, 1733, 1737, 421, 1747, 1740])).
% 0.91/1.08 tff(1755,plain,(hskp6 | hskp28 | (~c2_1(a2282)) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2282) | (~c1_1(a2282)) | c3_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(1756,plain,
% 0.91/1.08 (hskp6),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1755, 1720, 912, 35, 1450, 363, 913, 1595, 911])).
% 0.91/1.09 tff(1757,plain,
% 0.91/1.09 (~c3_1(a2285)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[394, 1756])).
% 0.91/1.09 tff(1758,plain,
% 0.91/1.09 (c0_1(a2285)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[381, 1756])).
% 0.91/1.09 tff(1759,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1760,plain,
% 0.91/1.09 (((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282))) <=> ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1761,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1760])).
% 0.91/1.09 tff(1762,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1761, 1759])).
% 0.91/1.09 tff(1763,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2285) | (~c0_1(a2285)) | (~c2_1(a2285)) | c0_1(a2282) | (~c2_1(a2282)) | (~c1_1(a2282)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1764,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2285)) | (~c0_1(a2285))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 0.91/1.09 tff(1765,plain,
% 0.91/1.09 (~c2_1(a2285)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1764, 160, 1758, 912, 1720, 1450, 363, 1757, 913, 675, 1595])).
% 0.91/1.09 tff(1766,plain,
% 0.91/1.09 (c1_1(a2285)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[373, 1756])).
% 0.91/1.09 tff(1767,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1768,plain,
% 0.91/1.09 ((hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1769,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285)))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1768])).
% 0.91/1.09 tff(1770,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1769, 1767])).
% 0.91/1.09 tff(1771,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1772,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c3_1(a2285) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c1_1(a2285)) | c2_1(a2285)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 0.91/1.09 tff(1773,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1772, 160, 1711, 1766, 912, 1757, 913, 1440, 1595, 1765])).
% 0.91/1.09 tff(1774,plain,(c3_1(a2306) | hskp28 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(1775,plain,
% 0.91/1.09 (c3_1(a2306)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1774, 36, 35])).
% 0.91/1.09 tff(1776,plain,
% 0.91/1.09 (~hskp17),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[265, 1775])).
% 0.91/1.09 tff(1777,plain,
% 0.91/1.09 (hskp7),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1070, 1343, 1061])).
% 0.91/1.09 tff(1778,plain,
% 0.91/1.09 (~c2_1(a2286)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[957, 1777])).
% 0.91/1.09 tff(1779,plain,
% 0.91/1.09 (c1_1(a2286)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[979, 1777])).
% 0.91/1.09 tff(1780,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1781,plain,
% 0.91/1.09 ((hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1782,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1781])).
% 0.91/1.09 tff(1783,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1782, 1780])).
% 0.91/1.09 tff(1784,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1785,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2286) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2286) | (~c1_1(a2286))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1784, 1783])).
% 0.91/1.09 tff(1786,plain,
% 0.91/1.09 (c3_1(a2286)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1785, 160, 825, 1779, 707, 1778, 702, 1440, 1092])).
% 0.91/1.09 tff(1787,plain,
% 0.91/1.09 ((~c3_1(a2286)) | (~c2_1(a2345))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1746, 160, 1687, 1779, 1686, 1685, 1778, 196])).
% 0.91/1.09 tff(1788,plain,
% 0.91/1.09 (~c2_1(a2345)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1787, 1786])).
% 0.91/1.09 tff(1789,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1753, 160, 35, 1779, 1686, 1685, 1778, 421, 1788, 1786])).
% 0.91/1.09 tff(1790,plain,(hskp6 | hskp28 | hskp17 | (~c2_1(a2282)) | c0_1(a2282) | (~c1_1(a2282)) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(1791,plain,
% 0.91/1.09 (hskp6),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1790, 1776, 35, 912, 913, 1091, 1125])).
% 0.91/1.09 tff(1792,plain,
% 0.91/1.09 (~c3_1(a2285)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[394, 1791])).
% 0.91/1.09 tff(1793,plain,
% 0.91/1.09 (c1_1(a2285)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[373, 1791])).
% 0.91/1.09 tff(1794,plain,
% 0.91/1.09 (c0_1(a2285)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[381, 1791])).
% 0.91/1.09 tff(1795,plain,
% 0.91/1.09 (~c2_1(a2285)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1194, 160, 1794, 1793, 912, 1792, 913, 675, 1091])).
% 0.91/1.09 tff(1796,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1772, 160, 1776, 1793, 912, 1792, 913, 1440, 1091, 1795])).
% 0.91/1.09 tff(1797,plain,(hskp1 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(1798,plain,
% 0.91/1.09 (hskp1),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1797, 35])).
% 0.91/1.09 tff(1799,plain,
% 0.91/1.09 (c1_1(a2277)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[336, 1798])).
% 0.91/1.09 tff(1800,plain,
% 0.91/1.09 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1801,plain,
% 0.91/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1800])).
% 0.91/1.09 tff(1802,plain,
% 0.91/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1803,plain,
% 0.91/1.09 (^[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)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1804,plain,
% 0.91/1.09 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1803])).
% 0.91/1.09 tff(1805,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.91/1.09 tff(1806,plain,
% 0.91/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 0.91/1.09 tff(1807,plain,
% 0.91/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1806, 1802])).
% 0.91/1.09 tff(1808,plain,(
% 0.91/1.09 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(skolemize,[status(sab)],[1807])).
% 0.91/1.09 tff(1809,plain,
% 0.91/1.09 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1808, 1801])).
% 0.91/1.09 tff(1810,plain,
% 0.91/1.09 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1811,plain,
% 0.91/1.09 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323))) <=> (hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1812,plain,
% 0.91/1.09 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1811])).
% 0.91/1.09 tff(1813,plain,
% 0.91/1.09 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1812, 1810])).
% 0.91/1.09 tff(1814,plain,
% 0.91/1.09 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1815,plain,
% 0.91/1.09 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 0.91/1.09 tff(1816,plain,
% 0.91/1.09 (hskp4 | hskp3),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1815, 160, 908, 907, 906, 1809])).
% 0.91/1.09 tff(1817,plain,
% 0.91/1.09 (hskp3),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1816, 679])).
% 0.91/1.09 tff(1818,plain,
% 0.91/1.09 (~c2_1(a2280)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[526, 1817])).
% 0.91/1.09 tff(1819,plain,
% 0.91/1.09 (c3_1(a2280)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[534, 1817])).
% 0.91/1.09 tff(1820,plain,
% 0.91/1.09 (c1_1(a2280)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[542, 1817])).
% 0.91/1.09 tff(1821,plain,
% 0.91/1.09 (c1_1(a2302)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1407, 160, 908, 907, 898, 1820, 1819, 906, 882, 1818, 196])).
% 0.91/1.09 tff(1822,plain,
% 0.91/1.09 (c1_1(a2327)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1414, 160, 35, 706, 705, 1079, 1076, 701, 421])).
% 0.91/1.09 tff(1823,plain,
% 0.91/1.09 (~hskp26),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1359, 1822, 1077, 1076, 35])).
% 0.91/1.09 tff(1824,plain,
% 0.91/1.09 (hskp16),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1028, 1823, 35])).
% 0.91/1.09 tff(1825,plain,
% 0.91/1.09 (hskp9),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1016, 1824, 35])).
% 0.91/1.09 tff(1826,plain,
% 0.91/1.09 (~c2_1(a2291)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[919, 1825])).
% 0.91/1.09 tff(1827,plain,
% 0.91/1.09 (~c1_1(a2291)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[925, 1825])).
% 0.91/1.09 tff(1828,plain,
% 0.91/1.09 (~c0_1(a2291)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[931, 1825])).
% 0.91/1.09 tff(1829,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1830,plain,
% 0.91/1.09 ((hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291)) <=> (hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1831,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1830])).
% 0.91/1.09 tff(1832,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1831, 1829])).
% 0.91/1.09 tff(1833,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2291) | c1_1(a2291) | c0_1(a2291))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1834,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2291) | c1_1(a2291) | c2_1(a2291) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 0.91/1.09 tff(1835,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1834, 160, 35, 1077, 1076, 1828, 1827, 1826, 421, 1822])).
% 0.91/1.09 tff(1836,plain,((~hskp23) | hskp28 | (~c1_1(a2280)) | (~c3_1(a2280)) | c2_1(a2280)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(1837,plain,
% 0.91/1.09 (~hskp23),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1836, 706, 35, 705, 701])).
% 0.91/1.09 tff(1838,plain,
% 0.91/1.09 (~c0_1(a2306)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[272, 160, 1837, 365, 364, 363, 260])).
% 0.91/1.09 tff(1839,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[549, 160, 35, 706, 705, 365, 364, 701, 421, 1838])).
% 0.91/1.09 tff(1840,plain,(c2_1(a2306) | hskp28 | (~c1_1(a2280)) | (~c3_1(a2280)) | c1_1(a2306) | c2_1(a2280) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(1841,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1840, 318, 319, 706, 705, 35, 701, 317])).
% 0.91/1.09 tff(1842,plain,((~hskp17) | (~c1_1(a2280)) | (~c3_1(a2280)) | hskp28 | c2_1(a2280)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(1843,plain,
% 0.91/1.09 (~hskp17),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1842, 1820, 1819, 35, 1818])).
% 0.91/1.09 tff(1844,assumption,(c1_1(a2302)), introduced(assumption)).
% 0.91/1.09 tff(1845,assumption,(hskp19), introduced(assumption)).
% 0.91/1.09 tff(1846,plain,
% 0.91/1.09 (((~hskp19) | (~c3_1(a2316))) <=> ((~hskp19) | (~c3_1(a2316)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1847,plain,
% 0.91/1.09 (((~c3_1(a2316)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a2316)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1848,axiom,((~c3_1(a2316)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.91/1.09 tff(1849,plain,
% 0.91/1.09 ((~hskp19) | (~c3_1(a2316))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 0.91/1.09 tff(1850,plain,
% 0.91/1.09 ((~hskp19) | (~c3_1(a2316))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1849, 1846])).
% 0.91/1.09 tff(1851,plain,
% 0.91/1.09 (~c3_1(a2316)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1850, 1845])).
% 0.91/1.09 tff(1852,plain,
% 0.91/1.09 (((~hskp19) | (~c2_1(a2316))) <=> ((~hskp19) | (~c2_1(a2316)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1853,plain,
% 0.91/1.09 (((~c2_1(a2316)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a2316)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1854,axiom,((~c2_1(a2316)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.91/1.09 tff(1855,plain,
% 0.91/1.09 ((~hskp19) | (~c2_1(a2316))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 0.91/1.09 tff(1856,plain,
% 0.91/1.09 ((~hskp19) | (~c2_1(a2316))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1855, 1852])).
% 0.91/1.09 tff(1857,plain,
% 0.91/1.09 (~c2_1(a2316)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1856, 1845])).
% 0.91/1.09 tff(1858,plain,
% 0.91/1.09 (((~hskp19) | c1_1(a2316)) <=> ((~hskp19) | c1_1(a2316))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1859,axiom,((~hskp19) | c1_1(a2316)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.91/1.09 tff(1860,plain,
% 0.91/1.09 ((~hskp19) | c1_1(a2316)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 0.91/1.09 tff(1861,plain,
% 0.91/1.09 ((~hskp19) | c1_1(a2316)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1860, 1858])).
% 0.91/1.09 tff(1862,plain,
% 0.91/1.09 ((~hskp19) | c1_1(a2316)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1861, 1858])).
% 0.91/1.09 tff(1863,plain,
% 0.91/1.09 ((~hskp19) | c1_1(a2316)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1862, 1858])).
% 0.91/1.09 tff(1864,plain,
% 0.91/1.09 ((~hskp19) | c1_1(a2316)),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1863, 1858])).
% 0.91/1.09 tff(1865,plain,
% 0.91/1.09 (c1_1(a2316)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1864, 1845])).
% 0.91/1.09 tff(1866,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1867,plain,
% 0.91/1.09 ((hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302))) <=> (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1868,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[1867])).
% 0.91/1.09 tff(1869,plain,
% 0.91/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[1868, 1866])).
% 0.91/1.09 tff(1870,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(1871,plain,
% 0.91/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c1_1(a2316))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1870, 1869])).
% 0.91/1.09 tff(1872,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1871, 160, 825, 1865, 898, 1857, 1851, 882, 1440, 1844])).
% 0.91/1.09 tff(1873,plain,((~hskp19) | hskp17 | (~c1_1(a2302))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(1874,plain,
% 0.91/1.09 (~hskp19),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1873, 1843, 1821])).
% 0.91/1.09 tff(1875,plain,
% 0.91/1.09 (^[U: $i] : refl((hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1876,plain,
% 0.91/1.09 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1875])).
% 0.91/1.09 tff(1877,plain,
% 0.91/1.09 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1878,plain,
% 0.91/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(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)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp4) <=> ((hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp4))), rewrite(((hskp19 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp4) <=> (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp4) <=> (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1879,plain,
% 0.91/1.09 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp4) <=> ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1878])).
% 0.91/1.09 tff(1880,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp19) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.91/1.09 tff(1881,plain,
% 0.91/1.09 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 0.91/1.09 tff(1882,plain,
% 0.91/1.09 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1881, 1877])).
% 0.91/1.09 tff(1883,plain,(
% 0.91/1.09 ![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.91/1.09 inference(skolemize,[status(sab)],[1882])).
% 0.91/1.09 tff(1884,plain,
% 0.91/1.09 (![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1883, 1876])).
% 0.91/1.09 tff(1885,plain,
% 0.91/1.09 (~hskp23),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1836, 1820, 35, 1819, 1818])).
% 0.91/1.09 tff(1886,plain,
% 0.91/1.09 (^[U: $i] : refl((hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1887,plain,
% 0.91/1.09 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1886])).
% 0.91/1.09 tff(1888,plain,
% 0.91/1.09 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1889,plain,
% 0.91/1.09 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp25))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp23) <=> ((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp23))), rewrite(((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp23) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp23) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 0.91/1.09 inference(bind,[status(th)],[])).
% 0.91/1.09 tff(1890,plain,
% 0.91/1.09 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp23) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(quant_intro,[status(thm)],[1889])).
% 0.91/1.09 tff(1891,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.91/1.09 tff(1892,plain,
% 0.91/1.09 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 0.91/1.09 tff(1893,plain,
% 0.91/1.09 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1892, 1888])).
% 0.91/1.09 tff(1894,plain,(
% 0.91/1.09 ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(skolemize,[status(sab)],[1893])).
% 0.91/1.09 tff(1895,plain,
% 0.91/1.09 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[1894, 1887])).
% 0.91/1.09 tff(1896,plain,
% 0.91/1.09 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(1897,plain,
% 0.91/1.09 ((hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2302)) | (~c1_1(a2302)) | (~c2_1(a2302))) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1898,plain,
% 0.91/1.10 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2302)) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1897])).
% 0.91/1.10 tff(1899,plain,
% 0.91/1.10 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2302)) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1898, 1896])).
% 0.91/1.10 tff(1900,plain,
% 0.91/1.10 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2302)) | (~c1_1(a2302)) | (~c2_1(a2302)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1901,plain,
% 0.91/1.10 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2302))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1900, 1899])).
% 0.91/1.10 tff(1902,plain,
% 0.91/1.10 (hskp25 | hskp23 | (~c1_1(a2302))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1901, 160, 898, 890, 1895])).
% 0.91/1.10 tff(1903,plain,
% 0.91/1.10 (hskp25),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1902, 1885, 1821])).
% 0.91/1.10 tff(1904,plain,
% 0.91/1.10 (c3_1(a2342)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[24, 1903])).
% 0.91/1.10 tff(1905,plain,
% 0.91/1.10 (c0_1(a2342)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[32, 1903])).
% 0.91/1.10 tff(1906,plain,
% 0.91/1.10 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1907,plain,
% 0.91/1.10 ((hskp19 | hskp4 | (~ndr1_0) | c1_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342))) <=> (hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1908,plain,
% 0.91/1.10 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1907])).
% 0.91/1.10 tff(1909,plain,
% 0.91/1.10 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1908, 1906])).
% 0.91/1.10 tff(1910,plain,
% 0.91/1.10 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1911,plain,
% 0.91/1.10 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | (~ndr1_0) | (~c3_1(a2342)) | c1_1(a2342) | (~c0_1(a2342))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 0.91/1.10 tff(1912,plain,
% 0.91/1.10 (hskp19 | c1_1(a2342)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1911, 160, 679, 1905, 1904, 1884])).
% 0.91/1.10 tff(1913,plain,
% 0.91/1.10 (c1_1(a2342)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1912, 1874])).
% 0.91/1.10 tff(1914,plain,
% 0.91/1.10 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1915,plain,
% 0.91/1.10 ((hskp19 | hskp4 | (~ndr1_0) | c1_1(a2323) | (~c0_1(a2323)) | (~c3_1(a2323))) <=> (hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1916,plain,
% 0.91/1.10 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2323) | (~c0_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1915])).
% 0.91/1.10 tff(1917,plain,
% 0.91/1.10 (((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2323) | (~c0_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1916, 1914])).
% 0.91/1.10 tff(1918,plain,
% 0.91/1.10 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp4 | (~ndr1_0) | c1_1(a2323) | (~c0_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1919,plain,
% 0.91/1.10 ((~![U: $i] : (hskp19 | hskp4 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp4 | c1_1(a2323) | (~ndr1_0) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 0.91/1.10 tff(1920,plain,
% 0.91/1.10 (hskp19 | hskp4 | (~c0_1(a2323))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1919, 160, 907, 906, 1884])).
% 0.91/1.10 tff(1921,plain,
% 0.91/1.10 (~c0_1(a2323)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1920, 1874, 679])).
% 0.91/1.10 tff(1922,plain,
% 0.91/1.10 (~c2_1(a2342)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[16, 1903])).
% 0.91/1.10 tff(1923,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1924,plain,
% 0.91/1.10 (((~ndr1_0) | c2_1(a2342) | (~c3_1(a2342)) | (~c1_1(a2342)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323))) <=> (c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1925,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2342) | (~c3_1(a2342)) | (~c1_1(a2342)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1924])).
% 0.91/1.10 tff(1926,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2342) | (~c3_1(a2342)) | (~c1_1(a2342)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1925, 1923])).
% 0.91/1.10 tff(1927,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2342) | (~c3_1(a2342)) | (~c1_1(a2342)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1928,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2342) | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | (~c3_1(a2342)) | (~c1_1(a2342))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 0.91/1.10 tff(1929,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1928, 160, 1904, 908, 907, 1922, 906, 196, 1921, 1913])).
% 0.91/1.10 tff(1930,plain,(hskp4 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(1931,plain,
% 0.91/1.10 (hskp4),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1930, 35])).
% 0.91/1.10 tff(1932,plain,
% 0.91/1.10 (~c3_1(a2282)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[172, 1931])).
% 0.91/1.10 tff(1933,plain,
% 0.91/1.10 (c2_1(a2282)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[223, 1931])).
% 0.91/1.10 tff(1934,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1935,plain,
% 0.91/1.10 ((hskp30 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1936,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1935])).
% 0.91/1.10 tff(1937,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1936, 1934])).
% 0.91/1.10 tff(1938,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1939,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp30 | c0_1(a2302) | c3_1(a2282) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1938, 1937])).
% 0.91/1.10 tff(1940,plain,
% 0.91/1.10 (hskp30),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1939, 160, 898, 890, 1933, 882, 1932, 1616, 37])).
% 0.91/1.10 tff(1941,plain,
% 0.91/1.10 (c1_1(a2315)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[751, 1940])).
% 0.91/1.10 tff(1942,plain,
% 0.91/1.10 (~c0_1(a2282)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[178, 1931])).
% 0.91/1.10 tff(1943,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1944,plain,
% 0.91/1.10 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282))) <=> (c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1945,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1944])).
% 0.91/1.10 tff(1946,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1945, 1943])).
% 0.91/1.10 tff(1947,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2282) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1948,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282) | (~c2_1(a2282)) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 0.91/1.10 tff(1949,plain,
% 0.91/1.10 ((~c3_1(a2277)) | c1_1(a2282)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1948, 160, 908, 907, 1933, 1799, 906, 1942, 34, 196])).
% 0.91/1.10 tff(1950,plain,
% 0.91/1.10 (~c3_1(a2277)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1949, 37])).
% 0.91/1.10 tff(1951,plain,
% 0.91/1.10 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(1952,plain,
% 0.91/1.10 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[1951])).
% 0.91/1.10 tff(1953,plain,
% 0.91/1.10 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1954,plain,
% 0.91/1.10 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.91/1.10 inference(bind,[status(th)],[])).
% 0.91/1.10 tff(1955,plain,
% 0.91/1.10 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.91/1.10 inference(quant_intro,[status(thm)],[1954])).
% 0.91/1.10 tff(1956,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 0.91/1.10 tff(1957,plain,
% 0.91/1.10 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 0.91/1.10 tff(1958,plain,
% 0.91/1.10 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1957, 1953])).
% 0.91/1.10 tff(1959,plain,(
% 0.91/1.10 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.91/1.10 inference(skolemize,[status(sab)],[1958])).
% 0.91/1.10 tff(1960,plain,
% 0.91/1.10 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1959, 1952])).
% 0.91/1.10 tff(1961,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1962,plain,
% 0.91/1.10 ((hskp19 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1963,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1962])).
% 0.91/1.10 tff(1964,plain,
% 0.91/1.10 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1963, 1961])).
% 0.91/1.10 tff(1965,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1966,plain,
% 0.91/1.10 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 0.91/1.10 tff(1967,plain,
% 0.91/1.10 (hskp19 | (~c1_1(a2277)) | c3_1(a2277)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1966, 160, 898, 890, 882, 34, 1960])).
% 0.91/1.10 tff(1968,plain,
% 0.91/1.10 (hskp19),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1967, 1950, 1799])).
% 0.91/1.10 tff(1969,assumption,(~c0_1(a2277)), introduced(assumption)).
% 0.91/1.10 tff(1970,plain,
% 0.91/1.10 (~hskp1),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[344, 1969])).
% 0.91/1.10 tff(1971,assumption,(hskp28), introduced(assumption)).
% 0.91/1.10 tff(1972,plain,
% 0.91/1.10 (c0_1(a2278)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[573, 1971])).
% 0.91/1.10 tff(1973,plain,
% 0.91/1.10 (c3_1(a2278)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[557, 1971])).
% 0.91/1.10 tff(1974,plain,
% 0.91/1.10 (c1_1(a2278)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[565, 1971])).
% 0.91/1.10 tff(1975,assumption,(~c2_1(a2278)), introduced(assumption)).
% 0.91/1.10 tff(1976,assumption,(c0_1(a2323)), introduced(assumption)).
% 0.91/1.10 tff(1977,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1978,plain,
% 0.91/1.10 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c1_1(a2278)) | (~c0_1(a2278)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323))) <=> (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1979,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c1_1(a2278)) | (~c0_1(a2278)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[1978])).
% 0.91/1.10 tff(1980,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c1_1(a2278)) | (~c0_1(a2278)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.10 inference(transitivity,[status(thm)],[1979, 1977])).
% 0.91/1.10 tff(1981,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c1_1(a2278)) | (~c0_1(a2278)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(1982,plain,
% 0.91/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 0.91/1.10 tff(1983,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1982, 160, 613, 612, 611, 907, 906, 88, 1976, 1975])).
% 0.91/1.10 tff(1984,plain,(c2_1(a2278) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c0_1(a2323))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(1985,plain,
% 0.91/1.10 (~c0_1(a2323)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[1984, 1975, 612, 611, 613])).
% 0.91/1.10 tff(1986,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1987,plain,
% 0.91/1.10 (((~ndr1_0) | c2_1(a2278) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323))) <=> (c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(1988,plain,
% 0.91/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2278) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[1987])).
% 0.91/1.11 tff(1989,plain,
% 0.91/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2278) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 0.91/1.11 inference(transitivity,[status(thm)],[1988, 1986])).
% 0.91/1.11 tff(1990,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2278) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(1991,plain,
% 0.91/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c1_1(a2278)) | c2_1(a2278) | (~c3_1(a2278)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 0.91/1.11 tff(1992,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1991, 160, 612, 611, 908, 907, 906, 196, 1985, 1975])).
% 0.91/1.11 tff(1993,plain,(c2_1(a2278) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c0_1(a2278))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(1994,plain,
% 0.91/1.11 (c2_1(a2278)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1993, 1974, 1973, 1972])).
% 0.91/1.11 tff(1995,plain,
% 0.91/1.11 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(1996,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[1995])).
% 0.91/1.11 tff(1997,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(1998,plain,
% 0.91/1.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_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) | (~c0_1(U)) | (~c1_1(U)) | (~c2_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) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_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) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_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)) | hskp1) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp1))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_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)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(1999,plain,
% 0.91/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[1998])).
% 0.91/1.11 tff(2000,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)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 0.91/1.11 tff(2001,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2000, 1999])).
% 0.91/1.11 tff(2002,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2001, 1997])).
% 0.91/1.11 tff(2003,plain,(
% 0.91/1.11 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.91/1.11 inference(skolemize,[status(sab)],[2002])).
% 0.91/1.11 tff(2004,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2003, 1996])).
% 0.91/1.11 tff(2005,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2006,plain,
% 0.91/1.11 ((hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2007,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[2006])).
% 0.91/1.11 tff(2008,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[2007, 2005])).
% 0.91/1.11 tff(2009,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(2010,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2306))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 0.91/1.11 tff(2011,plain,
% 0.91/1.11 ((~c2_1(a2278)) | (~c0_1(a2306))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2010, 160, 36, 1972, 1974, 365, 363, 2004])).
% 0.91/1.11 tff(2012,plain,
% 0.91/1.11 (~c0_1(a2306)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2011, 1994])).
% 0.91/1.11 tff(2013,assumption,(c2_1(a2278)), introduced(assumption)).
% 0.91/1.11 tff(2014,plain,
% 0.91/1.11 (~c1_1(a2295)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1254, 676])).
% 0.91/1.11 tff(2015,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2016,plain,
% 0.91/1.11 ((hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2017,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[2016])).
% 0.91/1.11 tff(2018,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[2017, 2015])).
% 0.91/1.11 tff(2019,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(2020,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2295))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 0.91/1.11 tff(2021,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2020, 160, 36, 613, 612, 678, 2014, 677, 2004, 2013])).
% 0.91/1.11 tff(2022,plain,((~hskp12) | hskp1 | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(2023,plain,
% 0.91/1.11 (~hskp12),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2022, 1994, 1972, 1974, 36])).
% 0.91/1.11 tff(2024,plain,
% 0.91/1.11 (hskp13),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1247, 2023])).
% 0.91/1.11 tff(2025,plain,
% 0.91/1.11 (~c3_1(a2299)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1201, 2024])).
% 0.91/1.11 tff(2026,plain,
% 0.91/1.11 (~c1_1(a2299)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1215, 2024])).
% 0.91/1.11 tff(2027,plain,
% 0.91/1.11 (c2_1(a2299)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1209, 2024])).
% 0.91/1.11 tff(2028,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2029,plain,
% 0.91/1.11 ((hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306)) <=> (hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2030,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306)))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[2029])).
% 0.91/1.11 tff(2031,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306))),
% 0.91/1.11 inference(transitivity,[status(thm)],[2030, 2028])).
% 0.91/1.11 tff(2032,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2306) | c1_1(a2306) | c0_1(a2306))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(2033,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2306) | c2_1(a2306) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2306)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 0.91/1.11 tff(2034,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2033, 160, 36, 2027, 365, 364, 2026, 2025, 206, 2012])).
% 0.91/1.11 tff(2035,plain,((~hskp28) | hskp1 | c1_1(a2306) | c2_1(a2306) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(2036,plain,
% 0.91/1.11 (~hskp28),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2035, 365, 1970, 364, 363])).
% 0.91/1.11 tff(2037,plain,
% 0.91/1.11 (hskp4),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[909, 1970])).
% 0.91/1.11 tff(2038,plain,
% 0.91/1.11 (~c3_1(a2282)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[172, 2037])).
% 0.91/1.11 tff(2039,assumption,(~c1_1(a2277)), introduced(assumption)).
% 0.91/1.11 tff(2040,plain,
% 0.91/1.11 (c2_1(a2282)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[223, 2037])).
% 0.91/1.11 tff(2041,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2042,plain,
% 0.91/1.11 ((hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2043,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[2042])).
% 0.91/1.11 tff(2044,plain,
% 0.91/1.11 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[2043, 2041])).
% 0.91/1.11 tff(2045,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(2046,plain,
% 0.91/1.11 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2277) | c1_1(a2277) | c3_1(a2282) | c2_1(a2277) | (~ndr1_0) | c1_1(a2282) | (~c2_1(a2282))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2045, 2044])).
% 0.91/1.11 tff(2047,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2046, 160, 1970, 2040, 1969, 2039, 2038, 34, 206, 37])).
% 0.91/1.11 tff(2048,plain,(c1_1(a2282) | c0_1(a2277) | c1_1(a2277) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(2049,plain,
% 0.91/1.11 (c1_1(a2282)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2048, 2039, 1969, 34])).
% 0.91/1.11 tff(2050,plain,
% 0.91/1.11 (~c0_1(a2282)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[178, 2037])).
% 0.91/1.11 tff(2051,plain,
% 0.91/1.11 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(2052,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[2051])).
% 0.91/1.11 tff(2053,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2054,plain,
% 0.91/1.11 (^[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) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(2055,plain,
% 0.91/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[2054])).
% 0.91/1.11 tff(2056,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 0.91/1.11 tff(2057,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 0.91/1.11 tff(2058,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2057, 2053])).
% 0.91/1.11 tff(2059,plain,(
% 0.91/1.11 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.91/1.11 inference(skolemize,[status(sab)],[2058])).
% 0.91/1.11 tff(2060,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2059, 2052])).
% 0.91/1.11 tff(2061,plain,
% 0.91/1.11 (~hskp10),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1124, 2049, 2050, 2038, 2040])).
% 0.91/1.11 tff(2062,plain,
% 0.91/1.11 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2063,plain,
% 0.91/1.11 ((hskp10 | hskp6 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277)) <=> (hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2064,plain,
% 0.91/1.11 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277)))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[2063])).
% 0.91/1.11 tff(2065,plain,
% 0.91/1.11 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 0.91/1.11 inference(transitivity,[status(thm)],[2064, 2062])).
% 0.91/1.11 tff(2066,plain,
% 0.91/1.11 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp6 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(2067,plain,
% 0.91/1.11 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp6 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 0.91/1.11 tff(2068,plain,
% 0.91/1.11 (hskp10 | hskp6 | c0_1(a2277) | c3_1(a2277)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2067, 160, 34, 1177])).
% 0.91/1.11 tff(2069,plain,
% 0.91/1.11 (c3_1(a2277)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2068, 1061, 1969, 2061])).
% 0.91/1.11 tff(2070,plain,
% 0.91/1.11 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2071,plain,
% 0.91/1.11 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a2277) | c0_1(a2277) | (~c3_1(a2277))) <=> (hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2072,plain,
% 0.91/1.11 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2277) | c0_1(a2277) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[2071])).
% 0.91/1.11 tff(2073,plain,
% 0.91/1.11 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2277) | c0_1(a2277) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277)))),
% 0.91/1.11 inference(transitivity,[status(thm)],[2072, 2070])).
% 0.91/1.11 tff(2074,plain,
% 0.91/1.11 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2277) | c0_1(a2277) | (~c3_1(a2277)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(2075,plain,
% 0.91/1.11 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a2277) | c1_1(a2277) | (~ndr1_0) | (~c3_1(a2277))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 0.91/1.11 tff(2076,plain,
% 0.91/1.11 (hskp7 | hskp6 | c1_1(a2277) | (~c3_1(a2277))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2075, 160, 1969, 1039])).
% 0.91/1.11 tff(2077,plain,
% 0.91/1.11 (hskp7),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[2076, 2069, 2039, 1061])).
% 0.91/1.11 tff(2078,plain,
% 0.91/1.11 (~c2_1(a2286)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[957, 2077])).
% 0.91/1.11 tff(2079,plain,
% 0.91/1.11 (~c0_1(a2286)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[963, 2077])).
% 0.91/1.11 tff(2080,plain,
% 0.91/1.11 (c3_1(a2286)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[1385, 160, 2061, 1061, 2079, 2078, 1177])).
% 0.91/1.11 tff(2081,plain,
% 0.91/1.11 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(2082,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[2081])).
% 0.91/1.11 tff(2083,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(2084,plain,
% 0.91/1.11 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.91/1.11 inference(bind,[status(th)],[])).
% 0.91/1.11 tff(2085,plain,
% 0.91/1.11 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.91/1.11 inference(quant_intro,[status(thm)],[2084])).
% 0.91/1.11 tff(2086,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 0.91/1.11 tff(2087,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 0.91/1.11 tff(2088,plain,
% 0.91/1.11 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2087, 2083])).
% 0.91/1.12 tff(2089,plain,(
% 0.91/1.12 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.91/1.12 inference(skolemize,[status(sab)],[2088])).
% 0.91/1.12 tff(2090,plain,
% 0.91/1.12 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2089, 2082])).
% 0.91/1.12 tff(2091,plain,
% 0.91/1.12 (c1_1(a2286)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[979, 2077])).
% 0.91/1.12 tff(2092,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2093,plain,
% 0.91/1.12 ((hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | c0_1(a2323) | (~c2_1(a2323))) <=> (hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2094,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | c0_1(a2323) | (~c2_1(a2323)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323)))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[2093])).
% 0.91/1.12 tff(2095,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | c0_1(a2323) | (~c2_1(a2323)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323))),
% 0.91/1.12 inference(transitivity,[status(thm)],[2094, 2092])).
% 0.91/1.12 tff(2096,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2323) | c0_1(a2323) | (~c2_1(a2323)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(2097,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2323) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2323)) | c0_1(a2323)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 0.91/1.12 tff(2098,plain,
% 0.91/1.12 (c0_1(a2323)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2097, 160, 1970, 908, 2091, 906, 2078, 2090, 2080])).
% 0.91/1.12 tff(2099,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2100,plain,
% 0.91/1.12 ((hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2101,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[2100])).
% 0.91/1.12 tff(2102,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[2101, 2099])).
% 0.91/1.12 tff(2103,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(2104,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2286) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2103, 2102])).
% 0.91/1.12 tff(2105,plain,
% 0.91/1.12 (hskp28),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2104, 160, 2091, 1969, 2039, 2078, 34, 421, 2080])).
% 0.91/1.12 tff(2106,plain,
% 0.91/1.12 (c3_1(a2278)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[557, 2105])).
% 0.91/1.12 tff(2107,plain,
% 0.91/1.12 (c1_1(a2278)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[565, 2105])).
% 0.91/1.12 tff(2108,plain,
% 0.91/1.12 (c0_1(a2278)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[573, 2105])).
% 0.91/1.12 tff(2109,plain,
% 0.91/1.12 (c2_1(a2278)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1984, 2108, 2107, 2106, 2098])).
% 0.91/1.12 tff(2110,plain,
% 0.91/1.12 (~hskp12),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2022, 2108, 1970, 2107, 2109])).
% 0.91/1.12 tff(2111,plain,
% 0.91/1.12 (hskp13),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1247, 2110])).
% 0.91/1.12 tff(2112,plain,
% 0.91/1.12 (~c3_1(a2299)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1201, 2111])).
% 0.91/1.12 tff(2113,plain,
% 0.91/1.12 (~c1_1(a2299)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1215, 2111])).
% 0.91/1.12 tff(2114,plain,
% 0.91/1.12 (c2_1(a2299)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1209, 2111])).
% 0.91/1.12 tff(2115,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2116,plain,
% 0.91/1.12 ((hskp12 | (~ndr1_0) | c3_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)) | c1_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299))) <=> (hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2117,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)) | c1_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[2116])).
% 0.91/1.12 tff(2118,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)) | c1_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[2117, 2115])).
% 0.91/1.12 tff(2119,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)) | c1_1(a2299) | (~c0_1(a2299)) | (~c2_1(a2299)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(2120,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | (~c0_1(a2299))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 0.91/1.12 tff(2121,plain,
% 0.91/1.12 (~c0_1(a2299)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2120, 160, 2110, 2114, 2113, 2112, 2060])).
% 0.91/1.12 tff(2122,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2123,plain,
% 0.91/1.12 ((hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299))) <=> (hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2124,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299)))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[2123])).
% 0.91/1.12 tff(2125,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299))),
% 0.91/1.12 inference(transitivity,[status(thm)],[2124, 2122])).
% 0.91/1.12 tff(2126,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(2127,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | (~c2_1(a2299)) | c0_1(a2299)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 0.91/1.12 tff(2128,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2127, 160, 1970, 2114, 2091, 2113, 2078, 2090, 2080, 2121])).
% 0.91/1.12 tff(2129,plain,(hskp6 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.12 tff(2130,plain,
% 0.91/1.12 (hskp6),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2129, 2039, 1969, 34])).
% 0.91/1.12 tff(2131,plain,
% 0.91/1.12 (~c3_1(a2285)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[394, 2130])).
% 0.91/1.12 tff(2132,plain,
% 0.91/1.12 (c1_1(a2285)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[373, 2130])).
% 0.91/1.12 tff(2133,plain,
% 0.91/1.12 (c0_1(a2285)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[381, 2130])).
% 0.91/1.12 tff(2134,plain,
% 0.91/1.12 (~c2_1(a2285)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1194, 160, 2133, 2132, 2040, 2131, 2050, 675, 2049])).
% 0.91/1.12 tff(2135,plain,
% 0.91/1.12 (hskp17),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1772, 160, 2132, 2040, 2131, 2050, 1440, 2049, 2134])).
% 0.91/1.12 tff(2136,plain,
% 0.91/1.12 (~c3_1(a2306)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[265, 2135])).
% 0.91/1.12 tff(2137,plain,
% 0.91/1.12 (~c1_1(a2306)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[242, 2135])).
% 0.91/1.12 tff(2138,plain,
% 0.91/1.12 (~c2_1(a2306)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[236, 2135])).
% 0.91/1.12 tff(2139,plain,
% 0.91/1.12 (hskp6 | c2_1(a2306) | c0_1(a2306)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1183, 160, 2061, 363, 1177])).
% 0.91/1.12 tff(2140,plain,
% 0.91/1.12 (c0_1(a2306)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2139, 1061, 364])).
% 0.91/1.12 tff(2141,plain,
% 0.91/1.12 (~c2_1(a2278)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2010, 160, 1970, 2108, 2107, 365, 363, 2004, 2140])).
% 0.91/1.12 tff(2142,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1982, 160, 2108, 2107, 2106, 907, 906, 88, 2098, 2141])).
% 0.91/1.12 tff(2143,plain,(hskp6 | c1_1(a2306) | c3_1(a2306) | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.12 tff(2144,plain,
% 0.91/1.12 (hskp6),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2143, 365, 363, 1969, 2039, 34, 364])).
% 0.91/1.12 tff(2145,plain,
% 0.91/1.12 (~c3_1(a2285)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[394, 2144])).
% 0.91/1.12 tff(2146,plain,
% 0.91/1.12 (c1_1(a2285)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[373, 2144])).
% 0.91/1.12 tff(2147,plain,
% 0.91/1.12 (c0_1(a2285)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[381, 2144])).
% 0.91/1.12 tff(2148,plain,
% 0.91/1.12 (~c2_1(a2285)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1194, 160, 2147, 2146, 2040, 2145, 2050, 675, 2049])).
% 0.91/1.12 tff(2149,plain,
% 0.91/1.12 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.91/1.12 inference(bind,[status(th)],[])).
% 0.91/1.12 tff(2150,plain,
% 0.91/1.12 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.91/1.12 inference(quant_intro,[status(thm)],[2149])).
% 0.91/1.12 tff(2151,plain,
% 0.91/1.12 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2152,plain,
% 0.91/1.12 (^[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(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.91/1.12 inference(bind,[status(th)],[])).
% 0.91/1.12 tff(2153,plain,
% 0.91/1.12 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.91/1.12 inference(quant_intro,[status(thm)],[2152])).
% 0.91/1.12 tff(2154,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.91/1.12 tff(2155,plain,
% 0.91/1.12 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 0.91/1.12 tff(2156,plain,
% 0.91/1.12 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2155, 2151])).
% 0.91/1.12 tff(2157,plain,(
% 0.91/1.12 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.91/1.12 inference(skolemize,[status(sab)],[2156])).
% 0.91/1.12 tff(2158,plain,
% 0.91/1.12 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2157, 2150])).
% 0.91/1.12 tff(2159,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2160,plain,
% 0.91/1.12 ((hskp11 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282))) <=> (hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2161,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[2160])).
% 0.91/1.12 tff(2162,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[2161, 2159])).
% 0.91/1.12 tff(2163,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c0_1(a2285)) | c0_1(a2282) | c3_1(a2282) | (~c1_1(a2282)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(2164,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp11 | c3_1(a2285) | c0_1(a2282) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | c2_1(a2285) | (~c0_1(a2285))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 0.91/1.12 tff(2165,plain,
% 0.91/1.12 (hskp11),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2164, 160, 2147, 2145, 2050, 2038, 2158, 2049, 2148])).
% 0.91/1.12 tff(2166,plain,
% 0.91/1.12 (~c1_1(a2294)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[599, 2165])).
% 0.91/1.12 tff(2167,plain,
% 0.91/1.12 (c0_1(a2294)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[609, 2165])).
% 0.91/1.12 tff(2168,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2169,plain,
% 0.91/1.12 ((hskp19 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2170,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[2169])).
% 0.91/1.12 tff(2171,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.12 inference(transitivity,[status(thm)],[2170, 2168])).
% 0.91/1.12 tff(2172,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2285) | c3_1(a2285) | (~c1_1(a2285)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(2173,plain,
% 0.91/1.12 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c3_1(a2285) | (~ndr1_0) | (~c1_1(a2285)) | c2_1(a2285) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 0.91/1.12 tff(2174,plain,
% 0.91/1.12 (hskp19),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2173, 160, 898, 890, 2146, 882, 2145, 1960, 2148])).
% 0.91/1.12 tff(2175,plain,
% 0.91/1.12 (~c3_1(a2316)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1850, 2174])).
% 0.91/1.12 tff(2176,plain,
% 0.91/1.12 (~c2_1(a2316)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1856, 2174])).
% 0.91/1.12 tff(2177,plain,
% 0.91/1.12 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2178,plain,
% 0.91/1.12 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2179,plain,
% 0.91/1.12 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0)))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[2178])).
% 0.91/1.12 tff(2180,plain,
% 0.91/1.12 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0))),
% 0.91/1.12 inference(transitivity,[status(thm)],[2179, 2177])).
% 0.91/1.12 tff(2181,plain,
% 0.91/1.12 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 0.91/1.12 inference(quant_inst,[status(thm)],[])).
% 0.91/1.12 tff(2182,plain,
% 0.91/1.12 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | (~ndr1_0)),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 0.91/1.12 tff(2183,plain,
% 0.91/1.12 (hskp3 | hskp2 | c0_1(a2277) | c1_1(a2277)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2182, 160, 34, 481])).
% 0.91/1.12 tff(2184,plain,
% 0.91/1.12 (hskp2),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[2183, 422, 1969, 2039])).
% 0.91/1.12 tff(2185,plain,
% 0.91/1.12 (~c3_1(a2279)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[488, 2184])).
% 0.91/1.12 tff(2186,plain,
% 0.91/1.12 (~c2_1(a2279)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[494, 2184])).
% 0.91/1.12 tff(2187,plain,
% 0.91/1.12 (c0_1(a2279)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[502, 2184])).
% 0.91/1.12 tff(2188,assumption,(~c3_1(a2279)), introduced(assumption)).
% 0.91/1.12 tff(2189,assumption,(~c2_1(a2279)), introduced(assumption)).
% 0.91/1.12 tff(2190,plain,
% 0.91/1.12 (~hskp13),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1229, 1165, 366])).
% 0.91/1.12 tff(2191,plain,
% 0.91/1.12 (hskp12),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1247, 2190])).
% 0.91/1.12 tff(2192,plain,
% 0.91/1.12 (~c3_1(a2295)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[644, 2191])).
% 0.91/1.12 tff(2193,plain,
% 0.91/1.12 (~c1_1(a2295)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[1254, 2191])).
% 0.91/1.12 tff(2194,assumption,(c0_1(a2279)), introduced(assumption)).
% 0.91/1.12 tff(2195,plain,
% 0.91/1.12 (c0_1(a2295)),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[652, 2191])).
% 0.91/1.12 tff(2196,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2197,plain,
% 0.91/1.12 ((hskp23 | (~ndr1_0) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295)))),
% 0.91/1.12 inference(rewrite,[status(thm)],[])).
% 0.91/1.12 tff(2198,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295))))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[2197])).
% 0.91/1.12 tff(2199,plain,
% 0.91/1.12 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[2198, 2196])).
% 0.91/1.13 tff(2200,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(2201,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c0_1(a2295))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2200, 2199])).
% 0.91/1.13 tff(2202,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2201, 160, 1165, 2195, 2194, 2193, 2192, 2189, 2188, 260])).
% 0.91/1.13 tff(2203,plain,(hskp23 | (~c0_1(a2279)) | c2_1(a2279) | c3_1(a2279) | (~hskp6)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(2204,plain,
% 0.91/1.13 (hskp23),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2203, 2187, 2186, 2185, 2144])).
% 0.91/1.13 tff(2205,plain,
% 0.91/1.13 (~c2_1(a2327)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[278, 2204])).
% 0.91/1.13 tff(2206,plain,
% 0.91/1.13 (~c0_1(a2327)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[299, 2204])).
% 0.91/1.13 tff(2207,plain,
% 0.91/1.13 (c3_1(a2327)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[286, 2204])).
% 0.91/1.13 tff(2208,plain,
% 0.91/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2209,plain,
% 0.91/1.13 (((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2316) | c2_1(a2316) | c0_1(a2316)) <=> (c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2210,plain,
% 0.91/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2316) | c2_1(a2316) | c0_1(a2316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[2209])).
% 0.91/1.13 tff(2211,plain,
% 0.91/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2316) | c2_1(a2316) | c0_1(a2316))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[2210, 2208])).
% 0.91/1.13 tff(2212,plain,
% 0.91/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2316) | c2_1(a2316) | c0_1(a2316))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(2213,plain,
% 0.91/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c2_1(a2316) | c3_1(a2316) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c0_1(a2316) | (~c3_1(a2327))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 0.91/1.13 tff(2214,plain,
% 0.91/1.13 (c0_1(a2316)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2213, 160, 2207, 2040, 2206, 2205, 2176, 2175, 2050, 1162, 2049])).
% 0.91/1.13 tff(2215,plain,
% 0.91/1.13 (c0_1(a2306)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1274, 160, 2207, 2040, 2206, 2205, 364, 363, 2050, 1162, 2049])).
% 0.91/1.13 tff(2216,plain,
% 0.91/1.13 (hskp8),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1292, 2215])).
% 0.91/1.13 tff(2217,plain,
% 0.91/1.13 (c2_1(a2287)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1308, 2216])).
% 0.91/1.13 tff(2218,plain,
% 0.91/1.13 (c0_1(a2287)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1300, 2216])).
% 0.91/1.13 tff(2219,plain,
% 0.91/1.13 (c1_1(a2316)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1864, 2174])).
% 0.91/1.13 tff(2220,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2221,plain,
% 0.91/1.13 ((hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2316) | (~c1_1(a2316)) | (~c0_1(a2316))) <=> (hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2222,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2316) | (~c1_1(a2316)) | (~c0_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[2221])).
% 0.91/1.13 tff(2223,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2316) | (~c1_1(a2316)) | (~c0_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[2222, 2220])).
% 0.91/1.13 tff(2224,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c3_1(a2316) | (~c1_1(a2316)) | (~c0_1(a2316)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(2225,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a2316) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c1_1(a2316)) | (~c0_1(a2316))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2224, 2223])).
% 0.91/1.13 tff(2226,plain,
% 0.91/1.13 (~c3_1(a2287)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2225, 160, 422, 2219, 2218, 2217, 2175, 1331, 2214])).
% 0.91/1.13 tff(2227,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2228,plain,
% 0.91/1.13 ((hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2229,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[2228])).
% 0.91/1.13 tff(2230,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[2229, 2227])).
% 0.91/1.13 tff(2231,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(2232,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2327)) | (~c1_1(a2327))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 0.91/1.13 tff(2233,plain,
% 0.91/1.13 (~c1_1(a2327)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2232, 160, 35, 2207, 1969, 2039, 2205, 34, 421])).
% 0.91/1.13 tff(2234,plain,
% 0.91/1.13 (((~hskp8) | (~c1_1(a2287))) <=> ((~hskp8) | (~c1_1(a2287)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2235,plain,
% 0.91/1.13 (((~c1_1(a2287)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a2287)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2236,axiom,((~c1_1(a2287)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.91/1.13 tff(2237,plain,
% 0.91/1.13 ((~hskp8) | (~c1_1(a2287))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 0.91/1.13 tff(2238,plain,
% 0.91/1.13 ((~hskp8) | (~c1_1(a2287))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2237, 2234])).
% 0.91/1.13 tff(2239,plain,
% 0.91/1.13 (~c1_1(a2287)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2238, 2216])).
% 0.91/1.13 tff(2240,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2241,plain,
% 0.91/1.13 ((hskp1 | (~ndr1_0) | c1_1(a2287) | c3_1(a2287) | (~c2_1(a2287)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2242,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2287) | c3_1(a2287) | (~c2_1(a2287)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327)))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[2241])).
% 0.91/1.13 tff(2243,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2287) | c3_1(a2287) | (~c2_1(a2287)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327))),
% 0.91/1.13 inference(transitivity,[status(thm)],[2242, 2240])).
% 0.91/1.13 tff(2244,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2287) | c3_1(a2287) | (~c2_1(a2287)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(2245,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2327) | c2_1(a2327) | c1_1(a2287) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | c1_1(a2327)),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 0.91/1.13 tff(2246,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2245, 160, 1970, 2217, 2206, 2205, 2239, 206, 2233, 2226])).
% 0.91/1.13 tff(2247,plain,(hskp3 | c1_1(a2306) | c3_1(a2306) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(2248,plain,
% 0.91/1.13 (hskp3),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2247, 35, 363, 365, 1969, 2039, 34, 364])).
% 0.91/1.13 tff(2249,plain,
% 0.91/1.13 (~c2_1(a2280)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[526, 2248])).
% 0.91/1.13 tff(2250,plain,
% 0.91/1.13 (c3_1(a2280)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[534, 2248])).
% 0.91/1.13 tff(2251,plain,
% 0.91/1.13 (c1_1(a2280)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[542, 2248])).
% 0.91/1.13 tff(2252,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2253,plain,
% 0.91/1.13 ((hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277)) <=> (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2254,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[2253])).
% 0.91/1.13 tff(2255,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[2254, 2252])).
% 0.91/1.13 tff(2256,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c2_1(a2277) | c1_1(a2277) | c0_1(a2277))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(2257,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2280) | c2_1(a2277) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 0.91/1.13 tff(2258,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2257, 160, 35, 2251, 2250, 1969, 2039, 2249, 34, 421])).
% 0.91/1.13 tff(2259,plain,(hskp28 | c0_1(a2277) | c1_1(a2277) | c2_1(a2277) | c3_1(a2306) | c1_1(a2306) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(2260,plain,
% 0.91/1.13 (hskp28),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2259, 365, 2039, 34, 363, 1969, 364])).
% 0.91/1.13 tff(2261,plain,
% 0.91/1.13 (c3_1(a2278)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[557, 2260])).
% 0.91/1.13 tff(2262,plain,
% 0.91/1.13 (c1_1(a2278)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[565, 2260])).
% 0.91/1.13 tff(2263,plain,
% 0.91/1.13 (c0_1(a2278)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[573, 2260])).
% 0.91/1.13 tff(2264,plain,
% 0.91/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2265,plain,
% 0.91/1.13 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294))) <=> (c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2266,plain,
% 0.91/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[2265])).
% 0.91/1.13 tff(2267,plain,
% 0.91/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[2266, 2264])).
% 0.91/1.13 tff(2268,plain,
% 0.91/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2294) | (~c3_1(a2294)) | (~c0_1(a2294)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(2269,plain,
% 0.91/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2294)) | (~c0_1(a2294))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 0.91/1.13 tff(2270,plain,
% 0.91/1.13 (~c3_1(a2294)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2269, 160, 2263, 2262, 2261, 2167, 2147, 2146, 2166, 88, 2148])).
% 0.91/1.13 tff(2271,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2272,plain,
% 0.91/1.13 ((hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294))) <=> (hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2273,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[2272])).
% 0.91/1.13 tff(2274,plain,
% 0.91/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[2273, 2271])).
% 0.91/1.13 tff(2275,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2294) | c3_1(a2294) | (~c0_1(a2294)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(2276,plain,
% 0.91/1.13 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2294) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c3_1(a2294) | (~c0_1(a2294))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 0.91/1.13 tff(2277,plain,
% 0.91/1.13 (~c2_1(a2278)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2276, 160, 1970, 2263, 2262, 2167, 2166, 2004, 2270])).
% 0.91/1.13 tff(2278,plain,
% 0.91/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2279,plain,
% 0.91/1.13 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323))) <=> (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2280,plain,
% 0.91/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 0.91/1.13 inference(monotonicity,[status(thm)],[2279])).
% 0.91/1.13 tff(2281,plain,
% 0.91/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.13 inference(transitivity,[status(thm)],[2280, 2278])).
% 0.91/1.13 tff(2282,plain,
% 0.91/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2285) | (~c1_1(a2285)) | (~c0_1(a2285)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
% 0.91/1.13 tff(2283,plain,
% 0.91/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2285)) | c2_1(a2285) | (~c0_1(a2285)) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 0.91/1.13 tff(2284,plain,
% 0.91/1.13 (~c0_1(a2323)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2283, 160, 2263, 2262, 2261, 907, 2147, 2146, 906, 88, 2148])).
% 0.91/1.13 tff(2285,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1991, 160, 2262, 2261, 908, 907, 906, 196, 2284, 2277])).
% 0.91/1.13 tff(2286,plain,(c1_1(a2306) | c1_1(a2277) | c2_1(a2277) | c3_1(a2306) | c0_1(a2277) | c2_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(2287,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2286, 2138, 2137, 34, 2136, 1969, 2039])).
% 0.91/1.13 tff(2288,plain,(c1_1(a2277) | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(2289,plain,
% 0.91/1.13 (c1_1(a2277)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2288, 1969, 34])).
% 0.91/1.13 tff(2290,plain,
% 0.91/1.13 ((~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1948, 160, 908, 907, 2040, 906, 2050, 34, 196])).
% 0.91/1.13 tff(2291,plain,
% 0.91/1.13 (~c3_1(a2277)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[2290, 37, 2289])).
% 0.91/1.13 tff(2292,plain,
% 0.91/1.13 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2293,plain,
% 0.91/1.13 ((hskp28 | hskp9 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277)) <=> (hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
% 0.91/1.13 tff(2294,plain,
% 0.91/1.13 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277)))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2293])).
% 0.91/1.14 tff(2295,plain,
% 0.91/1.14 (((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))) <=> ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2294, 2292])).
% 0.91/1.14 tff(2296,plain,
% 0.91/1.14 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp9 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | c3_1(a2277))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2297,plain,
% 0.91/1.14 ((~![U: $i] : (hskp28 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp9 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | c3_1(a2277)),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2296, 2295])).
% 0.91/1.14 tff(2298,plain,
% 0.91/1.14 (hskp28 | hskp9 | c0_1(a2277) | c3_1(a2277)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2297, 160, 34, 951])).
% 0.91/1.14 tff(2299,plain,
% 0.91/1.14 (hskp9),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2298, 2291, 1969, 35])).
% 0.91/1.14 tff(2300,plain,
% 0.91/1.14 (~c2_1(a2291)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[919, 2299])).
% 0.91/1.14 tff(2301,plain,
% 0.91/1.14 (~c1_1(a2291)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[925, 2299])).
% 0.91/1.14 tff(2302,plain,
% 0.91/1.14 (~c0_1(a2291)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[931, 2299])).
% 0.91/1.14 tff(2303,plain,
% 0.91/1.14 ($false),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[938, 160, 1970, 2040, 2302, 2301, 2300, 2038, 206, 37])).
% 0.91/1.14 tff(2304,plain,(c1_1(a2282) | c0_1(a2277) | hskp28 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.14 tff(2305,plain,
% 0.91/1.14 (c1_1(a2282)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2304, 2036, 1969, 34])).
% 0.91/1.14 tff(2306,plain,
% 0.91/1.14 (^[U: $i] : refl((hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.91/1.14 inference(bind,[status(th)],[])).
% 0.91/1.14 tff(2307,plain,
% 0.91/1.14 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.91/1.14 inference(quant_intro,[status(thm)],[2306])).
% 0.91/1.14 tff(2308,plain,
% 0.91/1.14 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2309,plain,
% 0.91/1.14 (^[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) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.91/1.14 inference(bind,[status(th)],[])).
% 0.91/1.14 tff(2310,plain,
% 0.91/1.14 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp8) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.91/1.14 inference(quant_intro,[status(thm)],[2309])).
% 0.91/1.14 tff(2311,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.91/1.14 tff(2312,plain,
% 0.91/1.14 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 0.91/1.14 tff(2313,plain,
% 0.91/1.14 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2312, 2308])).
% 0.91/1.14 tff(2314,plain,(
% 0.91/1.14 ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.91/1.14 inference(skolemize,[status(sab)],[2313])).
% 0.91/1.14 tff(2315,plain,
% 0.91/1.14 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2314, 2307])).
% 0.91/1.14 tff(2316,plain,
% 0.91/1.14 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2317,plain,
% 0.91/1.14 ((hskp28 | hskp8 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | (~c1_1(a2277))) <=> (hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2318,plain,
% 0.91/1.14 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2317])).
% 0.91/1.14 tff(2319,plain,
% 0.91/1.14 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2318, 2316])).
% 0.91/1.14 tff(2320,plain,
% 0.91/1.14 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | c2_1(a2277) | c0_1(a2277) | (~c1_1(a2277)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2321,plain,
% 0.91/1.14 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp28 | hskp8 | c0_1(a2277) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 0.91/1.14 tff(2322,plain,
% 0.91/1.14 (hskp28 | hskp8 | c0_1(a2277) | (~c1_1(a2277))),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2321, 160, 34, 2315])).
% 0.91/1.14 tff(2323,plain,
% 0.91/1.14 (hskp8),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2322, 2036, 1969, 2289])).
% 0.91/1.14 tff(2324,plain,
% 0.91/1.14 (c2_1(a2287)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1308, 2323])).
% 0.91/1.14 tff(2325,plain,
% 0.91/1.14 (c0_1(a2287)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1300, 2323])).
% 0.91/1.14 tff(2326,plain,
% 0.91/1.14 (c3_1(a2287)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1320, 2325, 2324, 2040, 2050, 2038, 2305])).
% 0.91/1.14 tff(2327,plain,
% 0.91/1.14 (c1_1(a2282)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2304, 35, 1969, 34])).
% 0.91/1.14 tff(2328,plain,
% 0.91/1.14 (~hskp10),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1124, 2327, 2050, 2038, 2040])).
% 0.91/1.14 tff(2329,plain,
% 0.91/1.14 (c3_1(a2277)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2068, 2328, 1969, 1061])).
% 0.91/1.14 tff(2330,plain,
% 0.91/1.14 (c0_1(a2306)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1184, 2328, 364, 1061])).
% 0.91/1.14 tff(2331,plain,
% 0.91/1.14 (hskp23),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1166, 2330])).
% 0.91/1.14 tff(2332,plain,
% 0.91/1.14 (~c2_1(a2327)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[278, 2331])).
% 0.91/1.14 tff(2333,plain,
% 0.91/1.14 (~c0_1(a2327)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[299, 2331])).
% 0.91/1.14 tff(2334,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2335,plain,
% 0.91/1.14 ((hskp28 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2336,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327)))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2335])).
% 0.91/1.14 tff(2337,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2336, 2334])).
% 0.91/1.14 tff(2338,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2339,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c0_1(a2327) | c2_1(a2327) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2327)),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 0.91/1.14 tff(2340,plain,
% 0.91/1.14 (c1_1(a2327)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2339, 160, 35, 2289, 2333, 2332, 34, 421, 2329])).
% 0.91/1.14 tff(2341,plain,
% 0.91/1.14 (~hskp16),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1341, 2328, 1061])).
% 0.91/1.14 tff(2342,plain,
% 0.91/1.14 (hskp26),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1028, 2341, 35])).
% 0.91/1.14 tff(2343,plain,
% 0.91/1.14 (~c1_1(a2345)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1045, 2342])).
% 0.91/1.14 tff(2344,plain,
% 0.91/1.14 (~c0_1(a2345)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1051, 2342])).
% 0.91/1.14 tff(2345,plain,
% 0.91/1.14 (c3_1(a2327)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[286, 2331])).
% 0.91/1.14 tff(2346,plain,
% 0.91/1.14 (c3_1(a2345)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1059, 2342])).
% 0.91/1.14 tff(2347,plain,
% 0.91/1.14 (~c2_1(a2345)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1350, 160, 2346, 2345, 2344, 2343, 2332, 196, 2340])).
% 0.91/1.14 tff(2348,plain,
% 0.91/1.14 ($false),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1357, 160, 35, 2345, 2344, 2343, 2332, 421, 2340, 2347])).
% 0.91/1.14 tff(2349,plain,(hskp28 | hskp6 | c2_1(a2277) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.14 tff(2350,plain,
% 0.91/1.14 (hskp6),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2349, 2036, 34, 365, 364, 363, 1969])).
% 0.91/1.14 tff(2351,plain,
% 0.91/1.14 (~c3_1(a2285)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[394, 2350])).
% 0.91/1.14 tff(2352,plain,
% 0.91/1.14 (c1_1(a2285)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[373, 2350])).
% 0.91/1.14 tff(2353,plain,
% 0.91/1.14 (c0_1(a2285)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[381, 2350])).
% 0.91/1.14 tff(2354,plain,
% 0.91/1.14 (hskp3 | (~c3_1(a2287))),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1397, 160, 2325, 2324, 2353, 2352, 2351, 1331])).
% 0.91/1.14 tff(2355,plain,
% 0.91/1.14 (hskp3),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2354, 2326])).
% 0.91/1.14 tff(2356,plain,
% 0.91/1.14 (~c2_1(a2280)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[526, 2355])).
% 0.91/1.14 tff(2357,plain,
% 0.91/1.14 (c3_1(a2280)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[534, 2355])).
% 0.91/1.14 tff(2358,plain,
% 0.91/1.14 (c1_1(a2280)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[542, 2355])).
% 0.91/1.14 tff(2359,plain,
% 0.91/1.14 (c1_1(a2302)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1407, 160, 908, 907, 898, 2358, 2357, 906, 882, 2356, 196])).
% 0.91/1.14 tff(2360,plain,
% 0.91/1.14 (c0_1(a2306)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[549, 160, 2036, 2358, 2357, 365, 364, 2356, 421])).
% 0.91/1.14 tff(2361,plain,
% 0.91/1.14 (hskp23),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1166, 2360])).
% 0.91/1.14 tff(2362,plain,
% 0.91/1.14 (~c2_1(a2327)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[278, 2361])).
% 0.91/1.14 tff(2363,plain,
% 0.91/1.14 (~c0_1(a2327)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[299, 2361])).
% 0.91/1.14 tff(2364,plain,
% 0.91/1.14 (c1_1(a2327)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1414, 160, 2036, 2358, 2357, 2363, 2362, 2356, 421])).
% 0.91/1.14 tff(2365,plain,
% 0.91/1.14 (c3_1(a2327)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[286, 2361])).
% 0.91/1.14 tff(2366,plain,
% 0.91/1.14 (~hskp26),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1359, 2036, 2365, 2362, 2364])).
% 0.91/1.14 tff(2367,plain,
% 0.91/1.14 (hskp16),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1028, 2366, 2036])).
% 0.91/1.14 tff(2368,plain,
% 0.91/1.14 (~c3_1(a2304)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[995, 2367])).
% 0.91/1.14 tff(2369,plain,
% 0.91/1.14 (~c2_1(a2304)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1001, 2367])).
% 0.91/1.14 tff(2370,plain,
% 0.91/1.14 (~c0_1(a2304)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1007, 2367])).
% 0.91/1.14 tff(2371,plain,
% 0.91/1.14 ($false),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1426, 160, 2365, 898, 2363, 2362, 2370, 2369, 2368, 882, 1162, 2359])).
% 0.91/1.14 tff(2372,plain,(c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.14 tff(2373,plain,
% 0.91/1.14 (c1_1(a2306)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2372, 364, 363, 34, 1969])).
% 0.91/1.14 tff(2374,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2375,plain,
% 0.91/1.14 ((hskp19 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2376,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2375])).
% 0.91/1.14 tff(2377,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2376, 2374])).
% 0.91/1.14 tff(2378,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c1_1(a2306)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2379,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | (~c1_1(a2306)) | c2_1(a2306) | c3_1(a2306) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2378, 2377])).
% 0.91/1.14 tff(2380,plain,
% 0.91/1.14 (hskp19 | (~c1_1(a2306))),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2379, 160, 898, 890, 364, 363, 882, 1960])).
% 0.91/1.14 tff(2381,plain,
% 0.91/1.14 (hskp19),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2380, 2373])).
% 0.91/1.14 tff(2382,plain,
% 0.91/1.14 (~hskp17),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[242, 2373])).
% 0.91/1.14 tff(2383,plain,
% 0.91/1.14 (~c1_1(a2302)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1873, 2382, 2381])).
% 0.91/1.14 tff(2384,plain,
% 0.91/1.14 (hskp17 | (~c1_1(a2306)) | (~c1_1(a2282))),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1446, 160, 2040, 364, 363, 2050, 1440])).
% 0.91/1.14 tff(2385,plain,
% 0.91/1.14 (~c1_1(a2282)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2384, 2382, 2373])).
% 0.91/1.14 tff(2386,plain,
% 0.91/1.14 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.91/1.14 inference(bind,[status(th)],[])).
% 0.91/1.14 tff(2387,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.91/1.14 inference(quant_intro,[status(thm)],[2386])).
% 0.91/1.14 tff(2388,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2389,plain,
% 0.91/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp0))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.91/1.14 inference(bind,[status(th)],[])).
% 0.91/1.14 tff(2390,plain,
% 0.91/1.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.91/1.14 inference(quant_intro,[status(thm)],[2389])).
% 0.91/1.14 tff(2391,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 0.91/1.14 tff(2392,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 0.91/1.14 tff(2393,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2392, 2388])).
% 0.91/1.14 tff(2394,plain,(
% 0.91/1.14 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.91/1.14 inference(skolemize,[status(sab)],[2393])).
% 0.91/1.14 tff(2395,plain,
% 0.91/1.14 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2394, 2387])).
% 0.91/1.14 tff(2396,plain,
% 0.91/1.14 (hskp28),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2304, 2385, 1969, 34])).
% 0.91/1.14 tff(2397,plain,
% 0.91/1.14 (c3_1(a2278)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[557, 2396])).
% 0.91/1.14 tff(2398,plain,
% 0.91/1.14 (c1_1(a2278)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[565, 2396])).
% 0.91/1.14 tff(2399,plain,
% 0.91/1.14 (c0_1(a2278)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[573, 2396])).
% 0.91/1.14 tff(2400,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2401,plain,
% 0.91/1.14 ((hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2402,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2401])).
% 0.91/1.14 tff(2403,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2402, 2400])).
% 0.91/1.14 tff(2404,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2405,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | c1_1(a2282) | (~c2_1(a2282))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 0.91/1.14 tff(2406,plain,
% 0.91/1.14 (hskp0),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2405, 160, 2399, 2398, 2397, 2040, 2038, 2395, 2385])).
% 0.91/1.14 tff(2407,plain,
% 0.91/1.14 (~c0_1(a2276)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[807, 2406])).
% 0.91/1.14 tff(2408,plain,
% 0.91/1.14 (~c3_1(a2316)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1850, 2381])).
% 0.91/1.14 tff(2409,plain,
% 0.91/1.14 (~c2_1(a2316)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1856, 2381])).
% 0.91/1.14 tff(2410,plain,
% 0.91/1.14 (c1_1(a2276)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[823, 2406])).
% 0.91/1.14 tff(2411,plain,
% 0.91/1.14 (c1_1(a2316)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[1864, 2381])).
% 0.91/1.14 tff(2412,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2413,plain,
% 0.91/1.14 ((hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276))) <=> (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2414,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2413])).
% 0.91/1.14 tff(2415,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2414, 2412])).
% 0.91/1.14 tff(2416,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2316) | c3_1(a2316) | (~c1_1(a2316)) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2417,plain,
% 0.91/1.14 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a2316) | c3_1(a2316) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | (~c1_1(a2316))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 0.91/1.14 tff(2418,plain,
% 0.91/1.14 (~c2_1(a2276)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2417, 160, 2382, 2411, 2410, 2409, 2408, 2407, 1440])).
% 0.91/1.14 tff(2419,plain,
% 0.91/1.14 (c3_1(a2276)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[815, 2406])).
% 0.91/1.14 tff(2420,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2421,plain,
% 0.91/1.14 (((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302))) <=> (c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2422,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 0.91/1.14 inference(monotonicity,[status(thm)],[2421])).
% 0.91/1.14 tff(2423,plain,
% 0.91/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.14 inference(transitivity,[status(thm)],[2422, 2420])).
% 0.91/1.14 tff(2424,plain,
% 0.91/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))),
% 0.91/1.14 inference(quant_inst,[status(thm)],[])).
% 0.91/1.14 tff(2425,plain,
% 0.91/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 0.91/1.14 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 0.91/1.14 tff(2426,plain,
% 0.91/1.14 ($false),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2425, 160, 908, 907, 898, 2410, 2419, 906, 882, 196, 2418, 2383])).
% 0.91/1.14 tff(2427,plain,(c2_1(a2306) | c0_1(a2277) | c2_1(a2277) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.14 tff(2428,plain,
% 0.91/1.14 (c2_1(a2306)),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[2427, 363, 34, 1969])).
% 0.91/1.14 tff(2429,plain,
% 0.91/1.14 (~hskp17),
% 0.91/1.14 inference(unit_resolution,[status(thm)],[236, 2428])).
% 0.91/1.14 tff(2430,plain,
% 0.91/1.14 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.14 inference(rewrite,[status(thm)],[])).
% 0.91/1.14 tff(2431,plain,
% 0.91/1.14 ((hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2432,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2431])).
% 0.91/1.15 tff(2433,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2432, 2430])).
% 0.91/1.15 tff(2434,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2435,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2282) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282)) | (~c2_1(a2282))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2434, 2433])).
% 0.91/1.15 tff(2436,plain,
% 0.91/1.15 (hskp17 | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2435, 160, 2040, 2050, 34, 1440])).
% 0.91/1.15 tff(2437,plain,
% 0.91/1.15 (c3_1(a2277)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2436, 2327, 2289, 2429])).
% 0.91/1.15 tff(2438,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2439,plain,
% 0.91/1.15 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302))) <=> (c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2440,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2439])).
% 0.91/1.15 tff(2441,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2440, 2438])).
% 0.91/1.15 tff(2442,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2443,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2302)) | c1_1(a2302) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 0.91/1.15 tff(2444,plain,
% 0.91/1.15 ((~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2302)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2443, 160, 908, 907, 898, 906, 882, 34, 196])).
% 0.91/1.15 tff(2445,plain,
% 0.91/1.15 (c1_1(a2302)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2444, 2437, 2289])).
% 0.91/1.15 tff(2446,plain,
% 0.91/1.15 ((~c2_1(a2306)) | (~c1_1(a2282)) | (~c0_1(a2306))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1661, 160, 2040, 363, 2050, 2038, 675])).
% 0.91/1.15 tff(2447,plain,
% 0.91/1.15 (~c0_1(a2306)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2446, 2327, 2428])).
% 0.91/1.15 tff(2448,plain,
% 0.91/1.15 (~hskp19),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1873, 2445, 2429])).
% 0.91/1.15 tff(2449,plain,
% 0.91/1.15 (^[U: $i] : refl((hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(2450,plain,
% 0.91/1.15 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[2449])).
% 0.91/1.15 tff(2451,plain,
% 0.91/1.15 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2452,plain,
% 0.91/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp19) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp19))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp19) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(2453,plain,
% 0.91/1.15 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp19) <=> ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[2452])).
% 0.91/1.15 tff(2454,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.91/1.15 tff(2455,plain,
% 0.91/1.15 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 0.91/1.15 tff(2456,plain,
% 0.91/1.15 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2455, 2451])).
% 0.91/1.15 tff(2457,plain,(
% 0.91/1.15 ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.15 inference(skolemize,[status(sab)],[2456])).
% 0.91/1.15 tff(2458,plain,
% 0.91/1.15 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2457, 2450])).
% 0.91/1.15 tff(2459,plain,
% 0.91/1.15 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2460,plain,
% 0.91/1.15 ((hskp19 | hskp7 | (~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2461,plain,
% 0.91/1.15 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2460])).
% 0.91/1.15 tff(2462,plain,
% 0.91/1.15 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2461, 2459])).
% 0.91/1.15 tff(2463,plain,
% 0.91/1.15 ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2464,plain,
% 0.91/1.15 ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp19 | hskp7 | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 0.91/1.15 tff(2465,plain,
% 0.91/1.15 (hskp19 | hskp7 | (~c1_1(a2282))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2464, 160, 2040, 2038, 2458])).
% 0.91/1.15 tff(2466,plain,
% 0.91/1.15 (hskp7),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2465, 2448, 2327])).
% 0.91/1.15 tff(2467,plain,
% 0.91/1.15 (~c2_1(a2286)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[957, 2466])).
% 0.91/1.15 tff(2468,plain,
% 0.91/1.15 (hskp8),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2322, 35, 1969, 2289])).
% 0.91/1.15 tff(2469,plain,
% 0.91/1.15 (c0_1(a2287)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1300, 2468])).
% 0.91/1.15 tff(2470,plain,
% 0.91/1.15 (c2_1(a2287)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1308, 2468])).
% 0.91/1.15 tff(2471,plain,
% 0.91/1.15 (c3_1(a2287)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[1320, 2327, 2470, 2040, 2050, 2038, 2469])).
% 0.91/1.15 tff(2472,plain,
% 0.91/1.15 (~c1_1(a2287)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2238, 2468])).
% 0.91/1.15 tff(2473,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2474,plain,
% 0.91/1.15 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2287) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306))) <=> (c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2475,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2287) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306)))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2474])).
% 0.91/1.15 tff(2476,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2287) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2475, 2473])).
% 0.91/1.15 tff(2477,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2287) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306) | c1_1(a2306) | (~c2_1(a2306)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2478,plain,
% 0.91/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2306) | (~c2_1(a2306)) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2287)) | (~c3_1(a2287)) | c0_1(a2306)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 0.91/1.15 tff(2479,plain,
% 0.91/1.15 (c1_1(a2306)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2478, 160, 2470, 2289, 2428, 2472, 34, 196, 2437, 2447, 2471])).
% 0.91/1.15 tff(2480,plain,
% 0.91/1.15 (c1_1(a2286)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[979, 2466])).
% 0.91/1.15 tff(2481,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2482,plain,
% 0.91/1.15 ((hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306))) <=> (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2483,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306)))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2482])).
% 0.91/1.15 tff(2484,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2483, 2481])).
% 0.91/1.15 tff(2485,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2486,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | (~c1_1(a2306)) | (~c2_1(a2306)) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2306)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2485, 2484])).
% 0.91/1.15 tff(2487,plain,
% 0.91/1.15 (c3_1(a2286)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2486, 160, 2429, 2480, 2479, 2428, 2467, 1440, 2447])).
% 0.91/1.15 tff(2488,plain,
% 0.91/1.15 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(2489,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[2488])).
% 0.91/1.15 tff(2490,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2491,plain,
% 0.91/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.91/1.15 inference(bind,[status(th)],[])).
% 0.91/1.15 tff(2492,plain,
% 0.91/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.91/1.15 inference(quant_intro,[status(thm)],[2491])).
% 0.91/1.15 tff(2493,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 0.91/1.15 tff(2494,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 0.91/1.15 tff(2495,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2494, 2490])).
% 0.91/1.15 tff(2496,plain,(
% 0.91/1.15 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.91/1.15 inference(skolemize,[status(sab)],[2495])).
% 0.91/1.15 tff(2497,plain,
% 0.91/1.15 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2496, 2489])).
% 0.91/1.15 tff(2498,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2499,plain,
% 0.91/1.15 ((hskp18 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302))) <=> (hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2500,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2499])).
% 0.91/1.15 tff(2501,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2500, 2498])).
% 0.91/1.15 tff(2502,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2287)) | (~c3_1(a2287)) | (~c2_1(a2287)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2503,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2287)) | (~c3_1(a2287)) | (~c0_1(a2287)) | (~c2_1(a2302)) | (~c1_1(a2302))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 0.91/1.15 tff(2504,plain,
% 0.91/1.15 (hskp18),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2503, 160, 898, 2469, 2470, 882, 2497, 2445, 2471])).
% 0.91/1.15 tff(2505,plain,
% 0.91/1.15 (((~hskp18) | (~c2_1(a2308))) <=> ((~hskp18) | (~c2_1(a2308)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2506,plain,
% 0.91/1.15 (((~c2_1(a2308)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2308)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2507,axiom,((~c2_1(a2308)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.91/1.15 tff(2508,plain,
% 0.91/1.15 ((~hskp18) | (~c2_1(a2308))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 0.91/1.15 tff(2509,plain,
% 0.91/1.15 ((~hskp18) | (~c2_1(a2308))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2508, 2505])).
% 0.91/1.15 tff(2510,plain,
% 0.91/1.15 (~c2_1(a2308)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2509, 2504])).
% 0.91/1.15 tff(2511,plain,
% 0.91/1.15 (((~hskp18) | (~c1_1(a2308))) <=> ((~hskp18) | (~c1_1(a2308)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2512,plain,
% 0.91/1.15 (((~c1_1(a2308)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a2308)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2513,axiom,((~c1_1(a2308)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.91/1.15 tff(2514,plain,
% 0.91/1.15 ((~hskp18) | (~c1_1(a2308))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 0.91/1.15 tff(2515,plain,
% 0.91/1.15 ((~hskp18) | (~c1_1(a2308))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2514, 2511])).
% 0.91/1.15 tff(2516,plain,
% 0.91/1.15 (~c1_1(a2308)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2515, 2504])).
% 0.91/1.15 tff(2517,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2518,plain,
% 0.91/1.15 ((hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308)) <=> (hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2519,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308)))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2518])).
% 0.91/1.15 tff(2520,plain,
% 0.91/1.15 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2519, 2517])).
% 0.91/1.15 tff(2521,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2286) | (~c3_1(a2286)) | (~c1_1(a2286)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2522,plain,
% 0.91/1.15 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c1_1(a2308) | c2_1(a2308) | c2_1(a2286) | (~ndr1_0) | (~c3_1(a2286)) | (~c1_1(a2286)) | c0_1(a2308)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 0.91/1.15 tff(2523,plain,
% 0.91/1.15 (c0_1(a2308)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2522, 160, 35, 2480, 2516, 2510, 2467, 421, 2487])).
% 0.91/1.15 tff(2524,plain,
% 0.91/1.15 (((~hskp18) | c3_1(a2308)) <=> ((~hskp18) | c3_1(a2308))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2525,axiom,((~hskp18) | c3_1(a2308)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.91/1.15 tff(2526,plain,
% 0.91/1.15 ((~hskp18) | c3_1(a2308)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2525, 2524])).
% 0.91/1.15 tff(2527,plain,
% 0.91/1.15 ((~hskp18) | c3_1(a2308)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2526, 2524])).
% 0.91/1.15 tff(2528,plain,
% 0.91/1.15 ((~hskp18) | c3_1(a2308)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2527, 2524])).
% 0.91/1.15 tff(2529,plain,
% 0.91/1.15 ((~hskp18) | c3_1(a2308)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2528, 2524])).
% 0.91/1.15 tff(2530,plain,
% 0.91/1.15 ((~hskp18) | c3_1(a2308)),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2529, 2524])).
% 0.91/1.15 tff(2531,plain,
% 0.91/1.15 (c3_1(a2308)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2530, 2504])).
% 0.91/1.15 tff(2532,plain,
% 0.91/1.15 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2533,plain,
% 0.91/1.15 ((hskp19 | hskp12 | (~ndr1_0) | c2_1(a2308) | (~c0_1(a2308)) | (~c3_1(a2308))) <=> (hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308)))),
% 0.91/1.15 inference(rewrite,[status(thm)],[])).
% 0.91/1.15 tff(2534,plain,
% 0.91/1.15 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2308) | (~c0_1(a2308)) | (~c3_1(a2308)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308))))),
% 0.91/1.15 inference(monotonicity,[status(thm)],[2533])).
% 0.91/1.15 tff(2535,plain,
% 0.91/1.15 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2308) | (~c0_1(a2308)) | (~c3_1(a2308)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308)))),
% 0.91/1.15 inference(transitivity,[status(thm)],[2534, 2532])).
% 0.91/1.15 tff(2536,plain,
% 0.91/1.15 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2308) | (~c0_1(a2308)) | (~c3_1(a2308)))),
% 0.91/1.15 inference(quant_inst,[status(thm)],[])).
% 0.91/1.15 tff(2537,plain,
% 0.91/1.15 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2308) | (~ndr1_0) | (~c3_1(a2308)) | (~c0_1(a2308))),
% 0.91/1.15 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 0.91/1.15 tff(2538,plain,
% 0.91/1.15 (hskp12 | (~c0_1(a2308))),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2537, 160, 2448, 2531, 2510, 10])).
% 0.91/1.15 tff(2539,plain,
% 0.91/1.15 (hskp12),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[2538, 2523])).
% 0.91/1.15 tff(2540,plain,
% 0.91/1.15 (~c3_1(a2295)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[644, 2539])).
% 0.91/1.15 tff(2541,plain,
% 0.91/1.15 (c0_1(a2295)),
% 0.91/1.15 inference(unit_resolution,[status(thm)],[652, 2539])).
% 0.91/1.15 tff(2542,plain,
% 0.91/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2543,plain,
% 0.91/1.16 (((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302))) <=> ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2544,plain,
% 0.91/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302))))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[2543])).
% 0.91/1.16 tff(2545,plain,
% 0.91/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.91/1.16 inference(transitivity,[status(thm)],[2544, 2542])).
% 0.91/1.16 tff(2546,plain,
% 0.91/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2306) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(2547,plain,
% 0.91/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c1_1(a2306)) | (~c2_1(a2306)) | c3_1(a2306) | c0_1(a2302) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 0.91/1.16 tff(2548,plain,
% 0.91/1.16 (~c2_1(a2295)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2547, 160, 898, 2541, 2479, 2428, 363, 882, 2540, 675, 2445])).
% 0.91/1.16 tff(2549,plain,
% 0.91/1.16 (~c1_1(a2295)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1254, 2539])).
% 0.91/1.16 tff(2550,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2551,plain,
% 0.91/1.16 ((hskp23 | (~ndr1_0) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295))) <=> (hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2552,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295))))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[2551])).
% 0.91/1.16 tff(2553,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295)))),
% 0.91/1.16 inference(transitivity,[status(thm)],[2552, 2550])).
% 0.91/1.16 tff(2554,plain,
% 0.91/1.16 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a2295) | c3_1(a2295) | (~c0_1(a2295)) | c1_1(a2295) | c3_1(a2295) | (~c0_1(a2295)))),
% 0.91/1.16 inference(quant_inst,[status(thm)],[])).
% 0.91/1.16 tff(2555,plain,
% 0.91/1.16 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | c2_1(a2295) | (~c0_1(a2295))),
% 0.91/1.16 inference(modus_ponens,[status(thm)],[2554, 2553])).
% 0.91/1.16 tff(2556,plain,
% 0.91/1.16 (hskp23),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[2555, 160, 2541, 2549, 2540, 260, 2548])).
% 0.91/1.16 tff(2557,plain,
% 0.91/1.16 (~c2_1(a2327)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[278, 2556])).
% 0.91/1.16 tff(2558,plain,
% 0.91/1.16 (c3_1(a2327)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[286, 2556])).
% 0.91/1.16 tff(2559,plain,
% 0.91/1.16 (~c0_1(a2327)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[299, 2556])).
% 0.91/1.16 tff(2560,plain,
% 0.91/1.16 (c1_1(a2327)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1377, 160, 35, 2480, 2559, 2557, 2467, 421, 2487])).
% 0.91/1.16 tff(2561,plain,
% 0.91/1.16 (~hskp26),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1359, 2560, 2558, 2557, 35])).
% 0.91/1.16 tff(2562,plain,
% 0.91/1.16 (hskp16),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1028, 2561, 35])).
% 0.91/1.16 tff(2563,plain,
% 0.91/1.16 (~c3_1(a2304)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[995, 2562])).
% 0.91/1.16 tff(2564,plain,
% 0.91/1.16 (~c2_1(a2304)),
% 0.91/1.16 inference(unit_resolution,[status(thm)],[1001, 2562])).
% 0.91/1.16 tff(2565,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2566,plain,
% 0.91/1.16 ((hskp19 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304)))),
% 0.91/1.16 inference(rewrite,[status(thm)],[])).
% 0.91/1.16 tff(2567,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304))))),
% 0.91/1.16 inference(monotonicity,[status(thm)],[2566])).
% 0.91/1.16 tff(2568,plain,
% 0.91/1.16 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304)))),
% 0.99/1.16 inference(transitivity,[status(thm)],[2567, 2565])).
% 0.99/1.16 tff(2569,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2304) | c3_1(a2304) | (~c1_1(a2304)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(2570,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c2_1(a2304) | c3_1(a2304) | c0_1(a2302) | (~ndr1_0) | (~c2_1(a2302)) | (~c3_1(a2302)) | (~c1_1(a2304))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 0.99/1.16 tff(2571,plain,
% 0.99/1.16 (~c1_1(a2304)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2570, 160, 2448, 898, 890, 2564, 2563, 882, 1960])).
% 0.99/1.16 tff(2572,plain,
% 0.99/1.16 (~c0_1(a2304)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1007, 2562])).
% 0.99/1.16 tff(2573,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2574,plain,
% 0.99/1.16 ((hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304)) <=> (hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2575,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327))))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[2574])).
% 0.99/1.16 tff(2576,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327)))),
% 0.99/1.16 inference(transitivity,[status(thm)],[2575, 2573])).
% 0.99/1.16 tff(2577,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a2327) | (~c3_1(a2327)) | (~c1_1(a2327)) | c2_1(a2304) | c1_1(a2304) | c0_1(a2304))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(2578,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp28 | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | (~ndr1_0) | c1_1(a2304) | (~c3_1(a2327)) | (~c1_1(a2327))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 0.99/1.16 tff(2579,plain,
% 0.99/1.16 ($false),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2578, 160, 35, 2558, 2557, 2572, 2564, 421, 2560, 2571])).
% 0.99/1.16 tff(2580,plain,(hskp28 | c3_1(a2306) | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.16 tff(2581,plain,
% 0.99/1.16 (hskp28),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2580, 363, 34, 1969])).
% 0.99/1.16 tff(2582,plain,
% 0.99/1.16 (c0_1(a2278)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[573, 2581])).
% 0.99/1.16 tff(2583,plain,
% 0.99/1.16 (c3_1(a2278)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[557, 2581])).
% 0.99/1.16 tff(2584,plain,
% 0.99/1.16 (c1_1(a2278)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[565, 2581])).
% 0.99/1.16 tff(2585,plain,
% 0.99/1.16 (c2_1(a2278)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1993, 2584, 2583, 2582])).
% 0.99/1.16 tff(2586,plain,
% 0.99/1.16 (~hskp12),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2022, 2585, 2582, 2584, 1970])).
% 0.99/1.16 tff(2587,plain,
% 0.99/1.16 (hskp13),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1247, 2586])).
% 0.99/1.16 tff(2588,plain,
% 0.99/1.16 (~c3_1(a2299)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1201, 2587])).
% 0.99/1.16 tff(2589,plain,
% 0.99/1.16 (~c1_1(a2299)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1215, 2587])).
% 0.99/1.16 tff(2590,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2591,plain,
% 0.99/1.16 ((hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c0_1(a2299))) <=> (hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2592,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c0_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299))))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[2591])).
% 0.99/1.16 tff(2593,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c0_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299)))),
% 0.99/1.16 inference(transitivity,[status(thm)],[2592, 2590])).
% 0.99/1.16 tff(2594,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c0_1(a2299)))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(2595,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c0_1(a2299))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[2594, 2593])).
% 0.99/1.16 tff(2596,plain,
% 0.99/1.16 (~c0_1(a2299)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2595, 160, 1970, 2582, 2584, 2589, 2588, 2004, 2585])).
% 0.99/1.16 tff(2597,plain,
% 0.99/1.16 (c2_1(a2299)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1209, 2587])).
% 0.99/1.16 tff(2598,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2599,plain,
% 0.99/1.16 ((hskp1 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299))) <=> (hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2600,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299)))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[2599])).
% 0.99/1.16 tff(2601,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299))),
% 0.99/1.16 inference(transitivity,[status(thm)],[2600, 2598])).
% 0.99/1.16 tff(2602,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2299) | c0_1(a2299) | (~c2_1(a2299)))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(2603,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a2299) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2299)) | c0_1(a2299)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[2602, 2601])).
% 0.99/1.16 tff(2604,plain,
% 0.99/1.16 (~c3_1(a2277)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2603, 160, 1970, 2597, 2289, 2589, 34, 2090, 2596])).
% 0.99/1.16 tff(2605,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2606,plain,
% 0.99/1.16 ((hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302))) <=> (hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2607,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302))))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[2606])).
% 0.99/1.16 tff(2608,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.99/1.16 inference(transitivity,[status(thm)],[2607, 2605])).
% 0.99/1.16 tff(2609,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c1_1(a2277)) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(2610,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp17 | c0_1(a2302) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | c3_1(a2277) | (~c2_1(a2302)) | (~c1_1(a2302))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 0.99/1.16 tff(2611,plain,
% 0.99/1.16 (hskp17 | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2302))),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2610, 160, 898, 882, 34, 1440])).
% 0.99/1.16 tff(2612,plain,
% 0.99/1.16 (~c1_1(a2302)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2611, 2604, 2289, 2429])).
% 0.99/1.16 tff(2613,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2614,plain,
% 0.99/1.16 ((hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299))) <=> (hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299)))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(2615,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299))))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[2614])).
% 0.99/1.16 tff(2616,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299)))),
% 0.99/1.16 inference(transitivity,[status(thm)],[2615, 2613])).
% 0.99/1.16 tff(2617,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(2618,plain,
% 0.99/1.16 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp0 | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2299))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 0.99/1.16 tff(2619,plain,
% 0.99/1.16 (hskp0),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2618, 160, 2582, 2584, 2583, 2597, 2589, 2588, 2395])).
% 0.99/1.16 tff(2620,plain,
% 0.99/1.16 (~c0_1(a2276)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[807, 2619])).
% 0.99/1.16 tff(2621,plain,
% 0.99/1.16 (hskp19),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1967, 2604, 2289])).
% 0.99/1.16 tff(2622,plain,
% 0.99/1.16 (~c3_1(a2316)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1850, 2621])).
% 0.99/1.16 tff(2623,plain,
% 0.99/1.16 (~c2_1(a2316)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1856, 2621])).
% 0.99/1.16 tff(2624,plain,
% 0.99/1.16 (c1_1(a2276)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[823, 2619])).
% 0.99/1.16 tff(2625,plain,
% 0.99/1.16 (c1_1(a2316)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1864, 2621])).
% 0.99/1.16 tff(2626,plain,
% 0.99/1.16 (~c2_1(a2276)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2417, 160, 2429, 2625, 2624, 2623, 2622, 2620, 1440])).
% 0.99/1.16 tff(2627,plain,
% 0.99/1.16 (c3_1(a2276)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[815, 2619])).
% 0.99/1.16 tff(2628,plain,
% 0.99/1.16 ($false),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2425, 160, 908, 907, 898, 2624, 2627, 906, 882, 196, 2626, 2612])).
% 0.99/1.16 tff(2629,plain,(c3_1(a2306) | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.16 tff(2630,plain,
% 0.99/1.16 (c3_1(a2306)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2629, 1969, 34])).
% 0.99/1.16 tff(2631,plain,
% 0.99/1.16 (~hskp17),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[265, 2630])).
% 0.99/1.16 tff(2632,plain,
% 0.99/1.16 (c3_1(a2277)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2436, 2327, 2289, 2631])).
% 0.99/1.16 tff(2633,plain,
% 0.99/1.16 (c1_1(a2302)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2444, 2632, 2289])).
% 0.99/1.16 tff(2634,plain,
% 0.99/1.16 (~hskp19),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[1873, 2633, 2631])).
% 0.99/1.16 tff(2635,plain,
% 0.99/1.16 (hskp7),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[2465, 2634, 2327])).
% 0.99/1.16 tff(2636,plain,
% 0.99/1.16 (~c2_1(a2286)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[957, 2635])).
% 0.99/1.16 tff(2637,plain,
% 0.99/1.16 (c1_1(a2286)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[979, 2635])).
% 0.99/1.16 tff(2638,plain,
% 0.99/1.16 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2639,plain,
% 0.99/1.17 ((hskp19 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302))) <=> (hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2640,plain,
% 0.99/1.17 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[2639])).
% 0.99/1.17 tff(2641,plain,
% 0.99/1.17 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[2640, 2638])).
% 0.99/1.17 tff(2642,plain,
% 0.99/1.17 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a2286) | c3_1(a2286) | (~c1_1(a2286)) | c0_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(2643,plain,
% 0.99/1.17 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp19 | c0_1(a2302) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c1_1(a2286)) | (~c2_1(a2302)) | (~c3_1(a2302))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 0.99/1.17 tff(2644,plain,
% 0.99/1.17 (c3_1(a2286)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2643, 160, 2634, 898, 890, 2637, 882, 2636, 1960])).
% 0.99/1.17 tff(2645,plain,
% 0.99/1.17 (hskp18),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2503, 160, 898, 2469, 2470, 882, 2497, 2633, 2471])).
% 0.99/1.17 tff(2646,plain,
% 0.99/1.17 (~c2_1(a2308)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2509, 2645])).
% 0.99/1.17 tff(2647,plain,
% 0.99/1.17 (~c1_1(a2308)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2515, 2645])).
% 0.99/1.17 tff(2648,plain,
% 0.99/1.17 (c0_1(a2308)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2522, 160, 35, 2637, 2647, 2646, 2636, 421, 2644])).
% 0.99/1.17 tff(2649,plain,
% 0.99/1.17 (c3_1(a2308)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2530, 2645])).
% 0.99/1.17 tff(2650,plain,
% 0.99/1.17 (hskp12 | (~c0_1(a2308))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2537, 160, 2634, 2649, 2646, 10])).
% 0.99/1.17 tff(2651,plain,
% 0.99/1.17 (hskp12),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2650, 2648])).
% 0.99/1.17 tff(2652,plain,
% 0.99/1.17 (~c3_1(a2295)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[644, 2651])).
% 0.99/1.17 tff(2653,plain,
% 0.99/1.17 (c0_1(a2295)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[652, 2651])).
% 0.99/1.17 tff(2654,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2655,plain,
% 0.99/1.17 (((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302))) <=> (c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2656,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[2655])).
% 0.99/1.17 tff(2657,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[2656, 2654])).
% 0.99/1.17 tff(2658,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2302) | (~c2_1(a2302)) | (~c1_1(a2302)))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(2659,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2302) | c3_1(a2295) | c3_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c2_1(a2302)) | (~c1_1(a2302))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2658, 2657])).
% 0.99/1.17 tff(2660,plain,
% 0.99/1.17 (~c2_1(a2295)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2659, 160, 898, 2653, 2040, 882, 2652, 2038, 675, 2327, 2633])).
% 0.99/1.17 tff(2661,plain,
% 0.99/1.17 (~c1_1(a2295)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1254, 2651])).
% 0.99/1.17 tff(2662,plain,
% 0.99/1.17 (hskp23),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2555, 160, 2653, 2661, 2652, 260, 2660])).
% 0.99/1.17 tff(2663,plain,
% 0.99/1.17 (~c2_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[278, 2662])).
% 0.99/1.17 tff(2664,plain,
% 0.99/1.17 (c3_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[286, 2662])).
% 0.99/1.17 tff(2665,plain,
% 0.99/1.17 (~c0_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[299, 2662])).
% 0.99/1.17 tff(2666,plain,
% 0.99/1.17 (c1_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1377, 160, 35, 2637, 2665, 2663, 2636, 421, 2644])).
% 0.99/1.17 tff(2667,plain,
% 0.99/1.17 (~hskp26),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1359, 2666, 2664, 2663, 35])).
% 0.99/1.17 tff(2668,plain,
% 0.99/1.17 (hskp16),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1028, 2667, 35])).
% 0.99/1.17 tff(2669,plain,
% 0.99/1.17 (~c3_1(a2304)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[995, 2668])).
% 0.99/1.17 tff(2670,plain,
% 0.99/1.17 (~c2_1(a2304)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1001, 2668])).
% 0.99/1.17 tff(2671,plain,
% 0.99/1.17 (~c1_1(a2304)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2570, 160, 2634, 898, 890, 2670, 2669, 882, 1960])).
% 0.99/1.17 tff(2672,plain,
% 0.99/1.17 (~c0_1(a2304)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1007, 2668])).
% 0.99/1.17 tff(2673,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2578, 160, 35, 2664, 2663, 2672, 2670, 421, 2666, 2671])).
% 0.99/1.17 tff(2674,plain,(hskp28 | c2_1(a2277) | c0_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(2675,plain,
% 0.99/1.17 (hskp28),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2674, 1969, 34])).
% 0.99/1.17 tff(2676,plain,
% 0.99/1.17 (c0_1(a2278)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[573, 2675])).
% 0.99/1.17 tff(2677,plain,
% 0.99/1.17 (c3_1(a2278)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[557, 2675])).
% 0.99/1.17 tff(2678,plain,
% 0.99/1.17 (c1_1(a2278)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[565, 2675])).
% 0.99/1.17 tff(2679,plain,
% 0.99/1.17 (c2_1(a2278)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1993, 2678, 2677, 2676])).
% 0.99/1.17 tff(2680,plain,
% 0.99/1.17 (~hskp12),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2022, 2679, 2676, 2678, 1970])).
% 0.99/1.17 tff(2681,plain,
% 0.99/1.17 (hskp13),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1247, 2680])).
% 0.99/1.17 tff(2682,plain,
% 0.99/1.17 (~c3_1(a2299)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1201, 2681])).
% 0.99/1.17 tff(2683,plain,
% 0.99/1.17 (~c1_1(a2299)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1215, 2681])).
% 0.99/1.17 tff(2684,plain,
% 0.99/1.17 (~c0_1(a2299)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2595, 160, 1970, 2676, 2678, 2683, 2682, 2004, 2679])).
% 0.99/1.17 tff(2685,plain,
% 0.99/1.17 (c2_1(a2299)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1209, 2681])).
% 0.99/1.17 tff(2686,plain,
% 0.99/1.17 (~c3_1(a2277)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2603, 160, 1970, 2685, 2289, 2683, 34, 2090, 2684])).
% 0.99/1.17 tff(2687,plain,
% 0.99/1.17 (~c1_1(a2302)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2611, 2686, 2289, 2631])).
% 0.99/1.17 tff(2688,plain,
% 0.99/1.17 (hskp0),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2618, 160, 2676, 2678, 2677, 2685, 2683, 2682, 2395])).
% 0.99/1.17 tff(2689,plain,
% 0.99/1.17 (~c0_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[807, 2688])).
% 0.99/1.17 tff(2690,plain,
% 0.99/1.17 (hskp19),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1967, 2686, 2289])).
% 0.99/1.17 tff(2691,plain,
% 0.99/1.17 (~c3_1(a2316)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1850, 2690])).
% 0.99/1.17 tff(2692,plain,
% 0.99/1.17 (~c2_1(a2316)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1856, 2690])).
% 0.99/1.17 tff(2693,plain,
% 0.99/1.17 (c1_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[823, 2688])).
% 0.99/1.17 tff(2694,plain,
% 0.99/1.17 (c1_1(a2316)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1864, 2690])).
% 0.99/1.17 tff(2695,plain,
% 0.99/1.17 (~c2_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2417, 160, 2631, 2694, 2693, 2692, 2691, 2689, 1440])).
% 0.99/1.17 tff(2696,plain,
% 0.99/1.17 (c3_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[815, 2688])).
% 0.99/1.17 tff(2697,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2425, 160, 908, 907, 898, 2693, 2696, 906, 882, 196, 2695, 2687])).
% 0.99/1.17 tff(2698,plain,(c0_1(a2277) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(2699,plain,
% 0.99/1.17 (c0_1(a2277)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2698, 34])).
% 0.99/1.17 tff(2700,plain,
% 0.99/1.17 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2701,plain,
% 0.99/1.17 ((hskp23 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282))) <=> (hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2702,plain,
% 0.99/1.17 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[2701])).
% 0.99/1.17 tff(2703,plain,
% 0.99/1.17 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[2702, 2700])).
% 0.99/1.17 tff(2704,plain,
% 0.99/1.17 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)) | c1_1(a2282) | c3_1(a2282) | (~c2_1(a2282)))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(2705,plain,
% 0.99/1.17 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a2282) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277) | c1_1(a2282) | (~c2_1(a2282))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2704, 2703])).
% 0.99/1.17 tff(2706,plain,
% 0.99/1.17 (hskp23),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2705, 160, 1933, 2699, 1799, 1932, 47, 1950, 37])).
% 0.99/1.17 tff(2707,plain,
% 0.99/1.17 (~c2_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[278, 2706])).
% 0.99/1.17 tff(2708,plain,
% 0.99/1.17 (c3_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[286, 2706])).
% 0.99/1.17 tff(2709,plain,
% 0.99/1.17 (~c1_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[293, 160, 2708, 908, 907, 1933, 2707, 906, 1942, 196, 37])).
% 0.99/1.17 tff(2710,plain,
% 0.99/1.17 (^[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)))),
% 0.99/1.17 inference(bind,[status(th)],[])).
% 0.99/1.17 tff(2711,plain,
% 0.99/1.17 (![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))),
% 0.99/1.17 inference(quant_intro,[status(thm)],[2710])).
% 0.99/1.17 tff(2712,plain,
% 0.99/1.17 (![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))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2713,plain,
% 0.99/1.17 (^[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))))),
% 0.99/1.17 inference(bind,[status(th)],[])).
% 0.99/1.17 tff(2714,plain,
% 0.99/1.17 (![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))),
% 0.99/1.17 inference(quant_intro,[status(thm)],[2713])).
% 0.99/1.17 tff(2715,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','clause176')).
% 0.99/1.17 tff(2716,plain,
% 0.99/1.17 (![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))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 0.99/1.17 tff(2717,plain,
% 0.99/1.17 (![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))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2716, 2712])).
% 0.99/1.17 tff(2718,plain,(
% 0.99/1.17 ![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))),
% 0.99/1.17 inference(skolemize,[status(sab)],[2717])).
% 0.99/1.17 tff(2719,plain,
% 0.99/1.17 (![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))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2718, 2711])).
% 0.99/1.17 tff(2720,plain,
% 0.99/1.17 (~c0_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[299, 2706])).
% 0.99/1.17 tff(2721,plain,
% 0.99/1.17 (((~![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(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))) <=> ((~![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(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2722,plain,
% 0.99/1.17 ((hskp0 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp0 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2723,plain,
% 0.99/1.17 (((~![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(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![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(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[2722])).
% 0.99/1.17 tff(2724,plain,
% 0.99/1.17 (((~![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(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![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(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 0.99/1.17 inference(transitivity,[status(thm)],[2723, 2721])).
% 0.99/1.17 tff(2725,plain,
% 0.99/1.17 ((~![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(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(2726,plain,
% 0.99/1.17 ((~![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(a2327) | c2_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 0.99/1.17 tff(2727,plain,
% 0.99/1.17 (hskp0),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2726, 160, 2708, 2720, 2707, 2719, 2709])).
% 0.99/1.17 tff(2728,plain,
% 0.99/1.17 (~c0_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[807, 2727])).
% 0.99/1.17 tff(2729,plain,
% 0.99/1.17 (c3_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[815, 2727])).
% 0.99/1.17 tff(2730,plain,
% 0.99/1.17 (c1_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[823, 2727])).
% 0.99/1.17 tff(2731,plain,
% 0.99/1.17 (~c1_1(a2302)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1873, 825, 1845])).
% 0.99/1.17 tff(2732,assumption,(~c0_1(a2276)), introduced(assumption)).
% 0.99/1.17 tff(2733,assumption,(c1_1(a2276)), introduced(assumption)).
% 0.99/1.17 tff(2734,plain,
% 0.99/1.17 (hskp17 | (~c2_1(a2276))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2417, 160, 1865, 2733, 1857, 1851, 2732, 1440])).
% 0.99/1.17 tff(2735,plain,
% 0.99/1.17 (~c2_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2734, 825])).
% 0.99/1.17 tff(2736,assumption,(c3_1(a2276)), introduced(assumption)).
% 0.99/1.17 tff(2737,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2738,plain,
% 0.99/1.17 (((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302))) <=> (c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2739,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[2738])).
% 0.99/1.17 tff(2740,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[2739, 2737])).
% 0.99/1.17 tff(2741,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2276) | (~c3_1(a2276)) | (~c1_1(a2276)) | c1_1(a2302) | (~c2_1(a2302)) | (~c3_1(a2302)) | c0_1(a2302) | c1_1(a2302) | (~c2_1(a2302)))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(2742,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a2302) | (~ndr1_0) | (~c3_1(a2276)) | c2_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2302)) | c1_1(a2302) | (~c3_1(a2302))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2741, 2740])).
% 0.99/1.17 tff(2743,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2742, 160, 898, 890, 2733, 2736, 882, 196, 2735, 2731])).
% 0.99/1.17 tff(2744,plain,(hskp17 | (~c1_1(a2276)) | (~c3_1(a2276)) | c0_1(a2276) | (~hskp19)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(2745,plain,
% 0.99/1.17 (hskp17),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2744, 2730, 2729, 2728, 1968])).
% 0.99/1.17 tff(2746,plain,
% 0.99/1.17 (~c1_1(a2306)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[242, 2745])).
% 0.99/1.17 tff(2747,assumption,(hskp3), introduced(assumption)).
% 0.99/1.17 tff(2748,plain,
% 0.99/1.17 (~c2_1(a2280)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[526, 2747])).
% 0.99/1.17 tff(2749,plain,
% 0.99/1.17 (c1_1(a2280)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[542, 2747])).
% 0.99/1.17 tff(2750,plain,
% 0.99/1.17 (c3_1(a2280)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[534, 2747])).
% 0.99/1.17 tff(2751,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1836, 2750, 2749, 35, 1075, 2748])).
% 0.99/1.17 tff(2752,plain,((~hskp3) | hskp28 | (~hskp23)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(2753,plain,
% 0.99/1.17 (~hskp3),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2752, 2706, 35])).
% 0.99/1.17 tff(2754,plain,
% 0.99/1.17 (~c3_1(a2286)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[986, 160, 908, 907, 980, 707, 906, 958, 702, 196, 37])).
% 0.99/1.17 tff(2755,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2756,plain,
% 0.99/1.17 (((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2757,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[2756])).
% 0.99/1.17 tff(2758,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[2757, 2755])).
% 0.99/1.17 tff(2759,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2302) | (~c1_1(a2302)) | (~c2_1(a2302)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(2760,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2302) | c0_1(a2286) | c2_1(a2286) | (~ndr1_0) | c3_1(a2286) | (~c2_1(a2302)) | (~c1_1(a2302)) | (~c3_1(a2327))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 0.99/1.17 tff(2761,plain,
% 0.99/1.17 (~c1_1(a2302)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2760, 160, 1333, 898, 1361, 1332, 882, 964, 958, 1162, 2754])).
% 0.99/1.17 tff(2762,plain,
% 0.99/1.17 (~c1_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[293, 160, 1333, 908, 907, 707, 1332, 906, 702, 196, 37])).
% 0.99/1.17 tff(2763,plain,
% 0.99/1.17 (hskp0),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2726, 160, 1333, 1361, 1332, 2719, 2762])).
% 0.99/1.17 tff(2764,plain,
% 0.99/1.17 (~c0_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[807, 2763])).
% 0.99/1.17 tff(2765,plain,
% 0.99/1.17 (c1_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[823, 2763])).
% 0.99/1.17 tff(2766,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2767,plain,
% 0.99/1.17 (((~ndr1_0) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327)))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(2768,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[2767])).
% 0.99/1.17 tff(2769,plain,
% 0.99/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327)))),
% 0.99/1.17 inference(transitivity,[status(thm)],[2768, 2766])).
% 0.99/1.17 tff(2770,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2276) | (~c1_1(a2276)) | (~c2_1(a2276)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2286) | c2_1(a2286) | c0_1(a2286))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(2771,plain,
% 0.99/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2286) | c2_1(a2286) | c0_1(a2276) | (~ndr1_0) | (~c2_1(a2276)) | (~c1_1(a2276)) | c3_1(a2286) | (~c3_1(a2327))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 0.99/1.17 tff(2772,plain,
% 0.99/1.17 (~c2_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2771, 160, 1333, 2765, 1361, 1332, 964, 958, 2764, 1162, 2754])).
% 0.99/1.17 tff(2773,plain,
% 0.99/1.17 (c3_1(a2276)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[815, 2763])).
% 0.99/1.17 tff(2774,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2742, 160, 898, 890, 2765, 2773, 882, 196, 2772, 2761])).
% 0.99/1.17 tff(2775,plain,((~hskp7) | (~c3_1(a2327)) | c0_1(a2327) | c2_1(a2327) | (~c2_1(a2282)) | c0_1(a2282) | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(2776,plain,
% 0.99/1.17 (~hskp7),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2775, 2708, 2720, 2707, 1933, 1942, 37])).
% 0.99/1.17 tff(2777,plain,
% 0.99/1.17 (hskp7 | hskp6 | c1_1(a2327)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[1367, 160, 2708, 2720, 1039])).
% 0.99/1.17 tff(2778,plain,
% 0.99/1.17 (hskp6),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[2777, 2776, 2709])).
% 0.99/1.17 tff(2779,plain,
% 0.99/1.17 (~c3_1(a2285)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[394, 2778])).
% 0.99/1.17 tff(2780,plain,
% 0.99/1.17 (c1_1(a2285)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[373, 2778])).
% 0.99/1.17 tff(2781,plain,
% 0.99/1.17 (c0_1(a2285)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[381, 2778])).
% 0.99/1.17 tff(2782,plain,
% 0.99/1.17 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.99/1.18 inference(bind,[status(th)],[])).
% 0.99/1.18 tff(2783,plain,
% 0.99/1.18 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.99/1.18 inference(quant_intro,[status(thm)],[2782])).
% 0.99/1.18 tff(2784,plain,
% 0.99/1.18 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2785,plain,
% 0.99/1.18 (^[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)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp7) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp7) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.99/1.18 inference(bind,[status(th)],[])).
% 0.99/1.18 tff(2786,plain,
% 0.99/1.18 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp7) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.99/1.18 inference(quant_intro,[status(thm)],[2785])).
% 0.99/1.18 tff(2787,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.99/1.18 tff(2788,plain,
% 0.99/1.18 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 0.99/1.18 tff(2789,plain,
% 0.99/1.18 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2788, 2784])).
% 0.99/1.18 tff(2790,plain,(
% 0.99/1.18 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.99/1.18 inference(skolemize,[status(sab)],[2789])).
% 0.99/1.18 tff(2791,plain,
% 0.99/1.18 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2790, 2783])).
% 0.99/1.18 tff(2792,plain,
% 0.99/1.18 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2793,plain,
% 0.99/1.18 ((hskp8 | hskp7 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327))) <=> (hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2794,plain,
% 0.99/1.18 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[2793])).
% 0.99/1.18 tff(2795,plain,
% 0.99/1.18 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327))),
% 0.99/1.18 inference(transitivity,[status(thm)],[2794, 2792])).
% 0.99/1.18 tff(2796,plain,
% 0.99/1.18 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a2327) | c0_1(a2327) | (~c3_1(a2327)))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(2797,plain,
% 0.99/1.18 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c0_1(a2327) | (~ndr1_0) | (~c3_1(a2327)) | c1_1(a2327)),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2796, 2795])).
% 0.99/1.18 tff(2798,plain,
% 0.99/1.18 (hskp8 | hskp7 | c1_1(a2327)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2797, 160, 2708, 2720, 2791])).
% 0.99/1.18 tff(2799,plain,
% 0.99/1.18 (hskp8),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2798, 2776, 2709])).
% 0.99/1.18 tff(2800,plain,
% 0.99/1.18 (c2_1(a2287)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[1308, 2799])).
% 0.99/1.18 tff(2801,plain,
% 0.99/1.18 (c0_1(a2287)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[1300, 2799])).
% 0.99/1.18 tff(2802,plain,
% 0.99/1.18 (hskp3 | (~c3_1(a2287))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[1397, 160, 2801, 2800, 2781, 2780, 2779, 1331])).
% 0.99/1.18 tff(2803,plain,
% 0.99/1.18 (~c3_1(a2287)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2802, 2753])).
% 0.99/1.18 tff(2804,plain,
% 0.99/1.18 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.99/1.18 inference(bind,[status(th)],[])).
% 0.99/1.18 tff(2805,plain,
% 0.99/1.18 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.99/1.18 inference(quant_intro,[status(thm)],[2804])).
% 0.99/1.18 tff(2806,plain,
% 0.99/1.18 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2807,plain,
% 0.99/1.18 (^[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) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.99/1.18 inference(bind,[status(th)],[])).
% 0.99/1.18 tff(2808,plain,
% 0.99/1.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.99/1.18 inference(quant_intro,[status(thm)],[2807])).
% 0.99/1.18 tff(2809,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 0.99/1.18 tff(2810,plain,
% 0.99/1.18 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2809, 2808])).
% 0.99/1.18 tff(2811,plain,
% 0.99/1.18 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2810, 2806])).
% 0.99/1.18 tff(2812,plain,(
% 0.99/1.18 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.99/1.18 inference(skolemize,[status(sab)],[2811])).
% 0.99/1.18 tff(2813,plain,
% 0.99/1.18 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2812, 2805])).
% 0.99/1.18 tff(2814,plain,
% 0.99/1.18 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2815,plain,
% 0.99/1.18 ((hskp3 | hskp2 | (~ndr1_0) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327)) <=> (hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2816,plain,
% 0.99/1.18 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327)))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[2815])).
% 0.99/1.18 tff(2817,plain,
% 0.99/1.18 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327))),
% 0.99/1.18 inference(transitivity,[status(thm)],[2816, 2814])).
% 0.99/1.18 tff(2818,plain,
% 0.99/1.18 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c2_1(a2327) | c1_1(a2327) | c0_1(a2327))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(2819,plain,
% 0.99/1.18 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a2327) | c2_1(a2327) | (~ndr1_0) | c1_1(a2327)),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 0.99/1.18 tff(2820,plain,
% 0.99/1.18 (hskp3 | hskp2),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2819, 160, 2720, 2707, 481, 2709])).
% 0.99/1.18 tff(2821,plain,
% 0.99/1.18 (hskp2),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2820, 2753])).
% 0.99/1.18 tff(2822,plain,
% 0.99/1.18 (~c3_1(a2279)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[488, 2821])).
% 0.99/1.18 tff(2823,plain,
% 0.99/1.18 (~c2_1(a2279)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[494, 2821])).
% 0.99/1.18 tff(2824,plain,
% 0.99/1.18 (c0_1(a2279)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[502, 2821])).
% 0.99/1.18 tff(2825,plain,
% 0.99/1.18 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2826,plain,
% 0.99/1.18 ((hskp25 | (~ndr1_0) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279))) <=> (hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2827,plain,
% 0.99/1.18 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287))))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[2826])).
% 0.99/1.18 tff(2828,plain,
% 0.99/1.18 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)))),
% 0.99/1.18 inference(transitivity,[status(thm)],[2827, 2825])).
% 0.99/1.18 tff(2829,plain,
% 0.99/1.18 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c2_1(a2279) | c3_1(a2279) | (~c0_1(a2279)))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(2830,plain,
% 0.99/1.18 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp25 | c2_1(a2279) | c3_1(a2279) | (~ndr1_0) | (~c0_1(a2279)) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 0.99/1.18 tff(2831,plain,
% 0.99/1.18 (hskp25),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2830, 160, 2801, 2800, 2824, 2823, 2822, 2813, 2803])).
% 0.99/1.18 tff(2832,plain,
% 0.99/1.18 (c0_1(a2342)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[32, 2831])).
% 0.99/1.18 tff(2833,plain,
% 0.99/1.18 (~c2_1(a2342)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[16, 2831])).
% 0.99/1.18 tff(2834,plain,
% 0.99/1.18 (~c2_1(a2306)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[236, 2745])).
% 0.99/1.18 tff(2835,plain,
% 0.99/1.18 (c2_1(a2315)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[734, 1940])).
% 0.99/1.18 tff(2836,plain,
% 0.99/1.18 (~c3_1(a2306)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[265, 2745])).
% 0.99/1.18 tff(2837,plain,
% 0.99/1.18 (c3_1(a2342)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[24, 2831])).
% 0.99/1.18 tff(2838,assumption,(c0_1(a2315)), introduced(assumption)).
% 0.99/1.18 tff(2839,assumption,(~c2_1(a2342)), introduced(assumption)).
% 0.99/1.18 tff(2840,assumption,(c3_1(a2342)), introduced(assumption)).
% 0.99/1.18 tff(2841,assumption,(c0_1(a2342)), introduced(assumption)).
% 0.99/1.18 tff(2842,assumption,(c2_1(a2315)), introduced(assumption)).
% 0.99/1.18 tff(2843,assumption,(c1_1(a2315)), introduced(assumption)).
% 0.99/1.18 tff(2844,plain,
% 0.99/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2845,plain,
% 0.99/1.18 (((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306)) <=> (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2846,plain,
% 0.99/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342))))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[2845])).
% 0.99/1.18 tff(2847,plain,
% 0.99/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 0.99/1.18 inference(transitivity,[status(thm)],[2846, 2844])).
% 0.99/1.18 tff(2848,plain,
% 0.99/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(2849,plain,
% 0.99/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | (~c0_1(a2315)) | (~c3_1(a2342)) | (~c0_1(a2342))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2848, 2847])).
% 0.99/1.18 tff(2850,plain,
% 0.99/1.18 ($false),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2849, 160, 2843, 2842, 2841, 2840, 2839, 365, 364, 363, 362, 2838])).
% 0.99/1.18 tff(2851,plain,((~c0_1(a2315)) | (~c1_1(a2315)) | (~c2_1(a2315)) | (~c0_1(a2342)) | (~c3_1(a2342)) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.18 tff(2852,plain,
% 0.99/1.18 (~c0_1(a2315)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2851, 2837, 2836, 2835, 2834, 2833, 2832, 2746, 1941])).
% 0.99/1.18 tff(2853,assumption,(hskp21), introduced(assumption)).
% 0.99/1.18 tff(2854,plain,
% 0.99/1.18 (((~hskp21) | (~c3_1(a2324))) <=> ((~hskp21) | (~c3_1(a2324)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2855,plain,
% 0.99/1.18 (((~c3_1(a2324)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a2324)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2856,axiom,((~c3_1(a2324)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.99/1.18 tff(2857,plain,
% 0.99/1.18 ((~hskp21) | (~c3_1(a2324))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2856, 2855])).
% 0.99/1.18 tff(2858,plain,
% 0.99/1.18 ((~hskp21) | (~c3_1(a2324))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2857, 2854])).
% 0.99/1.18 tff(2859,plain,
% 0.99/1.18 (~c3_1(a2324)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2858, 2853])).
% 0.99/1.18 tff(2860,plain,
% 0.99/1.18 (((~hskp21) | (~c0_1(a2324))) <=> ((~hskp21) | (~c0_1(a2324)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2861,plain,
% 0.99/1.18 (((~c0_1(a2324)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a2324)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2862,axiom,((~c0_1(a2324)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.99/1.18 tff(2863,plain,
% 0.99/1.18 ((~hskp21) | (~c0_1(a2324))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 0.99/1.18 tff(2864,plain,
% 0.99/1.18 ((~hskp21) | (~c0_1(a2324))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2863, 2860])).
% 0.99/1.18 tff(2865,plain,
% 0.99/1.18 (~c0_1(a2324)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2864, 2853])).
% 0.99/1.18 tff(2866,plain,
% 0.99/1.18 (((~hskp21) | c1_1(a2324)) <=> ((~hskp21) | c1_1(a2324))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2867,axiom,((~hskp21) | c1_1(a2324)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.99/1.18 tff(2868,plain,
% 0.99/1.18 ((~hskp21) | c1_1(a2324)),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2867, 2866])).
% 0.99/1.18 tff(2869,plain,
% 0.99/1.18 ((~hskp21) | c1_1(a2324)),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2868, 2866])).
% 0.99/1.18 tff(2870,plain,
% 0.99/1.18 ((~hskp21) | c1_1(a2324)),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2869, 2866])).
% 0.99/1.18 tff(2871,plain,
% 0.99/1.18 ((~hskp21) | c1_1(a2324)),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2870, 2866])).
% 0.99/1.18 tff(2872,plain,
% 0.99/1.18 ((~hskp21) | c1_1(a2324)),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2871, 2866])).
% 0.99/1.18 tff(2873,plain,
% 0.99/1.18 (c1_1(a2324)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2872, 2853])).
% 0.99/1.18 tff(2874,plain,
% 0.99/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2875,plain,
% 0.99/1.18 (((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324))) <=> (c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2876,plain,
% 0.99/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324))))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[2875])).
% 0.99/1.18 tff(2877,plain,
% 0.99/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 0.99/1.18 inference(transitivity,[status(thm)],[2876, 2874])).
% 0.99/1.18 tff(2878,plain,
% 0.99/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2287) | (~c0_1(a2287)) | (~c2_1(a2287)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(2879,plain,
% 0.99/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2287)) | c3_1(a2287) | (~c0_1(a2287)) | (~c1_1(a2324)) | (~c2_1(a2324))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2878, 2877])).
% 0.99/1.18 tff(2880,plain,
% 0.99/1.18 (~c2_1(a2324)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2879, 160, 2873, 1312, 1311, 2865, 2859, 675, 1310])).
% 0.99/1.18 tff(2881,assumption,(~c0_1(a2315)), introduced(assumption)).
% 0.99/1.18 tff(2882,plain,
% 0.99/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2883,plain,
% 0.99/1.18 (((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2884,plain,
% 0.99/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327))))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[2883])).
% 0.99/1.18 tff(2885,plain,
% 0.99/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327)))),
% 0.99/1.18 inference(transitivity,[status(thm)],[2884, 2882])).
% 0.99/1.18 tff(2886,plain,
% 0.99/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(2887,plain,
% 0.99/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | c2_1(a2324) | (~c3_1(a2327))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[2886, 2885])).
% 0.99/1.18 tff(2888,plain,
% 0.99/1.18 ($false),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2887, 160, 2843, 2842, 1333, 1361, 1332, 2865, 2859, 1162, 2881, 2880])).
% 0.99/1.18 tff(2889,plain,((~hskp21) | (~c1_1(a2315)) | (~c2_1(a2315)) | (~c3_1(a2327)) | c0_1(a2327) | c2_1(a2327) | c0_1(a2315) | (~c0_1(a2287)) | (~c2_1(a2287)) | c3_1(a2287)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.18 tff(2890,plain,
% 0.99/1.18 (~hskp21),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[2889, 1941, 2835, 2708, 2720, 2707, 2852, 2801, 2800, 2803])).
% 0.99/1.18 tff(2891,plain,
% 0.99/1.18 (^[U: $i] : refl((hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.99/1.18 inference(bind,[status(th)],[])).
% 0.99/1.18 tff(2892,plain,
% 0.99/1.18 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.99/1.18 inference(quant_intro,[status(thm)],[2891])).
% 0.99/1.18 tff(2893,plain,
% 0.99/1.18 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(2894,plain,
% 0.99/1.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp16) <=> ((hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp16))), rewrite(((hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp16) <=> (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(2895,plain,
% 0.99/1.19 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp16) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[2894])).
% 0.99/1.19 tff(2896,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.99/1.19 tff(2897,plain,
% 0.99/1.19 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[2896, 2895])).
% 0.99/1.19 tff(2898,plain,
% 0.99/1.19 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[2897, 2893])).
% 0.99/1.19 tff(2899,plain,(
% 0.99/1.19 ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.99/1.19 inference(skolemize,[status(sab)],[2898])).
% 0.99/1.19 tff(2900,plain,
% 0.99/1.19 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[2899, 2892])).
% 0.99/1.19 tff(2901,plain,
% 0.99/1.19 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(2902,plain,
% 0.99/1.19 ((hskp21 | hskp16 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277))) <=> (hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(2903,plain,
% 0.99/1.19 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277)))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[2902])).
% 0.99/1.19 tff(2904,plain,
% 0.99/1.19 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277))),
% 0.99/1.19 inference(transitivity,[status(thm)],[2903, 2901])).
% 0.99/1.19 tff(2905,plain,
% 0.99/1.19 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c3_1(a2277) | (~c0_1(a2277)) | (~c1_1(a2277)))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(2906,plain,
% 0.99/1.19 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp21 | hskp16 | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | c3_1(a2277)),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[2905, 2904])).
% 0.99/1.19 tff(2907,plain,
% 0.99/1.19 (hskp21 | hskp16 | (~c1_1(a2277)) | c3_1(a2277)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2906, 160, 2699, 2900])).
% 0.99/1.19 tff(2908,plain,
% 0.99/1.19 (hskp16),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2907, 2890, 1799, 1950])).
% 0.99/1.19 tff(2909,plain,
% 0.99/1.19 (~c3_1(a2304)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[995, 2908])).
% 0.99/1.19 tff(2910,plain,
% 0.99/1.19 (~c2_1(a2304)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[1001, 2908])).
% 0.99/1.19 tff(2911,plain,
% 0.99/1.19 (~c0_1(a2304)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[1007, 2908])).
% 0.99/1.19 tff(2912,plain,
% 0.99/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327)))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(2913,plain,
% 0.99/1.19 (((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327)))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(2914,plain,
% 0.99/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327))))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[2913])).
% 0.99/1.19 tff(2915,plain,
% 0.99/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327)))),
% 0.99/1.19 inference(transitivity,[status(thm)],[2914, 2912])).
% 0.99/1.19 tff(2916,plain,
% 0.99/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2315) | (~c1_1(a2315)) | (~c2_1(a2315)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2304) | c2_1(a2304) | c0_1(a2304))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(2917,plain,
% 0.99/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2304) | c2_1(a2304) | c3_1(a2304) | (~ndr1_0) | (~c2_1(a2315)) | (~c1_1(a2315)) | c0_1(a2315) | (~c3_1(a2327))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[2916, 2915])).
% 0.99/1.19 tff(2918,plain,
% 0.99/1.19 ($false),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2917, 160, 1941, 2835, 2708, 2720, 2707, 2911, 2910, 2909, 1162, 2852])).
% 0.99/1.19 tff(2919,plain,(c1_1(a2282) | hskp28 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.19 tff(2920,plain,
% 0.99/1.19 (c1_1(a2282)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2919, 35, 34])).
% 0.99/1.19 tff(2921,plain,
% 0.99/1.19 ($false),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[1428, 317, 318, 35, 1933, 1942, 1932, 1092, 319])).
% 0.99/1.19 tff(2922,plain,((~hskp17) | hskp28 | (~c1_1(a2282))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.19 tff(2923,plain,
% 0.99/1.19 (~hskp17),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2922, 35, 2920])).
% 0.99/1.19 tff(2924,plain,
% 0.99/1.19 (hskp17 | c3_1(a2277) | (~c1_1(a2282))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2435, 160, 1933, 1799, 1942, 34, 1440])).
% 0.99/1.19 tff(2925,plain,
% 0.99/1.19 (c3_1(a2277)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2924, 2923, 2920])).
% 0.99/1.19 tff(2926,plain,
% 0.99/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(2927,plain,
% 0.99/1.19 (((~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323))) <=> (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(2928,plain,
% 0.99/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[2927])).
% 0.99/1.19 tff(2929,plain,
% 0.99/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.99/1.19 inference(transitivity,[status(thm)],[2928, 2926])).
% 0.99/1.19 tff(2930,plain,
% 0.99/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(2931,plain,
% 0.99/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[2930, 2929])).
% 0.99/1.19 tff(2932,plain,
% 0.99/1.19 ((~c1_1(a2277)) | (~c3_1(a2277)) | (~c0_1(a2323))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2931, 160, 907, 2699, 906, 34, 88])).
% 0.99/1.19 tff(2933,plain,
% 0.99/1.19 (~c0_1(a2323)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2932, 2925, 1799])).
% 0.99/1.19 tff(2934,plain,
% 0.99/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(2935,plain,
% 0.99/1.19 (((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323))) <=> (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(2936,plain,
% 0.99/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[2935])).
% 0.99/1.19 tff(2937,plain,
% 0.99/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 0.99/1.19 inference(transitivity,[status(thm)],[2936, 2934])).
% 0.99/1.19 tff(2938,plain,
% 0.99/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2277) | (~c3_1(a2277)) | (~c1_1(a2277)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(2939,plain,
% 0.99/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c1_1(a2277)) | (~c3_1(a2277)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[2938, 2937])).
% 0.99/1.19 tff(2940,plain,
% 0.99/1.19 ($false),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2939, 160, 908, 907, 1799, 906, 34, 196, 2925, 2933])).
% 0.99/1.19 tff(2941,plain,(hskp28 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.19 tff(2942,plain,
% 0.99/1.19 (hskp28),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[2941, 34])).
% 0.99/1.19 tff(2943,plain,
% 0.99/1.19 (c1_1(a2278)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[565, 2942])).
% 0.99/1.19 tff(2944,plain,
% 0.99/1.19 (c3_1(a2278)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[557, 2942])).
% 0.99/1.19 tff(2945,plain,
% 0.99/1.19 (c0_1(a2278)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[573, 2942])).
% 1.02/1.19 tff(2946,plain,
% 1.02/1.19 (c2_1(a2278)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1993, 2945, 2944, 2943])).
% 1.02/1.19 tff(2947,plain,
% 1.02/1.19 (hskp1),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[909, 679])).
% 1.02/1.19 tff(2948,plain,
% 1.02/1.19 (c1_1(a2277)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[336, 2947])).
% 1.02/1.19 tff(2949,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2950,plain,
% 1.02/1.19 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323))) <=> (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2951,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[2950])).
% 1.02/1.19 tff(2952,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[2951, 2949])).
% 1.02/1.19 tff(2953,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2323) | (~c3_1(a2323)) | (~c0_1(a2323)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(2954,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2323) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2323)) | (~c0_1(a2323))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2953, 2952])).
% 1.02/1.19 tff(2955,plain,
% 1.02/1.19 ((~c1_1(a2277)) | (~c0_1(a2323))),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2954, 160, 2945, 2943, 2944, 907, 2699, 906, 34, 88])).
% 1.02/1.19 tff(2956,plain,
% 1.02/1.19 (~c0_1(a2323)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2955, 2948])).
% 1.02/1.19 tff(2957,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2958,plain,
% 1.02/1.19 (((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323))) <=> (c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2959,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[2958])).
% 1.02/1.19 tff(2960,plain,
% 1.02/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323))),
% 1.02/1.19 inference(transitivity,[status(thm)],[2959, 2957])).
% 1.02/1.19 tff(2961,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2280) | (~c3_1(a2280)) | (~c1_1(a2280)) | c1_1(a2323) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323) | c1_1(a2323) | (~c2_1(a2323)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(2962,plain,
% 1.02/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a2323) | c2_1(a2280) | (~ndr1_0) | (~c3_1(a2280)) | (~c1_1(a2280)) | (~c2_1(a2323)) | (~c3_1(a2323)) | c0_1(a2323)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2961, 2960])).
% 1.02/1.19 tff(2963,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2962, 160, 908, 907, 1820, 1819, 906, 1818, 196, 2956])).
% 1.02/1.19 tff(2964,plain,(hskp4 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(2965,plain,
% 1.02/1.19 (hskp4),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2964, 34])).
% 1.02/1.19 tff(2966,plain,
% 1.02/1.19 (~c3_1(a2282)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[172, 2965])).
% 1.02/1.19 tff(2967,plain,
% 1.02/1.19 (c2_1(a2282)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[223, 2965])).
% 1.02/1.19 tff(2968,plain,
% 1.02/1.19 (hskp0),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2405, 160, 2945, 2943, 2944, 2967, 2966, 2395, 37])).
% 1.02/1.19 tff(2969,plain,
% 1.02/1.19 (c1_1(a2276)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[823, 2968])).
% 1.02/1.19 tff(2970,plain,
% 1.02/1.19 (~c0_1(a2276)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[807, 2968])).
% 1.02/1.19 tff(2971,plain,
% 1.02/1.19 (c3_1(a2276)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[815, 2968])).
% 1.02/1.19 tff(2972,assumption,(~hskp19), introduced(assumption)).
% 1.02/1.19 tff(2973,plain,
% 1.02/1.19 (~c0_1(a2282)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[178, 2965])).
% 1.02/1.19 tff(2974,plain,
% 1.02/1.19 ((~c1_1(a2277)) | (~c3_1(a2277)) | c1_1(a2282)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1948, 160, 908, 907, 2967, 906, 2973, 34, 196])).
% 1.02/1.19 tff(2975,plain,
% 1.02/1.19 (~c3_1(a2277)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2974, 601, 37])).
% 1.02/1.19 tff(2976,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1967, 2975, 601, 2972])).
% 1.02/1.19 tff(2977,plain,((~c1_1(a2277)) | hskp19 | c2_1(a2277) | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(2978,plain,
% 1.02/1.19 (~c1_1(a2277)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2977, 2972, 34, 37])).
% 1.02/1.19 tff(2979,plain,
% 1.02/1.19 (~hskp1),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[336, 2978])).
% 1.02/1.19 tff(2980,plain,
% 1.02/1.19 (~hskp12),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2022, 2979, 2945, 2943, 2946])).
% 1.02/1.19 tff(2981,plain,
% 1.02/1.19 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2982,plain,
% 1.02/1.19 ((hskp19 | hskp12 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277))) <=> (hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2983,plain,
% 1.02/1.19 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[2982])).
% 1.02/1.19 tff(2984,plain,
% 1.02/1.19 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[2983, 2981])).
% 1.02/1.19 tff(2985,plain,
% 1.02/1.19 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2277) | (~c0_1(a2277)) | (~c3_1(a2277)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(2986,plain,
% 1.02/1.19 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c3_1(a2277))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 1.02/1.19 tff(2987,plain,
% 1.02/1.19 (hskp19 | hskp12 | (~c0_1(a2277)) | (~c3_1(a2277))),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2986, 160, 34, 10])).
% 1.02/1.19 tff(2988,plain,
% 1.02/1.19 (~c3_1(a2277)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2987, 2980, 2699, 2972])).
% 1.02/1.19 tff(2989,plain,
% 1.02/1.19 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2990,plain,
% 1.02/1.19 ((hskp12 | (~ndr1_0) | c1_1(a2277) | c3_1(a2277) | (~c0_1(a2277))) <=> (hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2991,plain,
% 1.02/1.19 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277)))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[2990])).
% 1.02/1.19 tff(2992,plain,
% 1.02/1.19 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.02/1.19 inference(transitivity,[status(thm)],[2991, 2989])).
% 1.02/1.19 tff(2993,plain,
% 1.02/1.19 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(2994,plain,
% 1.02/1.19 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2993, 2992])).
% 1.02/1.19 tff(2995,plain,
% 1.02/1.19 (hskp12 | c1_1(a2277) | c3_1(a2277)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2994, 160, 2699, 630])).
% 1.02/1.19 tff(2996,plain,
% 1.02/1.19 ($false),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2995, 2988, 2980, 2978])).
% 1.02/1.19 tff(2997,plain,(hskp19 | c2_1(a2277) | c1_1(a2282)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.19 tff(2998,plain,
% 1.02/1.19 (hskp19),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2997, 37, 34])).
% 1.02/1.19 tff(2999,plain,
% 1.02/1.19 (hskp17),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2744, 2998, 2971, 2970, 2969])).
% 1.02/1.19 tff(3000,plain,
% 1.02/1.19 (~c3_1(a2306)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[265, 2999])).
% 1.02/1.19 tff(3001,plain,
% 1.02/1.19 (~c2_1(a2306)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[236, 2999])).
% 1.02/1.19 tff(3002,plain,
% 1.02/1.19 (~c1_1(a2306)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[242, 2999])).
% 1.02/1.19 tff(3003,plain,
% 1.02/1.19 (hskp1),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2035, 3001, 2942, 3002, 3000])).
% 1.02/1.19 tff(3004,plain,
% 1.02/1.19 (c1_1(a2277)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[336, 3003])).
% 1.02/1.19 tff(3005,assumption,(hskp24), introduced(assumption)).
% 1.02/1.19 tff(3006,plain,
% 1.02/1.19 (((~hskp24) | (~c1_1(a2337))) <=> ((~hskp24) | (~c1_1(a2337)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(3007,plain,
% 1.02/1.19 (((~c1_1(a2337)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a2337)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(3008,axiom,((~c1_1(a2337)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.02/1.19 tff(3009,plain,
% 1.02/1.19 ((~hskp24) | (~c1_1(a2337))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[3008, 3007])).
% 1.02/1.19 tff(3010,plain,
% 1.02/1.19 ((~hskp24) | (~c1_1(a2337))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[3009, 3006])).
% 1.02/1.19 tff(3011,plain,
% 1.02/1.19 (~c1_1(a2337)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[3010, 3005])).
% 1.02/1.19 tff(3012,plain,
% 1.02/1.19 (((~hskp24) | c3_1(a2337)) <=> ((~hskp24) | c3_1(a2337))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(3013,axiom,((~hskp24) | c3_1(a2337)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.02/1.20 tff(3014,plain,
% 1.02/1.20 ((~hskp24) | c3_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3013, 3012])).
% 1.02/1.20 tff(3015,plain,
% 1.02/1.20 ((~hskp24) | c3_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3014, 3012])).
% 1.02/1.20 tff(3016,plain,
% 1.02/1.20 ((~hskp24) | c3_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3015, 3012])).
% 1.02/1.20 tff(3017,plain,
% 1.02/1.20 ((~hskp24) | c3_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3016, 3012])).
% 1.02/1.20 tff(3018,plain,
% 1.02/1.20 ((~hskp24) | c3_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3017, 3012])).
% 1.02/1.20 tff(3019,plain,
% 1.02/1.20 (c3_1(a2337)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3018, 3005])).
% 1.02/1.20 tff(3020,plain,
% 1.02/1.20 (((~hskp24) | c0_1(a2337)) <=> ((~hskp24) | c0_1(a2337))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3021,axiom,((~hskp24) | c0_1(a2337)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.02/1.20 tff(3022,plain,
% 1.02/1.20 ((~hskp24) | c0_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3021, 3020])).
% 1.02/1.20 tff(3023,plain,
% 1.02/1.20 ((~hskp24) | c0_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3022, 3020])).
% 1.02/1.20 tff(3024,plain,
% 1.02/1.20 ((~hskp24) | c0_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3023, 3020])).
% 1.02/1.20 tff(3025,plain,
% 1.02/1.20 ((~hskp24) | c0_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3024, 3020])).
% 1.02/1.20 tff(3026,plain,
% 1.02/1.20 ((~hskp24) | c0_1(a2337)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3025, 3020])).
% 1.02/1.20 tff(3027,plain,
% 1.02/1.20 (c0_1(a2337)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3026, 3005])).
% 1.02/1.20 tff(3028,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3029,plain,
% 1.02/1.20 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2337) | (~c3_1(a2337)) | (~c0_1(a2337))) <=> (c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3030,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2337) | (~c3_1(a2337)) | (~c0_1(a2337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[3029])).
% 1.02/1.20 tff(3031,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2337) | (~c3_1(a2337)) | (~c0_1(a2337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[3030, 3028])).
% 1.02/1.20 tff(3032,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2337) | (~c3_1(a2337)) | (~c0_1(a2337)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(3033,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2337) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2337)) | (~c0_1(a2337))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3032, 3031])).
% 1.02/1.20 tff(3034,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3033, 160, 613, 612, 611, 3027, 3019, 602, 601, 3011, 34, 88])).
% 1.02/1.20 tff(3035,plain,((~hskp24) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c0_1(a2277)) | (~c1_1(a2277)) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(3036,plain,
% 1.02/1.20 (~hskp24),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3035, 3004, 2699, 2943, 2945, 2944, 34])).
% 1.02/1.20 tff(3037,plain,
% 1.02/1.20 (~c3_1(a2277)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2974, 3004, 37])).
% 1.02/1.20 tff(3038,plain,
% 1.02/1.20 (^[U: $i] : refl((hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(3039,plain,
% 1.02/1.20 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[3038])).
% 1.02/1.20 tff(3040,plain,
% 1.02/1.20 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3041,plain,
% 1.02/1.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp25) <=> ((hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25))), rewrite(((hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp25) <=> (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(3042,plain,
% 1.02/1.20 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp25) <=> ![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[3041])).
% 1.02/1.20 tff(3043,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp24) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.02/1.20 tff(3044,plain,
% 1.02/1.20 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3043, 3042])).
% 1.02/1.20 tff(3045,plain,
% 1.02/1.20 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3044, 3040])).
% 1.02/1.20 tff(3046,plain,(
% 1.02/1.20 ![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.02/1.20 inference(skolemize,[status(sab)],[3045])).
% 1.02/1.20 tff(3047,plain,
% 1.02/1.20 (![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3046, 3039])).
% 1.02/1.20 tff(3048,plain,
% 1.02/1.20 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3049,plain,
% 1.02/1.20 ((hskp25 | hskp24 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277))) <=> (hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3050,plain,
% 1.02/1.20 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277)))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[3049])).
% 1.02/1.20 tff(3051,plain,
% 1.02/1.20 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277))),
% 1.02/1.20 inference(transitivity,[status(thm)],[3050, 3048])).
% 1.02/1.20 tff(3052,plain,
% 1.02/1.20 ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2277) | c3_1(a2277) | (~c0_1(a2277)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(3053,plain,
% 1.02/1.20 ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | c3_1(a2277)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3052, 3051])).
% 1.02/1.20 tff(3054,plain,
% 1.02/1.20 (hskp25 | hskp24 | (~c0_1(a2277)) | c3_1(a2277)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3053, 160, 34, 3047])).
% 1.02/1.20 tff(3055,plain,
% 1.02/1.20 (hskp25),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3054, 3037, 2699, 3036])).
% 1.02/1.20 tff(3056,plain,
% 1.02/1.20 (~c2_1(a2342)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[16, 3055])).
% 1.02/1.20 tff(3057,plain,
% 1.02/1.20 (c3_1(a2342)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[24, 3055])).
% 1.02/1.20 tff(3058,plain,
% 1.02/1.20 (c0_1(a2342)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[32, 3055])).
% 1.02/1.20 tff(3059,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3060,plain,
% 1.02/1.20 (((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306)) <=> (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3061,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[3060])).
% 1.02/1.20 tff(3062,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[3061, 3059])).
% 1.02/1.20 tff(3063,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2306) | c2_1(a2306) | c1_1(a2306))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(3064,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2306) | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2342)) | (~c0_1(a2342))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3063, 3062])).
% 1.02/1.20 tff(3065,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3064, 160, 2945, 2943, 3058, 3057, 3056, 3002, 3001, 3000, 362, 2946])).
% 1.02/1.20 tff(3066,plain,(c1_1(a2282) | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(3067,plain,
% 1.02/1.20 (c1_1(a2282)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3066, 34])).
% 1.02/1.20 tff(3068,plain,
% 1.02/1.20 (~hskp10),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1124, 3067, 2973, 2966, 2967])).
% 1.02/1.20 tff(3069,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3070,plain,
% 1.02/1.20 ((hskp18 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2278)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282))) <=> (hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3071,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2278)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[3070])).
% 1.02/1.20 tff(3072,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2278)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[3071, 3069])).
% 1.02/1.20 tff(3073,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c2_1(a2278)) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(3074,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp18 | c0_1(a2282) | (~ndr1_0) | (~c0_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2282)) | (~c2_1(a2282))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3073, 3072])).
% 1.02/1.20 tff(3075,plain,
% 1.02/1.20 (hskp18 | (~c1_1(a2282))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3074, 160, 2945, 2944, 2967, 2973, 2497, 2946])).
% 1.02/1.20 tff(3076,plain,
% 1.02/1.20 (hskp18),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3075, 3067])).
% 1.02/1.20 tff(3077,plain,
% 1.02/1.20 (~c1_1(a2308)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2515, 3076])).
% 1.02/1.20 tff(3078,plain,
% 1.02/1.20 (~c2_1(a2308)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2509, 3076])).
% 1.02/1.20 tff(3079,plain,
% 1.02/1.20 (c3_1(a2308)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2530, 3076])).
% 1.02/1.20 tff(3080,plain,
% 1.02/1.20 (c2_1(a2278)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1993, 613, 611, 612])).
% 1.02/1.20 tff(3081,plain,
% 1.02/1.20 (~hskp12),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2022, 36, 613, 612, 3080])).
% 1.02/1.20 tff(3082,plain,
% 1.02/1.20 (hskp13),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1247, 3081])).
% 1.02/1.20 tff(3083,plain,
% 1.02/1.20 (~c3_1(a2299)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1201, 3082])).
% 1.02/1.20 tff(3084,plain,
% 1.02/1.20 (~c1_1(a2299)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1215, 3082])).
% 1.02/1.20 tff(3085,plain,
% 1.02/1.20 (c2_1(a2299)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1209, 3082])).
% 1.02/1.20 tff(3086,plain,
% 1.02/1.20 (hskp0),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2618, 160, 613, 612, 611, 3085, 3084, 3083, 2395])).
% 1.02/1.20 tff(3087,plain,
% 1.02/1.20 (c1_1(a2276)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[823, 3086])).
% 1.02/1.20 tff(3088,plain,
% 1.02/1.20 (~c0_1(a2276)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[807, 3086])).
% 1.02/1.20 tff(3089,plain,
% 1.02/1.20 (c3_1(a2276)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[815, 3086])).
% 1.02/1.20 tff(3090,assumption,(~c2_1(a2308)), introduced(assumption)).
% 1.02/1.20 tff(3091,assumption,(~c1_1(a2308)), introduced(assumption)).
% 1.02/1.20 tff(3092,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3093,plain,
% 1.02/1.20 ((hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308)) <=> (hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3094,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308)))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[3093])).
% 1.02/1.20 tff(3095,plain,
% 1.02/1.20 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308))),
% 1.02/1.20 inference(transitivity,[status(thm)],[3094, 3092])).
% 1.02/1.20 tff(3096,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2299) | c3_1(a2299) | (~c2_1(a2299)) | c2_1(a2308) | c1_1(a2308) | c0_1(a2308))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(3097,plain,
% 1.02/1.20 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a2308) | c2_1(a2308) | c1_1(a2299) | c3_1(a2299) | (~ndr1_0) | (~c2_1(a2299)) | c0_1(a2308)),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 1.02/1.20 tff(3098,plain,
% 1.02/1.20 (c0_1(a2308)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3097, 160, 36, 3085, 3091, 3090, 3084, 3083, 206])).
% 1.02/1.20 tff(3099,assumption,(c3_1(a2308)), introduced(assumption)).
% 1.02/1.20 tff(3100,plain,
% 1.02/1.20 (hskp19 | hskp12 | (~c0_1(a2308))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2537, 160, 3099, 3090, 10])).
% 1.02/1.20 tff(3101,plain,
% 1.02/1.20 (hskp19),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3100, 3098, 3081])).
% 1.02/1.20 tff(3102,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2744, 3101, 3089, 825, 3088, 3087])).
% 1.02/1.20 tff(3103,plain,(hskp1 | hskp17 | (~c3_1(a2308)) | c2_1(a2308) | c1_1(a2308) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278))), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(3104,plain,
% 1.02/1.20 (hskp1),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3103, 825, 3079, 3078, 3077, 2945, 2943, 2944])).
% 1.02/1.20 tff(3105,plain,
% 1.02/1.20 (c1_1(a2277)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[336, 3104])).
% 1.02/1.20 tff(3106,plain,
% 1.02/1.20 (hskp17 | (~c1_1(a2277)) | c3_1(a2277) | (~c1_1(a2282))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2435, 160, 2967, 2973, 34, 1440])).
% 1.02/1.20 tff(3107,plain,
% 1.02/1.20 (c3_1(a2277)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3106, 3105, 3067, 825])).
% 1.02/1.20 tff(3108,plain,
% 1.02/1.20 (c1_1(a2302)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2444, 3107, 3105])).
% 1.02/1.20 tff(3109,plain,
% 1.02/1.20 (~hskp19),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1873, 3108, 825])).
% 1.02/1.20 tff(3110,plain,
% 1.02/1.20 ((hskp19 | hskp10 | hskp8) <=> (hskp19 | hskp10 | hskp8)),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3111,plain,
% 1.02/1.20 (((hskp10 | hskp8) | hskp19) <=> (hskp19 | hskp10 | hskp8)),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3112,plain,
% 1.02/1.20 ((hskp8 | hskp10) <=> (hskp10 | hskp8)),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3113,plain,
% 1.02/1.20 (((hskp8 | hskp10) | hskp19) <=> ((hskp10 | hskp8) | hskp19)),
% 1.02/1.20 inference(monotonicity,[status(thm)],[3112])).
% 1.02/1.20 tff(3114,plain,
% 1.02/1.20 (((hskp8 | hskp10) | hskp19) <=> (hskp19 | hskp10 | hskp8)),
% 1.02/1.20 inference(transitivity,[status(thm)],[3113, 3111])).
% 1.02/1.20 tff(3115,axiom,((hskp8 | hskp10) | hskp19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.02/1.20 tff(3116,plain,
% 1.02/1.20 (hskp19 | hskp10 | hskp8),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3115, 3114])).
% 1.02/1.20 tff(3117,plain,
% 1.02/1.20 (hskp19 | hskp10 | hskp8),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3116, 3110])).
% 1.02/1.20 tff(3118,plain,
% 1.02/1.20 (hskp19 | hskp10 | hskp8),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3117, 3110])).
% 1.02/1.20 tff(3119,plain,
% 1.02/1.20 (hskp19 | hskp10 | hskp8),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3118, 3110])).
% 1.02/1.20 tff(3120,plain,
% 1.02/1.20 (hskp19 | hskp10 | hskp8),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3119, 3110])).
% 1.02/1.20 tff(3121,plain,
% 1.02/1.20 (hskp8),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3120, 3109, 3068])).
% 1.02/1.20 tff(3122,plain,
% 1.02/1.20 (c0_1(a2287)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1300, 3121])).
% 1.02/1.20 tff(3123,plain,
% 1.02/1.20 (c2_1(a2287)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1308, 3121])).
% 1.02/1.20 tff(3124,plain,
% 1.02/1.20 (c3_1(a2287)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[1320, 3123, 3067, 2967, 2973, 2966, 3122])).
% 1.02/1.20 tff(3125,plain,
% 1.02/1.20 (~c1_1(a2287)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2238, 3121])).
% 1.02/1.20 tff(3126,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3127,plain,
% 1.02/1.20 (((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2287) | (~c3_1(a2287)) | (~c0_1(a2287))) <=> (c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3128,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2287) | (~c3_1(a2287)) | (~c0_1(a2287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[3127])).
% 1.02/1.20 tff(3129,plain,
% 1.02/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2287) | (~c3_1(a2287)) | (~c0_1(a2287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[3128, 3126])).
% 1.02/1.20 tff(3130,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c3_1(a2278)) | (~c1_1(a2278)) | c2_1(a2277) | (~c1_1(a2277)) | (~c0_1(a2277)) | c1_1(a2287) | (~c3_1(a2287)) | (~c0_1(a2287)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(3131,plain,
% 1.02/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a2287) | c2_1(a2277) | (~ndr1_0) | (~c0_1(a2277)) | (~c1_1(a2277)) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c3_1(a2278)) | (~c3_1(a2287)) | (~c0_1(a2287))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3130, 3129])).
% 1.02/1.20 tff(3132,plain,
% 1.02/1.20 ($false),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3131, 160, 2945, 2943, 2944, 3122, 2699, 3105, 3125, 34, 88, 3124])).
% 1.02/1.20 tff(3133,plain,(hskp17 | c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.20 tff(3134,plain,
% 1.02/1.20 (hskp17),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3133, 34])).
% 1.02/1.20 tff(3135,plain,
% 1.02/1.20 (~c3_1(a2306)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[265, 3134])).
% 1.02/1.20 tff(3136,plain,
% 1.02/1.20 (~c1_1(a2306)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[242, 3134])).
% 1.02/1.20 tff(3137,plain,
% 1.02/1.20 (~c2_1(a2306)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[236, 3134])).
% 1.02/1.20 tff(3138,plain,
% 1.02/1.20 (hskp1),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[2035, 3137, 2942, 3136, 3135])).
% 1.02/1.20 tff(3139,plain,
% 1.02/1.20 (c1_1(a2277)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[336, 3138])).
% 1.02/1.20 tff(3140,plain,
% 1.02/1.20 (~hskp24),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[3035, 3139, 2699, 2943, 2945, 2944, 34])).
% 1.02/1.20 tff(3141,plain,
% 1.02/1.20 (^[U: $i] : refl((hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(3142,plain,
% 1.02/1.20 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[3141])).
% 1.02/1.20 tff(3143,plain,
% 1.02/1.20 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3144,plain,
% 1.02/1.20 (^[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)) | hskp24) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp21) <=> ((hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21))), rewrite(((hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp21) <=> (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(3145,plain,
% 1.02/1.20 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp21) <=> ![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[3144])).
% 1.02/1.20 tff(3146,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.02/1.20 tff(3147,plain,
% 1.02/1.20 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 1.02/1.20 tff(3148,plain,
% 1.02/1.20 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3147, 3143])).
% 1.02/1.20 tff(3149,plain,(
% 1.02/1.20 ![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.02/1.20 inference(skolemize,[status(sab)],[3148])).
% 1.02/1.20 tff(3150,plain,
% 1.02/1.20 (![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[3149, 3142])).
% 1.02/1.20 tff(3151,plain,
% 1.02/1.20 (((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))) <=> ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3152,plain,
% 1.02/1.20 ((hskp24 | hskp21 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323))) <=> (hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(3153,plain,
% 1.02/1.20 (((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[3152])).
% 1.02/1.20 tff(3154,plain,
% 1.02/1.20 (((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))) <=> ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[3153, 3151])).
% 1.02/1.21 tff(3155,plain,
% 1.02/1.21 ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp21 | (~ndr1_0) | c1_1(a2323) | (~c3_1(a2323)) | (~c2_1(a2323)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(3156,plain,
% 1.02/1.21 ((~![U: $i] : (hskp24 | hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp21 | c1_1(a2323) | (~ndr1_0) | (~c2_1(a2323)) | (~c3_1(a2323))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[3155, 3154])).
% 1.02/1.21 tff(3157,plain,
% 1.02/1.21 (hskp24 | hskp21),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3156, 160, 908, 907, 906, 3150])).
% 1.02/1.21 tff(3158,plain,
% 1.02/1.21 (hskp21),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3157, 3140])).
% 1.02/1.21 tff(3159,plain,
% 1.02/1.21 (~c3_1(a2324)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2858, 3158])).
% 1.02/1.21 tff(3160,plain,
% 1.02/1.21 (~c0_1(a2324)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2864, 3158])).
% 1.02/1.21 tff(3161,plain,
% 1.02/1.21 (hskp23),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1264, 3135, 2973, 3067, 3136, 3068, 3137, 2967])).
% 1.02/1.21 tff(3162,plain,
% 1.02/1.21 (~c2_1(a2327)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[278, 3161])).
% 1.02/1.21 tff(3163,plain,
% 1.02/1.21 (~c0_1(a2327)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[299, 3161])).
% 1.02/1.21 tff(3164,plain,
% 1.02/1.21 (c3_1(a2327)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[286, 3161])).
% 1.02/1.21 tff(3165,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3166,plain,
% 1.02/1.21 (((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324)) <=> (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3167,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[3166])).
% 1.02/1.21 tff(3168,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[3167, 3165])).
% 1.02/1.21 tff(3169,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a2282) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2327) | c0_1(a2327) | (~c3_1(a2327)) | c3_1(a2324) | c2_1(a2324) | c0_1(a2324))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(3170,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a2327) | c2_1(a2327) | c0_1(a2324) | c3_1(a2324) | c0_1(a2282) | (~ndr1_0) | (~c1_1(a2282)) | (~c2_1(a2282)) | c2_1(a2324) | (~c3_1(a2327))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[3169, 3168])).
% 1.02/1.21 tff(3171,plain,
% 1.02/1.21 (c2_1(a2324)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3170, 160, 3164, 2967, 3163, 3162, 3160, 3159, 2973, 1162, 3067])).
% 1.02/1.21 tff(3172,plain,
% 1.02/1.21 (c0_1(a2306)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1274, 160, 3164, 2967, 3163, 3162, 3137, 3135, 2973, 1162, 3067])).
% 1.02/1.21 tff(3173,plain,
% 1.02/1.21 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3174,plain,
% 1.02/1.21 ((hskp12 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3175,plain,
% 1.02/1.21 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[3174])).
% 1.02/1.21 tff(3176,plain,
% 1.02/1.21 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[3175, 3173])).
% 1.02/1.21 tff(3177,plain,
% 1.02/1.21 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(3178,plain,
% 1.02/1.21 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | c1_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[3177, 3176])).
% 1.02/1.21 tff(3179,plain,
% 1.02/1.21 (hskp12 | (~c0_1(a2306))),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3178, 160, 3136, 3135, 630])).
% 1.02/1.21 tff(3180,plain,
% 1.02/1.21 (hskp12),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3179, 3172])).
% 1.02/1.21 tff(3181,plain,
% 1.02/1.21 (~c3_1(a2295)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[644, 3180])).
% 1.02/1.21 tff(3182,plain,
% 1.02/1.21 (c0_1(a2295)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[652, 3180])).
% 1.02/1.21 tff(3183,plain,
% 1.02/1.21 (c1_1(a2324)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2872, 3158])).
% 1.02/1.21 tff(3184,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3185,plain,
% 1.02/1.21 (((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324))) <=> (c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3186,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[3185])).
% 1.02/1.21 tff(3187,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[3186, 3184])).
% 1.02/1.21 tff(3188,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2324) | (~c1_1(a2324)) | (~c2_1(a2324)) | c3_1(a2295) | (~c0_1(a2295)) | (~c2_1(a2295)) | c0_1(a2324) | (~c2_1(a2324)) | (~c1_1(a2324)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(3189,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2324) | c3_1(a2324) | c3_1(a2295) | (~ndr1_0) | (~c2_1(a2295)) | (~c0_1(a2295)) | (~c1_1(a2324)) | (~c2_1(a2324))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[3188, 3187])).
% 1.02/1.21 tff(3190,plain,
% 1.02/1.21 (~c2_1(a2295)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3189, 160, 3183, 3182, 3160, 3159, 3181, 675, 3171])).
% 1.02/1.21 tff(3191,plain,
% 1.02/1.21 (~c1_1(a2295)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1254, 3180])).
% 1.02/1.21 tff(3192,plain,
% 1.02/1.21 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3193,plain,
% 1.02/1.21 ((hskp25 | hskp24 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306))) <=> (hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3194,plain,
% 1.02/1.21 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[3193])).
% 1.02/1.21 tff(3195,plain,
% 1.02/1.21 (((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))) <=> ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[3194, 3192])).
% 1.02/1.21 tff(3196,plain,
% 1.02/1.21 ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp25 | hskp24 | (~ndr1_0) | c2_1(a2306) | c3_1(a2306) | (~c0_1(a2306)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(3197,plain,
% 1.02/1.21 ((~![U: $i] : (hskp25 | hskp24 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp25 | hskp24 | c2_1(a2306) | c3_1(a2306) | (~ndr1_0) | (~c0_1(a2306))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[3196, 3195])).
% 1.02/1.21 tff(3198,plain,
% 1.02/1.21 (hskp25),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3197, 160, 3140, 3137, 3135, 3047, 3172])).
% 1.02/1.21 tff(3199,plain,
% 1.02/1.21 (~c2_1(a2342)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[16, 3198])).
% 1.02/1.21 tff(3200,plain,
% 1.02/1.21 (c3_1(a2342)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[24, 3198])).
% 1.02/1.21 tff(3201,plain,
% 1.02/1.21 (c0_1(a2342)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[32, 3198])).
% 1.02/1.21 tff(3202,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3203,plain,
% 1.02/1.21 (((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2295) | c2_1(a2295) | c1_1(a2295)) <=> (c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3204,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2295) | c2_1(a2295) | c1_1(a2295))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[3203])).
% 1.02/1.21 tff(3205,plain,
% 1.02/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2295) | c2_1(a2295) | c1_1(a2295))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[3204, 3202])).
% 1.02/1.21 tff(3206,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)) | c3_1(a2295) | c2_1(a2295) | c1_1(a2295))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(3207,plain,
% 1.02/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2342) | c1_1(a2295) | c3_1(a2295) | (~ndr1_0) | (~c0_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)) | c2_1(a2295) | (~c3_1(a2342)) | (~c0_1(a2342))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[3206, 3205])).
% 1.02/1.21 tff(3208,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3207, 160, 2945, 2943, 3201, 3200, 3199, 3191, 3181, 362, 3190, 2946])).
% 1.02/1.21 tff(3209,plain,(c2_1(a2277)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(3210,plain,
% 1.02/1.21 (~hskp1),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[314, 3209])).
% 1.02/1.21 tff(3211,plain,
% 1.02/1.21 (hskp28),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1797, 3210])).
% 1.02/1.21 tff(3212,plain,
% 1.02/1.21 (c1_1(a2278)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[565, 3211])).
% 1.02/1.21 tff(3213,plain,
% 1.02/1.21 (c0_1(a2278)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[573, 3211])).
% 1.02/1.21 tff(3214,plain,
% 1.02/1.21 (c3_1(a2278)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[557, 3211])).
% 1.02/1.21 tff(3215,plain,
% 1.02/1.21 (c2_1(a2278)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1993, 3213, 3214, 3212])).
% 1.02/1.21 tff(3216,plain,
% 1.02/1.21 (~hskp12),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2022, 3215, 3213, 3212, 3210])).
% 1.02/1.21 tff(3217,plain,
% 1.02/1.21 (c1_1(a2306) | c2_1(a2306) | c3_1(a2306)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2035, 3211, 3210])).
% 1.02/1.21 tff(3218,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3217, 318, 319, 317])).
% 1.02/1.21 tff(3219,plain,(~hskp17), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(3220,plain,
% 1.02/1.21 (hskp13),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1247, 3216])).
% 1.02/1.21 tff(3221,plain,
% 1.02/1.21 (~c3_1(a2299)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1201, 3220])).
% 1.02/1.21 tff(3222,plain,
% 1.02/1.21 (~c1_1(a2299)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1215, 3220])).
% 1.02/1.21 tff(3223,plain,
% 1.02/1.21 (c2_1(a2299)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[1209, 3220])).
% 1.02/1.21 tff(3224,plain,
% 1.02/1.21 (hskp0),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2618, 160, 3213, 3212, 3214, 3223, 3222, 3221, 2395])).
% 1.02/1.21 tff(3225,plain,
% 1.02/1.21 (c1_1(a2276)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[823, 3224])).
% 1.02/1.21 tff(3226,plain,
% 1.02/1.21 (~c0_1(a2276)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[807, 3224])).
% 1.02/1.21 tff(3227,plain,
% 1.02/1.21 (c3_1(a2276)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[815, 3224])).
% 1.02/1.21 tff(3228,plain,
% 1.02/1.21 (hskp17 | (~hskp19)),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[2744, 3227, 3226, 3225])).
% 1.02/1.21 tff(3229,plain,
% 1.02/1.21 (~hskp19),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3228, 3219])).
% 1.02/1.21 tff(3230,plain,
% 1.02/1.21 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3231,plain,
% 1.02/1.21 ((hskp19 | hskp12 | (~ndr1_0) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342))) <=> (hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3232,plain,
% 1.02/1.21 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[3231])).
% 1.02/1.21 tff(3233,plain,
% 1.02/1.21 (((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))) <=> ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342)))),
% 1.02/1.21 inference(transitivity,[status(thm)],[3232, 3230])).
% 1.02/1.21 tff(3234,plain,
% 1.02/1.21 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp19 | hskp12 | (~ndr1_0) | c2_1(a2342) | (~c0_1(a2342)) | (~c3_1(a2342)))),
% 1.02/1.21 inference(quant_inst,[status(thm)],[])).
% 1.02/1.21 tff(3235,plain,
% 1.02/1.21 ((~![U: $i] : (hskp19 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp19 | hskp12 | c2_1(a2342) | (~ndr1_0) | (~c3_1(a2342)) | (~c0_1(a2342))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[3234, 3233])).
% 1.02/1.21 tff(3236,plain,
% 1.02/1.21 ($false),
% 1.02/1.21 inference(unit_resolution,[status(thm)],[3235, 160, 3229, 3216, 33, 25, 17, 10])).
% 1.02/1.21 tff(3237,plain,(~hskp25), inference(lemma,lemma(discharge,[]))).
% 1.02/1.21 tff(3238,plain,
% 1.02/1.21 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(3239,plain,
% 1.02/1.21 ((hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278))) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(3240,plain,
% 1.02/1.22 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[3239])).
% 1.02/1.22 tff(3241,plain,
% 1.02/1.22 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278)))),
% 1.02/1.22 inference(transitivity,[status(thm)],[3240, 3238])).
% 1.02/1.22 tff(3242,plain,
% 1.02/1.22 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(a2278)) | (~c1_1(a2278)) | (~c2_1(a2278)))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(3243,plain,
% 1.02/1.22 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c1_1(a2278)) | (~c2_1(a2278)) | (~c3_1(a2278))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[3242, 3241])).
% 1.02/1.22 tff(3244,plain,
% 1.02/1.22 (hskp25 | hskp23),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[3243, 160, 3212, 3214, 1895, 3215])).
% 1.02/1.22 tff(3245,plain,
% 1.02/1.22 (hskp23),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[3244, 3237])).
% 1.02/1.22 tff(3246,plain,
% 1.02/1.22 ((~hskp23) | c1_1(a2282)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[1081, 3210])).
% 1.02/1.22 tff(3247,plain,
% 1.02/1.22 (c1_1(a2282)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[3246, 3245])).
% 1.02/1.22 tff(3248,plain,
% 1.02/1.22 (hskp4),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[909, 3210])).
% 1.02/1.22 tff(3249,plain,
% 1.02/1.22 (~c0_1(a2282)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[178, 3248])).
% 1.02/1.22 tff(3250,plain,
% 1.02/1.22 (c2_1(a2282)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[223, 3248])).
% 1.02/1.22 tff(3251,plain,
% 1.02/1.22 (hskp18 | (~c1_1(a2282))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[3074, 160, 3213, 3214, 3250, 3249, 2497, 3215])).
% 1.02/1.22 tff(3252,plain,
% 1.02/1.22 (hskp18),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[3251, 3247])).
% 1.02/1.22 tff(3253,plain,
% 1.02/1.22 (~c1_1(a2308)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2515, 3252])).
% 1.02/1.22 tff(3254,plain,
% 1.02/1.22 (c3_1(a2308)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2530, 3252])).
% 1.02/1.22 tff(3255,plain,
% 1.02/1.22 (~c2_1(a2308)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[2509, 3252])).
% 1.02/1.22 tff(3256,plain,
% 1.02/1.22 (hskp17 | (~c3_1(a2308)) | c2_1(a2308) | c1_1(a2308)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[3103, 3210, 3213, 3212, 3214])).
% 1.02/1.22 tff(3257,plain,
% 1.02/1.22 ($false),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[3256, 3255, 3254, 3219, 3253])).
% 1.02/1.22 % SZS output end Proof
% 1.02/1.22 % E exiting
%------------------------------------------------------------------------------