%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN471-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:39:14 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.71s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN471-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n002.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:38:01 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.48/0.71 % SZS status Unsatisfiable
% 0.48/0.71 % SZS output start Proof
% 0.48/0.71 tff(c0_1_type, type, (
% 0.48/0.71 c0_1: $i > $o)).
% 0.48/0.71 tff(a651_type, type, (
% 0.48/0.71 a651: $i)).
% 0.48/0.71 tff(a615_type, type, (
% 0.48/0.71 a615: $i)).
% 0.48/0.71 tff(hskp14_type, type, (
% 0.48/0.71 hskp14: $o)).
% 0.48/0.71 tff(hskp10_type, type, (
% 0.48/0.71 hskp10: $o)).
% 0.48/0.71 tff(c2_1_type, type, (
% 0.48/0.71 c2_1: $i > $o)).
% 0.48/0.71 tff(c3_1_type, type, (
% 0.48/0.71 c3_1: $i > $o)).
% 0.48/0.71 tff(ndr1_0_type, type, (
% 0.48/0.71 ndr1_0: $o)).
% 0.48/0.71 tff(a605_type, type, (
% 0.48/0.71 a605: $i)).
% 0.48/0.71 tff(hskp1_type, type, (
% 0.48/0.71 hskp1: $o)).
% 0.48/0.71 tff(hskp31_type, type, (
% 0.48/0.71 hskp31: $o)).
% 0.48/0.71 tff(hskp24_type, type, (
% 0.48/0.71 hskp24: $o)).
% 0.48/0.71 tff(hskp12_type, type, (
% 0.48/0.71 hskp12: $o)).
% 0.48/0.71 tff(c1_1_type, type, (
% 0.48/0.71 c1_1: $i > $o)).
% 0.48/0.71 tff(a609_type, type, (
% 0.48/0.71 a609: $i)).
% 0.48/0.71 tff(a672_type, type, (
% 0.48/0.71 a672: $i)).
% 0.48/0.71 tff(a604_type, type, (
% 0.48/0.71 a604: $i)).
% 0.48/0.71 tff(hskp9_type, type, (
% 0.48/0.71 hskp9: $o)).
% 0.48/0.71 tff(a598_type, type, (
% 0.48/0.71 a598: $i)).
% 0.48/0.71 tff(hskp4_type, type, (
% 0.48/0.71 hskp4: $o)).
% 0.48/0.71 tff(a644_type, type, (
% 0.48/0.71 a644: $i)).
% 0.48/0.71 tff(hskp22_type, type, (
% 0.48/0.71 hskp22: $o)).
% 0.48/0.71 tff(a594_type, type, (
% 0.48/0.71 a594: $i)).
% 0.48/0.71 tff(a656_type, type, (
% 0.48/0.71 a656: $i)).
% 0.48/0.71 tff(hskp25_type, type, (
% 0.48/0.71 hskp25: $o)).
% 0.48/0.71 tff(a595_type, type, (
% 0.48/0.71 a595: $i)).
% 0.48/0.71 tff(hskp28_type, type, (
% 0.48/0.71 hskp28: $o)).
% 0.48/0.71 tff(a603_type, type, (
% 0.48/0.71 a603: $i)).
% 0.48/0.71 tff(hskp8_type, type, (
% 0.48/0.71 hskp8: $o)).
% 0.48/0.71 tff(hskp21_type, type, (
% 0.48/0.71 hskp21: $o)).
% 0.48/0.71 tff(a631_type, type, (
% 0.48/0.71 a631: $i)).
% 0.48/0.71 tff(hskp11_type, type, (
% 0.48/0.71 hskp11: $o)).
% 0.48/0.71 tff(a599_type, type, (
% 0.48/0.71 a599: $i)).
% 0.48/0.71 tff(hskp5_type, type, (
% 0.48/0.71 hskp5: $o)).
% 0.48/0.71 tff(a608_type, type, (
% 0.48/0.71 a608: $i)).
% 0.48/0.71 tff(a625_type, type, (
% 0.48/0.71 a625: $i)).
% 0.48/0.71 tff(a597_type, type, (
% 0.48/0.71 a597: $i)).
% 0.48/0.71 tff(hskp3_type, type, (
% 0.48/0.71 hskp3: $o)).
% 0.48/0.71 tff(a627_type, type, (
% 0.48/0.71 a627: $i)).
% 0.48/0.71 tff(hskp19_type, type, (
% 0.48/0.71 hskp19: $o)).
% 0.48/0.71 tff(hskp7_type, type, (
% 0.48/0.71 hskp7: $o)).
% 0.48/0.71 tff(hskp18_type, type, (
% 0.48/0.71 hskp18: $o)).
% 0.48/0.71 tff(a602_type, type, (
% 0.48/0.71 a602: $i)).
% 0.48/0.71 tff(1,assumption,(~c0_1(a651)), introduced(assumption)).
% 0.48/0.71 tff(2,assumption,(~hskp14), introduced(assumption)).
% 0.48/0.71 tff(3,plain,
% 0.48/0.71 (^[U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(4,plain,
% 0.48/0.71 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[3])).
% 0.48/0.71 tff(5,plain,
% 0.48/0.71 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(6,plain,
% 0.48/0.71 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(7,plain,
% 0.48/0.71 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[6])).
% 0.48/0.71 tff(8,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.48/0.71 tff(9,plain,
% 0.48/0.71 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.48/0.71 tff(10,plain,
% 0.48/0.71 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.48/0.71 tff(11,plain,(
% 0.48/0.71 ![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.48/0.71 inference(skolemize,[status(sab)],[10])).
% 0.48/0.71 tff(12,plain,
% 0.48/0.71 (![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.48/0.71 tff(13,assumption,(hskp10), introduced(assumption)).
% 0.48/0.71 tff(14,plain,
% 0.48/0.71 (((~hskp10) | (~c3_1(a605))) <=> ((~hskp10) | (~c3_1(a605)))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(15,plain,
% 0.48/0.71 (((~c3_1(a605)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a605)))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(16,axiom,((~c3_1(a605)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.48/0.71 tff(17,plain,
% 0.48/0.71 ((~hskp10) | (~c3_1(a605))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.48/0.71 tff(18,plain,
% 0.48/0.71 ((~hskp10) | (~c3_1(a605))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.48/0.71 tff(19,plain,
% 0.48/0.71 (~c3_1(a605)),
% 0.48/0.71 inference(unit_resolution,[status(thm)],[18, 13])).
% 0.48/0.71 tff(20,plain,
% 0.48/0.71 (((~hskp10) | c2_1(a605)) <=> ((~hskp10) | c2_1(a605))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(21,axiom,((~hskp10) | c2_1(a605)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.48/0.71 tff(22,plain,
% 0.48/0.71 ((~hskp10) | c2_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.48/0.71 tff(23,plain,
% 0.48/0.71 ((~hskp10) | c2_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.48/0.71 tff(24,plain,
% 0.48/0.71 ((~hskp10) | c2_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.48/0.71 tff(25,plain,
% 0.48/0.71 ((~hskp10) | c2_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.48/0.71 tff(26,plain,
% 0.48/0.71 ((~hskp10) | c2_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.48/0.71 tff(27,plain,
% 0.48/0.71 (c2_1(a605)),
% 0.48/0.71 inference(unit_resolution,[status(thm)],[26, 13])).
% 0.48/0.71 tff(28,plain,
% 0.48/0.71 (((~hskp10) | c0_1(a605)) <=> ((~hskp10) | c0_1(a605))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(29,axiom,((~hskp10) | c0_1(a605)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.48/0.71 tff(30,plain,
% 0.48/0.71 ((~hskp10) | c0_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.48/0.71 tff(31,plain,
% 0.48/0.71 ((~hskp10) | c0_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[30, 28])).
% 0.48/0.71 tff(32,plain,
% 0.48/0.71 ((~hskp10) | c0_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.48/0.71 tff(33,plain,
% 0.48/0.71 ((~hskp10) | c0_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.48/0.71 tff(34,plain,
% 0.48/0.71 ((~hskp10) | c0_1(a605)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.48/0.71 tff(35,plain,
% 0.48/0.71 (c0_1(a605)),
% 0.48/0.71 inference(unit_resolution,[status(thm)],[34, 13])).
% 0.48/0.71 tff(36,assumption,(~ndr1_0), introduced(assumption)).
% 0.48/0.71 tff(37,plain,
% 0.48/0.71 ((ndr1_0 | (~hskp1)) <=> (ndr1_0 | (~hskp1))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(38,plain,
% 0.48/0.71 (((~hskp1) | ndr1_0) <=> (ndr1_0 | (~hskp1))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(39,axiom,((~hskp1) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.48/0.71 tff(40,plain,
% 0.48/0.71 (ndr1_0 | (~hskp1)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.48/0.71 tff(41,plain,
% 0.48/0.71 (ndr1_0 | (~hskp1)),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.48/0.71 tff(42,plain,
% 0.48/0.71 (~hskp1),
% 0.48/0.71 inference(unit_resolution,[status(thm)],[41, 36])).
% 0.48/0.71 tff(43,plain,
% 0.48/0.71 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(44,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.48/0.71 tff(45,plain,
% 0.48/0.71 ((~hskp31) | ndr1_0),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.48/0.71 tff(46,plain,
% 0.48/0.71 ((~hskp31) | ndr1_0),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.48/0.71 tff(47,plain,
% 0.48/0.71 ((~hskp31) | ndr1_0),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.48/0.71 tff(48,plain,
% 0.48/0.71 ((~hskp31) | ndr1_0),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.48/0.71 tff(49,plain,
% 0.48/0.71 ((~hskp31) | ndr1_0),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.48/0.71 tff(50,plain,
% 0.48/0.71 (~hskp31),
% 0.48/0.71 inference(unit_resolution,[status(thm)],[49, 36])).
% 0.48/0.71 tff(51,plain,
% 0.48/0.71 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(52,plain,
% 0.48/0.71 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(53,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause9')).
% 0.55/0.71 tff(54,plain,
% 0.55/0.71 (ndr1_0 | (~hskp24)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.55/0.71 tff(55,plain,
% 0.55/0.71 (ndr1_0 | (~hskp24)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.55/0.71 tff(56,plain,
% 0.55/0.71 (~hskp24),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[55, 36])).
% 0.55/0.71 tff(57,plain,
% 0.55/0.71 ((hskp24 | hskp31 | hskp1) <=> (hskp24 | hskp31 | hskp1)),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(58,plain,
% 0.55/0.71 (((hskp1 | hskp31) | hskp24) <=> (hskp24 | hskp31 | hskp1)),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(59,axiom,((hskp1 | hskp31) | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.55/0.71 tff(60,plain,
% 0.55/0.71 (hskp24 | hskp31 | hskp1),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.55/0.71 tff(61,plain,
% 0.55/0.71 (hskp24 | hskp31 | hskp1),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.55/0.71 tff(62,plain,
% 0.55/0.71 (hskp24 | hskp31 | hskp1),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.55/0.71 tff(63,plain,
% 0.55/0.71 (hskp24 | hskp31 | hskp1),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[62, 57])).
% 0.55/0.71 tff(64,plain,
% 0.55/0.71 (hskp24 | hskp31 | hskp1),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[63, 57])).
% 0.55/0.71 tff(65,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[64, 56, 50, 42])).
% 0.55/0.71 tff(66,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(67,plain,
% 0.55/0.71 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(68,plain,
% 0.55/0.71 ((hskp14 | (~ndr1_0) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605))) <=> (hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(69,plain,
% 0.55/0.71 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[68])).
% 0.55/0.71 tff(70,plain,
% 0.55/0.71 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605)))),
% 0.55/0.71 inference(transitivity,[status(thm)],[69, 67])).
% 0.55/0.71 tff(71,plain,
% 0.55/0.71 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(72,plain,
% 0.55/0.71 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a605) | (~ndr1_0) | (~c2_1(a605)) | (~c0_1(a605))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.55/0.71 tff(73,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[72, 66, 2, 35, 27, 19, 12])).
% 0.55/0.71 tff(74,plain,((~hskp10) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(75,plain,
% 0.55/0.71 (~hskp10),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[74, 2])).
% 0.55/0.71 tff(76,assumption,(hskp12), introduced(assumption)).
% 0.55/0.71 tff(77,plain,
% 0.55/0.71 (((~hskp12) | (~c1_1(a609))) <=> ((~hskp12) | (~c1_1(a609)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(78,plain,
% 0.55/0.71 (((~c1_1(a609)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a609)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(79,axiom,((~c1_1(a609)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.55/0.71 tff(80,plain,
% 0.55/0.71 ((~hskp12) | (~c1_1(a609))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.55/0.71 tff(81,plain,
% 0.55/0.71 ((~hskp12) | (~c1_1(a609))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.55/0.71 tff(82,plain,
% 0.55/0.71 (~c1_1(a609)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[81, 76])).
% 0.55/0.71 tff(83,plain,
% 0.55/0.71 (((~hskp12) | c2_1(a609)) <=> ((~hskp12) | c2_1(a609))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(84,axiom,((~hskp12) | c2_1(a609)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.55/0.71 tff(85,plain,
% 0.55/0.71 ((~hskp12) | c2_1(a609)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.55/0.71 tff(86,plain,
% 0.55/0.71 ((~hskp12) | c2_1(a609)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[85, 83])).
% 0.55/0.71 tff(87,plain,
% 0.55/0.71 ((~hskp12) | c2_1(a609)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.55/0.71 tff(88,plain,
% 0.55/0.71 ((~hskp12) | c2_1(a609)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.55/0.71 tff(89,plain,
% 0.55/0.71 ((~hskp12) | c2_1(a609)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[88, 83])).
% 0.55/0.71 tff(90,plain,
% 0.55/0.71 (c2_1(a609)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[89, 76])).
% 0.55/0.71 tff(91,plain,
% 0.55/0.71 (((~hskp12) | (~c3_1(a609))) <=> ((~hskp12) | (~c3_1(a609)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(92,plain,
% 0.55/0.71 (((~c3_1(a609)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a609)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(93,axiom,((~c3_1(a609)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.55/0.71 tff(94,plain,
% 0.55/0.71 ((~hskp12) | (~c3_1(a609))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.55/0.71 tff(95,plain,
% 0.55/0.71 ((~hskp12) | (~c3_1(a609))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.55/0.71 tff(96,plain,
% 0.55/0.71 (~c3_1(a609)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[95, 76])).
% 0.55/0.71 tff(97,plain,
% 0.55/0.71 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(98,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[97])).
% 0.55/0.71 tff(99,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(100,plain,
% 0.55/0.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(101,plain,
% 0.55/0.71 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[100])).
% 0.55/0.71 tff(102,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.55/0.71 tff(103,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.55/0.71 tff(104,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.55/0.71 tff(105,plain,(
% 0.55/0.71 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.71 inference(skolemize,[status(sab)],[104])).
% 0.55/0.71 tff(106,plain,
% 0.55/0.71 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.55/0.71 tff(107,plain,
% 0.55/0.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_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)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(108,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_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)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[107])).
% 0.55/0.71 tff(109,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_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)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(110,plain,
% 0.55/0.71 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(111,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[110])).
% 0.55/0.71 tff(112,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 0.55/0.71 tff(113,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.55/0.71 tff(114,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.55/0.71 tff(115,plain,(
% 0.55/0.71 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.71 inference(skolemize,[status(sab)],[114])).
% 0.55/0.71 tff(116,plain,
% 0.55/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.55/0.71 tff(117,assumption,(~hskp24), introduced(assumption)).
% 0.55/0.71 tff(118,plain,
% 0.55/0.71 ((hskp9 | hskp24) <=> (hskp9 | hskp24)),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(119,axiom,(hskp9 | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.55/0.71 tff(120,plain,
% 0.55/0.71 (hskp9 | hskp24),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.55/0.71 tff(121,plain,
% 0.55/0.71 (hskp9 | hskp24),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[120, 118])).
% 0.55/0.71 tff(122,plain,
% 0.55/0.71 (hskp9 | hskp24),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.55/0.71 tff(123,plain,
% 0.55/0.71 (hskp9 | hskp24),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.55/0.71 tff(124,plain,
% 0.55/0.71 (hskp9 | hskp24),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[123, 118])).
% 0.55/0.71 tff(125,plain,
% 0.55/0.71 (hskp9),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[124, 117])).
% 0.55/0.71 tff(126,plain,
% 0.55/0.71 (((~hskp9) | (~c0_1(a604))) <=> ((~hskp9) | (~c0_1(a604)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(127,plain,
% 0.55/0.71 (((~c0_1(a604)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a604)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(128,axiom,((~c0_1(a604)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.55/0.71 tff(129,plain,
% 0.55/0.71 ((~hskp9) | (~c0_1(a604))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.55/0.71 tff(130,plain,
% 0.55/0.71 ((~hskp9) | (~c0_1(a604))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[129, 126])).
% 0.55/0.71 tff(131,plain,
% 0.55/0.71 (~c0_1(a604)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[130, 125])).
% 0.55/0.71 tff(132,plain,
% 0.55/0.71 (((~hskp9) | c2_1(a604)) <=> ((~hskp9) | c2_1(a604))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(133,axiom,((~hskp9) | c2_1(a604)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.55/0.71 tff(134,plain,
% 0.55/0.71 ((~hskp9) | c2_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.55/0.71 tff(135,plain,
% 0.55/0.71 ((~hskp9) | c2_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[134, 132])).
% 0.55/0.71 tff(136,plain,
% 0.55/0.71 ((~hskp9) | c2_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[135, 132])).
% 0.55/0.71 tff(137,plain,
% 0.55/0.71 ((~hskp9) | c2_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.55/0.71 tff(138,plain,
% 0.55/0.71 ((~hskp9) | c2_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[137, 132])).
% 0.55/0.71 tff(139,plain,
% 0.55/0.71 (c2_1(a604)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[138, 125])).
% 0.55/0.71 tff(140,plain,
% 0.55/0.71 (((~hskp9) | c1_1(a604)) <=> ((~hskp9) | c1_1(a604))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(141,axiom,((~hskp9) | c1_1(a604)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.55/0.71 tff(142,plain,
% 0.55/0.71 ((~hskp9) | c1_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.55/0.71 tff(143,plain,
% 0.55/0.71 ((~hskp9) | c1_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[142, 140])).
% 0.55/0.71 tff(144,plain,
% 0.55/0.71 ((~hskp9) | c1_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[143, 140])).
% 0.55/0.71 tff(145,plain,
% 0.55/0.71 ((~hskp9) | c1_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.55/0.71 tff(146,plain,
% 0.55/0.71 ((~hskp9) | c1_1(a604)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[145, 140])).
% 0.55/0.71 tff(147,plain,
% 0.55/0.71 (c1_1(a604)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[146, 125])).
% 0.55/0.71 tff(148,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(149,plain,
% 0.55/0.71 (((~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(150,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[149])).
% 0.55/0.71 tff(151,plain,
% 0.55/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 0.55/0.71 inference(transitivity,[status(thm)],[150, 148])).
% 0.55/0.71 tff(152,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(153,plain,
% 0.55/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.55/0.71 tff(154,plain,
% 0.55/0.71 (~c3_1(a604)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[153, 66, 147, 139, 131, 116])).
% 0.55/0.71 tff(155,plain,
% 0.55/0.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(156,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[155])).
% 0.55/0.72 tff(157,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(158,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(159,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[158])).
% 0.55/0.72 tff(160,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.55/0.72 tff(161,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.55/0.72 tff(162,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.55/0.72 tff(163,plain,(
% 0.55/0.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(skolemize,[status(sab)],[162])).
% 0.55/0.72 tff(164,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.55/0.72 tff(165,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(166,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[165])).
% 0.55/0.72 tff(167,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(168,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V) | c1_1(V))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V) | c1_1(V)))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c0_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V)))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c0_1(W))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c1_1(W) | c0_1(W))), ((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(169,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[168])).
% 0.55/0.72 tff(170,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.55/0.72 tff(171,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.55/0.72 tff(172,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.55/0.72 tff(173,plain,(
% 0.55/0.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(skolemize,[status(sab)],[172])).
% 0.55/0.72 tff(174,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.55/0.72 tff(175,assumption,(hskp1), introduced(assumption)).
% 0.55/0.72 tff(176,plain,
% 0.55/0.72 (((~hskp1) | (~c3_1(a594))) <=> ((~hskp1) | (~c3_1(a594)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(177,plain,
% 0.55/0.72 (((~c3_1(a594)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a594)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(178,axiom,((~c3_1(a594)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.55/0.72 tff(179,plain,
% 0.55/0.72 ((~hskp1) | (~c3_1(a594))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.55/0.72 tff(180,plain,
% 0.55/0.72 ((~hskp1) | (~c3_1(a594))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[179, 176])).
% 0.55/0.72 tff(181,plain,
% 0.55/0.72 (~c3_1(a594)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[180, 175])).
% 0.55/0.72 tff(182,plain,
% 0.55/0.72 (((~hskp1) | c1_1(a594)) <=> ((~hskp1) | c1_1(a594))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(183,axiom,((~hskp1) | c1_1(a594)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.55/0.72 tff(184,plain,
% 0.55/0.72 ((~hskp1) | c1_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.55/0.72 tff(185,plain,
% 0.55/0.72 ((~hskp1) | c1_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[184, 182])).
% 0.55/0.72 tff(186,plain,
% 0.55/0.72 ((~hskp1) | c1_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[185, 182])).
% 0.55/0.72 tff(187,plain,
% 0.55/0.72 ((~hskp1) | c1_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.55/0.72 tff(188,plain,
% 0.55/0.72 ((~hskp1) | c1_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[187, 182])).
% 0.55/0.72 tff(189,plain,
% 0.55/0.72 (c1_1(a594)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[188, 175])).
% 0.55/0.72 tff(190,plain,
% 0.55/0.72 (((~hskp1) | c0_1(a594)) <=> ((~hskp1) | c0_1(a594))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(191,axiom,((~hskp1) | c0_1(a594)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.55/0.72 tff(192,plain,
% 0.55/0.72 ((~hskp1) | c0_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.55/0.72 tff(193,plain,
% 0.55/0.72 ((~hskp1) | c0_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[192, 190])).
% 0.55/0.72 tff(194,plain,
% 0.55/0.72 ((~hskp1) | c0_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[193, 190])).
% 0.55/0.72 tff(195,plain,
% 0.55/0.72 ((~hskp1) | c0_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.55/0.72 tff(196,plain,
% 0.55/0.72 ((~hskp1) | c0_1(a594)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[195, 190])).
% 0.55/0.72 tff(197,plain,
% 0.55/0.72 (c0_1(a594)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[196, 175])).
% 0.55/0.72 tff(198,assumption,(~c3_1(a604)), introduced(assumption)).
% 0.55/0.72 tff(199,assumption,(~c3_1(a594)), introduced(assumption)).
% 0.55/0.72 tff(200,assumption,(~c0_1(a604)), introduced(assumption)).
% 0.55/0.72 tff(201,assumption,(c1_1(a594)), introduced(assumption)).
% 0.55/0.72 tff(202,assumption,(c0_1(a594)), introduced(assumption)).
% 0.55/0.72 tff(203,assumption,(c1_1(a604)), introduced(assumption)).
% 0.55/0.72 tff(204,assumption,(hskp4), introduced(assumption)).
% 0.55/0.72 tff(205,plain,
% 0.55/0.72 (((~hskp4) | (~c2_1(a598))) <=> ((~hskp4) | (~c2_1(a598)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(206,plain,
% 0.55/0.72 (((~c2_1(a598)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a598)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(207,axiom,((~c2_1(a598)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.55/0.72 tff(208,plain,
% 0.55/0.72 ((~hskp4) | (~c2_1(a598))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.55/0.72 tff(209,plain,
% 0.55/0.72 ((~hskp4) | (~c2_1(a598))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[208, 205])).
% 0.55/0.72 tff(210,plain,
% 0.55/0.72 (~c2_1(a598)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[209, 204])).
% 0.55/0.72 tff(211,plain,
% 0.55/0.72 (((~hskp4) | (~c0_1(a598))) <=> ((~hskp4) | (~c0_1(a598)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(212,plain,
% 0.55/0.72 (((~c0_1(a598)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a598)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(213,axiom,((~c0_1(a598)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.55/0.72 tff(214,plain,
% 0.55/0.72 ((~hskp4) | (~c0_1(a598))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.55/0.72 tff(215,plain,
% 0.55/0.72 ((~hskp4) | (~c0_1(a598))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[214, 211])).
% 0.55/0.72 tff(216,plain,
% 0.55/0.72 (~c0_1(a598)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[215, 204])).
% 0.55/0.72 tff(217,plain,
% 0.55/0.72 (((~hskp4) | (~c1_1(a598))) <=> ((~hskp4) | (~c1_1(a598)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(218,plain,
% 0.55/0.72 (((~c1_1(a598)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a598)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(219,axiom,((~c1_1(a598)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.55/0.72 tff(220,plain,
% 0.55/0.72 ((~hskp4) | (~c1_1(a598))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.55/0.72 tff(221,plain,
% 0.55/0.72 ((~hskp4) | (~c1_1(a598))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[220, 217])).
% 0.55/0.72 tff(222,plain,
% 0.55/0.72 (~c1_1(a598)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[221, 204])).
% 0.55/0.72 tff(223,assumption,(~c0_1(a598)), introduced(assumption)).
% 0.55/0.72 tff(224,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(225,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[224])).
% 0.55/0.72 tff(226,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(227,plain,
% 0.55/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(228,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[227])).
% 0.55/0.72 tff(229,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.55/0.72 tff(230,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.55/0.72 tff(231,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.55/0.72 tff(232,plain,(
% 0.55/0.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(skolemize,[status(sab)],[231])).
% 0.55/0.72 tff(233,plain,
% 0.55/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.55/0.72 tff(234,assumption,(~c1_1(a598)), introduced(assumption)).
% 0.55/0.72 tff(235,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(236,plain,
% 0.55/0.72 (((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)) | c1_1(a598) | c0_1(a598) | (~c3_1(a598))) <=> (c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(237,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)) | c1_1(a598) | c0_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[236])).
% 0.55/0.72 tff(238,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)) | c1_1(a598) | c0_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[237, 235])).
% 0.55/0.72 tff(239,plain,
% 0.55/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)) | c1_1(a598) | c0_1(a598) | (~c3_1(a598)))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(240,plain,
% 0.55/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a598)) | c3_1(a604) | (~c1_1(a604))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.55/0.72 tff(241,plain,
% 0.55/0.72 (c0_1(a598) | (~c3_1(a598))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[240, 66, 203, 202, 201, 200, 234, 199, 233, 198])).
% 0.55/0.72 tff(242,plain,
% 0.55/0.72 (~c3_1(a598)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[241, 223])).
% 0.55/0.72 tff(243,assumption,(~c2_1(a598)), introduced(assumption)).
% 0.55/0.72 tff(244,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(245,plain,
% 0.55/0.72 (((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a598) | c0_1(a598) | c1_1(a598) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(246,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a598) | c0_1(a598) | c1_1(a598) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598)))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[245])).
% 0.55/0.72 tff(247,plain,
% 0.55/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a598) | c0_1(a598) | c1_1(a598) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598))),
% 0.55/0.72 inference(transitivity,[status(thm)],[246, 244])).
% 0.55/0.72 tff(248,plain,
% 0.55/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a598) | c0_1(a598) | c1_1(a598) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(249,plain,
% 0.55/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.55/0.73 tff(250,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[249, 66, 223, 234, 243, 174, 242])).
% 0.55/0.73 tff(251,plain,(c0_1(a598) | c1_1(a598) | c2_1(a598) | (~c1_1(a604)) | (~c0_1(a594)) | (~c1_1(a594)) | c0_1(a604) | c3_1(a594) | c3_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(252,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[251, 222, 216, 210, 203, 202, 201, 200, 199, 198])).
% 0.55/0.73 tff(253,plain,((~hskp4) | (~c1_1(a604)) | (~c0_1(a594)) | (~c1_1(a594)) | c0_1(a604) | c3_1(a594) | c3_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(254,plain,
% 0.55/0.73 (~hskp4),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[253, 197, 147, 189, 131, 181, 154])).
% 0.55/0.73 tff(255,plain,
% 0.55/0.73 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(256,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[255])).
% 0.55/0.73 tff(257,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(258,plain,
% 0.55/0.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~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)) | 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) | (~c2_1(U)) | (~c3_1(U)) | (~c0_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)) | hskp24) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_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)) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(259,plain,
% 0.55/0.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[258])).
% 0.55/0.73 tff(260,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)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.55/0.73 tff(261,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.55/0.73 tff(262,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.55/0.73 tff(263,plain,(
% 0.55/0.73 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.55/0.73 inference(skolemize,[status(sab)],[262])).
% 0.55/0.73 tff(264,plain,
% 0.55/0.73 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[263, 256])).
% 0.55/0.73 tff(265,assumption,(hskp14), introduced(assumption)).
% 0.55/0.73 tff(266,plain,
% 0.55/0.73 (((~hskp14) | c2_1(a615)) <=> ((~hskp14) | c2_1(a615))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(267,axiom,((~hskp14) | c2_1(a615)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.55/0.73 tff(268,plain,
% 0.55/0.73 ((~hskp14) | c2_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.55/0.73 tff(269,plain,
% 0.55/0.73 ((~hskp14) | c2_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[268, 266])).
% 0.55/0.73 tff(270,plain,
% 0.55/0.73 ((~hskp14) | c2_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[269, 266])).
% 0.55/0.73 tff(271,plain,
% 0.55/0.73 ((~hskp14) | c2_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.55/0.73 tff(272,plain,
% 0.55/0.73 ((~hskp14) | c2_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[271, 266])).
% 0.55/0.73 tff(273,plain,
% 0.55/0.73 (c2_1(a615)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[272, 265])).
% 0.55/0.73 tff(274,plain,
% 0.55/0.73 (((~hskp14) | c0_1(a615)) <=> ((~hskp14) | c0_1(a615))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(275,axiom,((~hskp14) | c0_1(a615)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.55/0.73 tff(276,plain,
% 0.55/0.73 ((~hskp14) | c0_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.55/0.73 tff(277,plain,
% 0.55/0.73 ((~hskp14) | c0_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[276, 274])).
% 0.55/0.73 tff(278,plain,
% 0.55/0.73 ((~hskp14) | c0_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[277, 274])).
% 0.55/0.73 tff(279,plain,
% 0.55/0.73 ((~hskp14) | c0_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[278, 274])).
% 0.55/0.73 tff(280,plain,
% 0.55/0.73 ((~hskp14) | c0_1(a615)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[279, 274])).
% 0.55/0.73 tff(281,plain,
% 0.55/0.73 (c0_1(a615)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[280, 265])).
% 0.55/0.73 tff(282,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(283,plain,
% 0.55/0.73 ((hskp24 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c3_1(a594) | (~c1_1(a594)) | (~c0_1(a594))) <=> (hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(284,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c3_1(a594) | (~c1_1(a594)) | (~c0_1(a594)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[283])).
% 0.55/0.73 tff(285,plain,
% 0.55/0.73 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c3_1(a594) | (~c1_1(a594)) | (~c0_1(a594)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[284, 282])).
% 0.55/0.73 tff(286,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c3_1(a594) | (~c1_1(a594)) | (~c0_1(a594)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(287,plain,
% 0.55/0.73 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp24 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.55/0.73 tff(288,plain,
% 0.55/0.73 (~c3_1(a615)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[287, 117, 66, 281, 273, 202, 201, 199, 264])).
% 0.55/0.73 tff(289,plain,
% 0.55/0.73 (^[U: $i] : refl((hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(290,plain,
% 0.55/0.73 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[289])).
% 0.55/0.73 tff(291,plain,
% 0.55/0.73 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(292,plain,
% 0.55/0.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(293,plain,
% 0.55/0.73 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp25) <=> ![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[292])).
% 0.55/0.73 tff(294,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.55/0.73 tff(295,plain,
% 0.55/0.73 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.55/0.73 tff(296,plain,
% 0.55/0.73 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[295, 291])).
% 0.55/0.73 tff(297,plain,(
% 0.55/0.73 ![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(skolemize,[status(sab)],[296])).
% 0.55/0.73 tff(298,plain,
% 0.55/0.73 (![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[297, 290])).
% 0.55/0.73 tff(299,plain,
% 0.55/0.73 (((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(300,plain,
% 0.55/0.73 ((hskp25 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615))) <=> (hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(301,plain,
% 0.55/0.73 (((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[300])).
% 0.55/0.73 tff(302,plain,
% 0.55/0.73 (((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[301, 299])).
% 0.55/0.73 tff(303,plain,
% 0.55/0.73 ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(304,plain,
% 0.55/0.73 ((~![U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.55/0.73 tff(305,plain,
% 0.55/0.73 (hskp25 | c3_1(a615)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[304, 66, 281, 273, 298])).
% 0.55/0.73 tff(306,plain,
% 0.55/0.73 (hskp25),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[305, 288])).
% 0.55/0.73 tff(307,plain,
% 0.55/0.73 (((~hskp25) | (~c0_1(a656))) <=> ((~hskp25) | (~c0_1(a656)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(308,plain,
% 0.55/0.73 (((~c0_1(a656)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a656)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(309,axiom,((~c0_1(a656)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.55/0.73 tff(310,plain,
% 0.55/0.73 ((~hskp25) | (~c0_1(a656))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.55/0.73 tff(311,plain,
% 0.55/0.73 ((~hskp25) | (~c0_1(a656))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[310, 307])).
% 0.55/0.73 tff(312,plain,
% 0.55/0.73 (~c0_1(a656)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[311, 306])).
% 0.55/0.73 tff(313,plain,
% 0.55/0.73 (((~hskp25) | c3_1(a656)) <=> ((~hskp25) | c3_1(a656))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(314,axiom,((~hskp25) | c3_1(a656)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.55/0.73 tff(315,plain,
% 0.55/0.73 ((~hskp25) | c3_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.55/0.73 tff(316,plain,
% 0.55/0.73 ((~hskp25) | c3_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[315, 313])).
% 0.55/0.73 tff(317,plain,
% 0.55/0.73 ((~hskp25) | c3_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[316, 313])).
% 0.55/0.73 tff(318,plain,
% 0.55/0.73 ((~hskp25) | c3_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[317, 313])).
% 0.55/0.73 tff(319,plain,
% 0.55/0.73 ((~hskp25) | c3_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[318, 313])).
% 0.55/0.73 tff(320,plain,
% 0.55/0.73 (c3_1(a656)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[319, 306])).
% 0.55/0.73 tff(321,plain,
% 0.55/0.73 (((~hskp25) | c1_1(a656)) <=> ((~hskp25) | c1_1(a656))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(322,axiom,((~hskp25) | c1_1(a656)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.55/0.73 tff(323,plain,
% 0.55/0.73 ((~hskp25) | c1_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.55/0.73 tff(324,plain,
% 0.55/0.73 ((~hskp25) | c1_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[323, 321])).
% 0.55/0.73 tff(325,plain,
% 0.55/0.73 ((~hskp25) | c1_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[324, 321])).
% 0.55/0.73 tff(326,plain,
% 0.55/0.73 ((~hskp25) | c1_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[325, 321])).
% 0.55/0.73 tff(327,plain,
% 0.55/0.73 ((~hskp25) | c1_1(a656)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[326, 321])).
% 0.55/0.73 tff(328,plain,
% 0.55/0.73 (c1_1(a656)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[327, 306])).
% 0.55/0.73 tff(329,plain,
% 0.55/0.73 (^[U: $i] : refl((hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(330,plain,
% 0.55/0.73 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[329])).
% 0.55/0.73 tff(331,plain,
% 0.55/0.73 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(332,plain,
% 0.55/0.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp4) <=> ((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(333,plain,
% 0.55/0.73 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp4) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[332])).
% 0.55/0.73 tff(334,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.55/0.73 tff(335,plain,
% 0.55/0.73 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.55/0.73 tff(336,plain,
% 0.55/0.73 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[335, 331])).
% 0.55/0.73 tff(337,plain,(
% 0.55/0.73 ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(skolemize,[status(sab)],[336])).
% 0.55/0.73 tff(338,plain,
% 0.55/0.73 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[337, 330])).
% 0.55/0.73 tff(339,assumption,(~hskp4), introduced(assumption)).
% 0.55/0.73 tff(340,plain,
% 0.55/0.73 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(341,plain,
% 0.55/0.73 ((hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615))) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(342,plain,
% 0.55/0.73 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[341])).
% 0.55/0.73 tff(343,plain,
% 0.55/0.73 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[342, 340])).
% 0.55/0.73 tff(344,plain,
% 0.55/0.73 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(345,plain,
% 0.55/0.73 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp4 | (~ndr1_0) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.55/0.73 tff(346,plain,
% 0.55/0.73 (hskp28 | c3_1(a615)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[345, 66, 339, 281, 273, 338])).
% 0.55/0.73 tff(347,plain,
% 0.55/0.73 (hskp28),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[346, 288])).
% 0.55/0.73 tff(348,plain,
% 0.55/0.73 (((~hskp28) | c3_1(a595)) <=> ((~hskp28) | c3_1(a595))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(349,axiom,((~hskp28) | c3_1(a595)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.55/0.73 tff(350,plain,
% 0.55/0.73 ((~hskp28) | c3_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.55/0.73 tff(351,plain,
% 0.55/0.73 ((~hskp28) | c3_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[350, 348])).
% 0.55/0.73 tff(352,plain,
% 0.55/0.73 ((~hskp28) | c3_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[351, 348])).
% 0.55/0.73 tff(353,plain,
% 0.55/0.73 ((~hskp28) | c3_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[352, 348])).
% 0.55/0.73 tff(354,plain,
% 0.55/0.73 ((~hskp28) | c3_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[353, 348])).
% 0.55/0.73 tff(355,plain,
% 0.55/0.73 (c3_1(a595)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[354, 347])).
% 0.55/0.73 tff(356,plain,
% 0.55/0.73 (((~hskp28) | c2_1(a595)) <=> ((~hskp28) | c2_1(a595))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(357,axiom,((~hskp28) | c2_1(a595)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.55/0.73 tff(358,plain,
% 0.55/0.73 ((~hskp28) | c2_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.55/0.73 tff(359,plain,
% 0.55/0.73 ((~hskp28) | c2_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[358, 356])).
% 0.55/0.73 tff(360,plain,
% 0.55/0.73 ((~hskp28) | c2_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[359, 356])).
% 0.55/0.73 tff(361,plain,
% 0.55/0.73 ((~hskp28) | c2_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[360, 356])).
% 0.55/0.73 tff(362,plain,
% 0.55/0.73 ((~hskp28) | c2_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[361, 356])).
% 0.55/0.73 tff(363,plain,
% 0.55/0.73 (c2_1(a595)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[362, 347])).
% 0.55/0.73 tff(364,plain,
% 0.55/0.73 (((~hskp28) | c1_1(a595)) <=> ((~hskp28) | c1_1(a595))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(365,axiom,((~hskp28) | c1_1(a595)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.55/0.73 tff(366,plain,
% 0.55/0.73 ((~hskp28) | c1_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.55/0.73 tff(367,plain,
% 0.55/0.73 ((~hskp28) | c1_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[366, 364])).
% 0.55/0.73 tff(368,plain,
% 0.55/0.73 ((~hskp28) | c1_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[367, 364])).
% 0.55/0.73 tff(369,plain,
% 0.55/0.73 ((~hskp28) | c1_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[368, 364])).
% 0.55/0.73 tff(370,plain,
% 0.55/0.73 ((~hskp28) | c1_1(a595)),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[369, 364])).
% 0.55/0.73 tff(371,plain,
% 0.55/0.73 (c1_1(a595)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[370, 347])).
% 0.55/0.73 tff(372,plain,
% 0.55/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(373,plain,
% 0.55/0.74 (((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(374,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[373])).
% 0.55/0.74 tff(375,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[374, 372])).
% 0.55/0.74 tff(376,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(377,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a656)) | (~c1_1(a656))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.55/0.74 tff(378,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[377, 66, 371, 363, 355, 328, 320, 147, 139, 312, 131, 116])).
% 0.55/0.74 tff(379,plain,((~hskp14) | hskp4 | hskp24 | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a594)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(380,plain,
% 0.55/0.74 (~hskp14),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[379, 254, 117, 197, 189, 181])).
% 0.55/0.74 tff(381,plain,
% 0.55/0.74 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(382,plain,
% 0.55/0.74 ((hskp14 | (~ndr1_0) | c3_1(a594) | (~c2_1(a594)) | (~c0_1(a594))) <=> (hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(383,plain,
% 0.55/0.74 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a594) | (~c2_1(a594)) | (~c0_1(a594)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[382])).
% 0.55/0.74 tff(384,plain,
% 0.55/0.74 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a594) | (~c2_1(a594)) | (~c0_1(a594)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[383, 381])).
% 0.55/0.74 tff(385,plain,
% 0.55/0.74 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a594) | (~c2_1(a594)) | (~c0_1(a594)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(386,plain,
% 0.55/0.74 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c2_1(a594))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.55/0.74 tff(387,plain,
% 0.55/0.74 (hskp14 | (~c2_1(a594))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[386, 66, 197, 181, 12])).
% 0.55/0.74 tff(388,plain,
% 0.55/0.74 (~c2_1(a594)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[387, 380])).
% 0.55/0.74 tff(389,plain,
% 0.55/0.74 (^[U: $i] : refl((hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(390,plain,
% 0.55/0.74 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[389])).
% 0.55/0.74 tff(391,plain,
% 0.55/0.74 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(392,plain,
% 0.55/0.74 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp22) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp22))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp22) <=> (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp22) <=> (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(393,plain,
% 0.55/0.74 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp22) <=> ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[392])).
% 0.55/0.74 tff(394,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.55/0.74 tff(395,plain,
% 0.55/0.74 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.55/0.74 tff(396,plain,
% 0.55/0.74 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[395, 391])).
% 0.55/0.74 tff(397,plain,(
% 0.55/0.74 ![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(skolemize,[status(sab)],[396])).
% 0.55/0.74 tff(398,plain,
% 0.55/0.74 (![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[397, 390])).
% 0.55/0.74 tff(399,plain,
% 0.55/0.74 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(400,plain,
% 0.55/0.74 ((hskp22 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594))) <=> (hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(401,plain,
% 0.55/0.74 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[400])).
% 0.55/0.74 tff(402,plain,
% 0.55/0.74 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[401, 399])).
% 0.55/0.74 tff(403,plain,
% 0.55/0.74 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(404,plain,
% 0.55/0.74 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[403, 402])).
% 0.55/0.74 tff(405,plain,
% 0.55/0.74 (hskp22 | hskp4 | c2_1(a594)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[404, 66, 197, 189, 398])).
% 0.55/0.74 tff(406,plain,
% 0.55/0.74 (hskp22),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[405, 388, 254])).
% 0.55/0.74 tff(407,plain,
% 0.55/0.74 (((~hskp22) | (~c3_1(a644))) <=> ((~hskp22) | (~c3_1(a644)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(408,plain,
% 0.55/0.74 (((~c3_1(a644)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a644)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(409,axiom,((~c3_1(a644)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.55/0.74 tff(410,plain,
% 0.55/0.74 ((~hskp22) | (~c3_1(a644))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.55/0.74 tff(411,plain,
% 0.55/0.74 ((~hskp22) | (~c3_1(a644))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[410, 407])).
% 0.55/0.74 tff(412,plain,
% 0.55/0.74 (~c3_1(a644)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[411, 406])).
% 0.55/0.74 tff(413,plain,
% 0.55/0.74 (((~hskp22) | (~c2_1(a644))) <=> ((~hskp22) | (~c2_1(a644)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(414,plain,
% 0.55/0.74 (((~c2_1(a644)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a644)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(415,axiom,((~c2_1(a644)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.55/0.74 tff(416,plain,
% 0.55/0.74 ((~hskp22) | (~c2_1(a644))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.55/0.74 tff(417,plain,
% 0.55/0.74 ((~hskp22) | (~c2_1(a644))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[416, 413])).
% 0.55/0.74 tff(418,plain,
% 0.55/0.74 (~c2_1(a644)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[417, 406])).
% 0.55/0.74 tff(419,plain,
% 0.55/0.74 (((~hskp22) | (~c0_1(a644))) <=> ((~hskp22) | (~c0_1(a644)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(420,plain,
% 0.55/0.74 (((~c0_1(a644)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a644)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(421,axiom,((~c0_1(a644)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.55/0.74 tff(422,plain,
% 0.55/0.74 ((~hskp22) | (~c0_1(a644))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.55/0.74 tff(423,plain,
% 0.55/0.74 ((~hskp22) | (~c0_1(a644))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[422, 419])).
% 0.55/0.74 tff(424,plain,
% 0.55/0.74 (~c0_1(a644)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[423, 406])).
% 0.55/0.74 tff(425,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(426,plain,
% 0.55/0.74 (((~ndr1_0) | c3_1(a644) | c2_1(a644) | c0_1(a644) | c3_1(a644) | c0_1(a644) | c1_1(a644) | c2_1(a644) | c1_1(a644) | c0_1(a644)) <=> (c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(427,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a644) | c2_1(a644) | c0_1(a644) | c3_1(a644) | c0_1(a644) | c1_1(a644) | c2_1(a644) | c1_1(a644) | c0_1(a644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644)))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[426])).
% 0.55/0.74 tff(428,plain,
% 0.55/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a644) | c2_1(a644) | c0_1(a644) | c3_1(a644) | c0_1(a644) | c1_1(a644) | c2_1(a644) | c1_1(a644) | c0_1(a644))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644))),
% 0.55/0.74 inference(transitivity,[status(thm)],[427, 425])).
% 0.55/0.74 tff(429,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a644) | c2_1(a644) | c0_1(a644) | c3_1(a644) | c0_1(a644) | c1_1(a644) | c2_1(a644) | c1_1(a644) | c0_1(a644))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(430,plain,
% 0.55/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | c1_1(a644)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.55/0.74 tff(431,plain,
% 0.55/0.74 (c1_1(a644)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[430, 66, 424, 418, 412, 174])).
% 0.55/0.74 tff(432,plain,
% 0.55/0.74 (^[U: $i] : refl((hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(433,plain,
% 0.55/0.74 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[432])).
% 0.55/0.74 tff(434,plain,
% 0.55/0.74 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(435,plain,
% 0.55/0.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp4) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp4))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp4) <=> (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp4) <=> (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(436,plain,
% 0.55/0.74 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp4) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[435])).
% 0.55/0.74 tff(437,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.55/0.74 tff(438,plain,
% 0.55/0.74 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.55/0.74 tff(439,plain,
% 0.55/0.74 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[438, 434])).
% 0.55/0.74 tff(440,plain,(
% 0.55/0.74 ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.55/0.74 inference(skolemize,[status(sab)],[439])).
% 0.55/0.74 tff(441,plain,
% 0.55/0.74 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[440, 433])).
% 0.55/0.74 tff(442,plain,
% 0.55/0.74 (^[U: $i] : refl((hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(443,plain,
% 0.55/0.74 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[442])).
% 0.55/0.74 tff(444,plain,
% 0.55/0.74 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(445,plain,
% 0.55/0.74 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp4) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp4))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp4) <=> (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(446,plain,
% 0.55/0.74 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp4) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[445])).
% 0.55/0.74 tff(447,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp8) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.55/0.74 tff(448,plain,
% 0.55/0.74 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.55/0.74 tff(449,plain,
% 0.55/0.74 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[448, 444])).
% 0.55/0.74 tff(450,plain,(
% 0.55/0.74 ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(skolemize,[status(sab)],[449])).
% 0.55/0.74 tff(451,plain,
% 0.55/0.74 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[450, 443])).
% 0.55/0.74 tff(452,plain,
% 0.55/0.74 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(453,plain,
% 0.55/0.74 ((hskp8 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594))) <=> (hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(454,plain,
% 0.55/0.74 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[453])).
% 0.55/0.74 tff(455,plain,
% 0.55/0.74 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594)))),
% 0.55/0.74 inference(transitivity,[status(thm)],[454, 452])).
% 0.55/0.74 tff(456,plain,
% 0.55/0.74 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a594) | (~c0_1(a594)) | (~c1_1(a594)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(457,plain,
% 0.55/0.74 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | (~ndr1_0) | (~c0_1(a594)) | c2_1(a594) | (~c1_1(a594))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.55/0.74 tff(458,plain,
% 0.55/0.74 (hskp8 | hskp4 | c2_1(a594)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[457, 66, 197, 189, 451])).
% 0.55/0.74 tff(459,plain,
% 0.55/0.74 (hskp8),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[458, 388, 254])).
% 0.55/0.74 tff(460,plain,
% 0.55/0.74 (((~hskp8) | (~c2_1(a603))) <=> ((~hskp8) | (~c2_1(a603)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(461,plain,
% 0.55/0.74 (((~c2_1(a603)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a603)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(462,axiom,((~c2_1(a603)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.55/0.74 tff(463,plain,
% 0.55/0.74 ((~hskp8) | (~c2_1(a603))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.55/0.74 tff(464,plain,
% 0.55/0.74 ((~hskp8) | (~c2_1(a603))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[463, 460])).
% 0.55/0.74 tff(465,plain,
% 0.55/0.74 (~c2_1(a603)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[464, 459])).
% 0.55/0.74 tff(466,plain,
% 0.55/0.74 (((~hskp8) | (~c1_1(a603))) <=> ((~hskp8) | (~c1_1(a603)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(467,plain,
% 0.55/0.74 (((~c1_1(a603)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a603)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(468,axiom,((~c1_1(a603)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.55/0.74 tff(469,plain,
% 0.55/0.74 ((~hskp8) | (~c1_1(a603))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.55/0.74 tff(470,plain,
% 0.55/0.74 ((~hskp8) | (~c1_1(a603))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[469, 466])).
% 0.55/0.74 tff(471,plain,
% 0.55/0.74 (~c1_1(a603)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[470, 459])).
% 0.55/0.74 tff(472,plain,
% 0.55/0.74 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(473,plain,
% 0.55/0.75 ((hskp14 | hskp4 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | c1_1(a603)) <=> (hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(474,plain,
% 0.55/0.75 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | c1_1(a603))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603)))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[473])).
% 0.55/0.75 tff(475,plain,
% 0.55/0.75 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | c1_1(a603))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603))),
% 0.55/0.75 inference(transitivity,[status(thm)],[474, 472])).
% 0.55/0.75 tff(476,plain,
% 0.55/0.75 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | c1_1(a603))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(477,plain,
% 0.55/0.75 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | c3_1(a603)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.55/0.75 tff(478,plain,
% 0.55/0.75 (c3_1(a603)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[477, 66, 380, 254, 471, 465, 441])).
% 0.55/0.75 tff(479,plain,
% 0.55/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(480,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[479])).
% 0.55/0.75 tff(481,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(482,plain,
% 0.55/0.75 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(483,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[482])).
% 0.55/0.75 tff(484,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 0.55/0.75 tff(485,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.55/0.75 tff(486,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[485, 481])).
% 0.55/0.75 tff(487,plain,(
% 0.55/0.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.55/0.75 inference(skolemize,[status(sab)],[486])).
% 0.55/0.75 tff(488,plain,
% 0.55/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[487, 480])).
% 0.55/0.75 tff(489,plain,
% 0.55/0.75 (((~hskp8) | c0_1(a603)) <=> ((~hskp8) | c0_1(a603))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(490,axiom,((~hskp8) | c0_1(a603)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.55/0.75 tff(491,plain,
% 0.55/0.75 ((~hskp8) | c0_1(a603)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.55/0.75 tff(492,plain,
% 0.55/0.75 ((~hskp8) | c0_1(a603)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[491, 489])).
% 0.55/0.75 tff(493,plain,
% 0.55/0.75 ((~hskp8) | c0_1(a603)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[492, 489])).
% 0.55/0.75 tff(494,plain,
% 0.55/0.75 ((~hskp8) | c0_1(a603)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[493, 489])).
% 0.55/0.75 tff(495,plain,
% 0.55/0.75 ((~hskp8) | c0_1(a603)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[494, 489])).
% 0.55/0.75 tff(496,plain,
% 0.55/0.75 (c0_1(a603)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[495, 459])).
% 0.55/0.75 tff(497,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(498,plain,
% 0.55/0.75 (((~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a603) | (~c3_1(a603)) | (~c0_1(a603))) <=> (c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(499,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a603) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[498])).
% 0.55/0.75 tff(500,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a603) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[499, 497])).
% 0.55/0.75 tff(501,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a603) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(502,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)) | (~c1_1(a644))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.55/0.75 tff(503,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[502, 66, 147, 139, 496, 418, 412, 471, 488, 154, 478, 431])).
% 0.55/0.75 tff(504,plain,((~hskp1) | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(505,plain,
% 0.55/0.75 (~hskp1),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[504, 117])).
% 0.55/0.75 tff(506,plain,
% 0.55/0.75 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(507,plain,
% 0.55/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[506])).
% 0.55/0.75 tff(508,plain,
% 0.55/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(509,plain,
% 0.55/0.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(510,plain,
% 0.55/0.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[509])).
% 0.55/0.75 tff(511,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.55/0.75 tff(512,plain,
% 0.55/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.55/0.75 tff(513,plain,
% 0.55/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[512, 508])).
% 0.55/0.75 tff(514,plain,(
% 0.55/0.75 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.75 inference(skolemize,[status(sab)],[513])).
% 0.55/0.75 tff(515,plain,
% 0.55/0.75 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[514, 507])).
% 0.55/0.75 tff(516,assumption,(hskp21), introduced(assumption)).
% 0.55/0.75 tff(517,plain,
% 0.55/0.75 (((~hskp21) | (~c1_1(a631))) <=> ((~hskp21) | (~c1_1(a631)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(518,plain,
% 0.55/0.75 (((~c1_1(a631)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a631)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(519,axiom,((~c1_1(a631)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.55/0.75 tff(520,plain,
% 0.55/0.75 ((~hskp21) | (~c1_1(a631))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.55/0.75 tff(521,plain,
% 0.55/0.75 ((~hskp21) | (~c1_1(a631))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[520, 517])).
% 0.55/0.75 tff(522,plain,
% 0.55/0.75 (~c1_1(a631)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[521, 516])).
% 0.55/0.75 tff(523,plain,
% 0.55/0.75 (((~hskp21) | c3_1(a631)) <=> ((~hskp21) | c3_1(a631))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(524,axiom,((~hskp21) | c3_1(a631)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.55/0.75 tff(525,plain,
% 0.55/0.75 ((~hskp21) | c3_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.55/0.75 tff(526,plain,
% 0.55/0.75 ((~hskp21) | c3_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[525, 523])).
% 0.55/0.75 tff(527,plain,
% 0.55/0.75 ((~hskp21) | c3_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[526, 523])).
% 0.55/0.75 tff(528,plain,
% 0.55/0.75 ((~hskp21) | c3_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[527, 523])).
% 0.55/0.75 tff(529,plain,
% 0.55/0.75 ((~hskp21) | c3_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[528, 523])).
% 0.55/0.75 tff(530,plain,
% 0.55/0.75 (c3_1(a631)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[529, 516])).
% 0.55/0.75 tff(531,plain,
% 0.55/0.75 (((~hskp21) | c0_1(a631)) <=> ((~hskp21) | c0_1(a631))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(532,axiom,((~hskp21) | c0_1(a631)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.55/0.75 tff(533,plain,
% 0.55/0.75 ((~hskp21) | c0_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.55/0.75 tff(534,plain,
% 0.55/0.75 ((~hskp21) | c0_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[533, 531])).
% 0.55/0.75 tff(535,plain,
% 0.55/0.75 ((~hskp21) | c0_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[534, 531])).
% 0.55/0.75 tff(536,plain,
% 0.55/0.75 ((~hskp21) | c0_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[535, 531])).
% 0.55/0.75 tff(537,plain,
% 0.55/0.75 ((~hskp21) | c0_1(a631)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[536, 531])).
% 0.55/0.75 tff(538,plain,
% 0.55/0.75 (c0_1(a631)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[537, 516])).
% 0.55/0.75 tff(539,assumption,(~hskp1), introduced(assumption)).
% 0.55/0.75 tff(540,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(541,plain,
% 0.55/0.75 ((hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(542,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[541])).
% 0.55/0.75 tff(543,plain,
% 0.55/0.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[542, 540])).
% 0.55/0.75 tff(544,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(545,plain,
% 0.55/0.75 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c1_1(a631) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a631)) | (~c0_1(a631))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.55/0.75 tff(546,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[545, 66, 539, 538, 530, 203, 522, 200, 515, 198])).
% 0.55/0.75 tff(547,plain,((~hskp21) | hskp1 | (~c1_1(a604)) | c0_1(a604) | c3_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(548,plain,
% 0.55/0.75 (~hskp21),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[547, 505, 147, 131, 154])).
% 0.55/0.75 tff(549,plain,
% 0.55/0.75 ((hskp21 | hskp4 | hskp1) <=> (hskp21 | hskp4 | hskp1)),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(550,plain,
% 0.55/0.75 (((hskp1 | hskp21) | hskp4) <=> (hskp21 | hskp4 | hskp1)),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(551,axiom,((hskp1 | hskp21) | hskp4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.55/0.75 tff(552,plain,
% 0.55/0.75 (hskp21 | hskp4 | hskp1),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.55/0.75 tff(553,plain,
% 0.55/0.75 (hskp21 | hskp4 | hskp1),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[552, 549])).
% 0.55/0.75 tff(554,plain,
% 0.55/0.75 (hskp21 | hskp4 | hskp1),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[553, 549])).
% 0.55/0.75 tff(555,plain,
% 0.55/0.75 (hskp21 | hskp4 | hskp1),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[554, 549])).
% 0.55/0.75 tff(556,plain,
% 0.55/0.75 (hskp21 | hskp4 | hskp1),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[555, 549])).
% 0.55/0.75 tff(557,plain,
% 0.55/0.75 (hskp4),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[556, 548, 505])).
% 0.55/0.75 tff(558,plain,
% 0.55/0.75 (~c2_1(a598)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[209, 557])).
% 0.55/0.75 tff(559,plain,
% 0.55/0.75 (~c1_1(a598)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[221, 557])).
% 0.55/0.75 tff(560,plain,
% 0.55/0.75 (~c0_1(a598)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[215, 557])).
% 0.55/0.75 tff(561,plain,
% 0.55/0.75 (hskp31),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[64, 505, 117])).
% 0.55/0.75 tff(562,plain,
% 0.55/0.75 (((~hskp31) | c2_1(a672)) <=> ((~hskp31) | c2_1(a672))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(563,axiom,((~hskp31) | c2_1(a672)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.55/0.75 tff(564,plain,
% 0.55/0.75 ((~hskp31) | c2_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.55/0.75 tff(565,plain,
% 0.55/0.75 ((~hskp31) | c2_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[564, 562])).
% 0.55/0.75 tff(566,plain,
% 0.55/0.75 ((~hskp31) | c2_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[565, 562])).
% 0.55/0.75 tff(567,plain,
% 0.55/0.75 ((~hskp31) | c2_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[566, 562])).
% 0.55/0.75 tff(568,plain,
% 0.55/0.75 ((~hskp31) | c2_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[567, 562])).
% 0.55/0.75 tff(569,plain,
% 0.55/0.75 (c2_1(a672)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[568, 561])).
% 0.55/0.75 tff(570,plain,
% 0.55/0.75 (((~hskp31) | c0_1(a672)) <=> ((~hskp31) | c0_1(a672))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(571,axiom,((~hskp31) | c0_1(a672)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.55/0.75 tff(572,plain,
% 0.55/0.75 ((~hskp31) | c0_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.55/0.75 tff(573,plain,
% 0.55/0.75 ((~hskp31) | c0_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[572, 570])).
% 0.55/0.75 tff(574,plain,
% 0.55/0.75 ((~hskp31) | c0_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[573, 570])).
% 0.55/0.75 tff(575,plain,
% 0.55/0.75 ((~hskp31) | c0_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[574, 570])).
% 0.55/0.75 tff(576,plain,
% 0.55/0.75 ((~hskp31) | c0_1(a672)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[575, 570])).
% 0.55/0.75 tff(577,plain,
% 0.55/0.75 (c0_1(a672)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[576, 561])).
% 0.55/0.75 tff(578,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(579,plain,
% 0.55/0.75 (((~ndr1_0) | (~c2_1(a672)) | (~c0_1(a672)) | (~c1_1(a672)) | c3_1(a604) | (~c1_1(a604)) | (~c2_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(580,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a672)) | (~c0_1(a672)) | (~c1_1(a672)) | c3_1(a604) | (~c1_1(a604)) | (~c2_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[579])).
% 0.55/0.75 tff(581,plain,
% 0.55/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a672)) | (~c0_1(a672)) | (~c1_1(a672)) | c3_1(a604) | (~c1_1(a604)) | (~c2_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[580, 578])).
% 0.55/0.75 tff(582,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a672)) | (~c0_1(a672)) | (~c1_1(a672)) | c3_1(a604) | (~c1_1(a604)) | (~c2_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(583,plain,
% 0.55/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c1_1(a672)) | (~c2_1(a672)) | (~c0_1(a672)) | (~c2_1(a604)) | c3_1(a604) | (~c1_1(a604))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.55/0.75 tff(584,plain,
% 0.55/0.75 (~c1_1(a672)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[583, 66, 577, 569, 147, 139, 560, 559, 558, 164, 154])).
% 0.55/0.76 tff(585,plain,
% 0.55/0.76 (((~hskp31) | c3_1(a672)) <=> ((~hskp31) | c3_1(a672))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(586,axiom,((~hskp31) | c3_1(a672)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.55/0.76 tff(587,plain,
% 0.55/0.76 ((~hskp31) | c3_1(a672)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.55/0.76 tff(588,plain,
% 0.55/0.76 ((~hskp31) | c3_1(a672)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[587, 585])).
% 0.55/0.76 tff(589,plain,
% 0.55/0.76 ((~hskp31) | c3_1(a672)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[588, 585])).
% 0.55/0.76 tff(590,plain,
% 0.55/0.76 ((~hskp31) | c3_1(a672)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[589, 585])).
% 0.55/0.76 tff(591,plain,
% 0.55/0.76 ((~hskp31) | c3_1(a672)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[590, 585])).
% 0.55/0.76 tff(592,plain,
% 0.55/0.76 (c3_1(a672)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[591, 561])).
% 0.55/0.76 tff(593,plain,
% 0.55/0.76 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(594,plain,
% 0.55/0.76 ((hskp1 | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(595,plain,
% 0.55/0.76 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[594])).
% 0.55/0.76 tff(596,plain,
% 0.55/0.76 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604)))),
% 0.55/0.76 inference(transitivity,[status(thm)],[595, 593])).
% 0.55/0.76 tff(597,plain,
% 0.55/0.76 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(598,plain,
% 0.55/0.76 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a604) | (~ndr1_0) | c1_1(a672) | (~c3_1(a672)) | (~c0_1(a672)) | c3_1(a604) | (~c1_1(a604))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.55/0.76 tff(599,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[598, 66, 505, 577, 592, 147, 131, 515, 154, 584])).
% 0.55/0.76 tff(600,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 0.55/0.76 tff(601,plain,
% 0.55/0.76 (((~hskp24) | (~c2_1(a651))) <=> ((~hskp24) | (~c2_1(a651)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(602,plain,
% 0.55/0.76 (((~c2_1(a651)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a651)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(603,axiom,((~c2_1(a651)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.55/0.76 tff(604,plain,
% 0.55/0.76 ((~hskp24) | (~c2_1(a651))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.55/0.76 tff(605,plain,
% 0.55/0.76 ((~hskp24) | (~c2_1(a651))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[604, 601])).
% 0.55/0.76 tff(606,plain,
% 0.55/0.76 (~c2_1(a651)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[605, 600])).
% 0.55/0.76 tff(607,plain,
% 0.55/0.76 (((~hskp24) | c1_1(a651)) <=> ((~hskp24) | c1_1(a651))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(608,axiom,((~hskp24) | c1_1(a651)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.55/0.76 tff(609,plain,
% 0.55/0.76 ((~hskp24) | c1_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.55/0.76 tff(610,plain,
% 0.55/0.76 ((~hskp24) | c1_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[609, 607])).
% 0.55/0.76 tff(611,plain,
% 0.55/0.76 ((~hskp24) | c1_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[610, 607])).
% 0.55/0.76 tff(612,plain,
% 0.55/0.76 ((~hskp24) | c1_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[611, 607])).
% 0.55/0.76 tff(613,plain,
% 0.55/0.76 ((~hskp24) | c1_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[612, 607])).
% 0.55/0.76 tff(614,plain,
% 0.55/0.76 (c1_1(a651)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[613, 600])).
% 0.55/0.76 tff(615,assumption,(~c3_1(a609)), introduced(assumption)).
% 0.55/0.76 tff(616,assumption,(c2_1(a609)), introduced(assumption)).
% 0.55/0.76 tff(617,plain,
% 0.55/0.76 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(618,plain,
% 0.55/0.76 ((hskp14 | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609))) <=> (hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(619,plain,
% 0.55/0.76 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[618])).
% 0.55/0.76 tff(620,plain,
% 0.55/0.76 (((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.55/0.76 inference(transitivity,[status(thm)],[619, 617])).
% 0.55/0.76 tff(621,plain,
% 0.55/0.76 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(622,plain,
% 0.55/0.76 ((~![U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c0_1(a609))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.55/0.76 tff(623,plain,
% 0.55/0.76 (~c0_1(a609)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[622, 66, 2, 616, 615, 12])).
% 0.55/0.76 tff(624,plain,
% 0.55/0.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(625,plain,
% 0.55/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[624])).
% 0.55/0.76 tff(626,plain,
% 0.55/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(627,plain,
% 0.55/0.76 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(628,plain,
% 0.55/0.76 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[627])).
% 0.55/0.76 tff(629,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.55/0.76 tff(630,plain,
% 0.55/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.55/0.76 tff(631,plain,
% 0.55/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[630, 626])).
% 0.55/0.76 tff(632,plain,(
% 0.55/0.76 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.55/0.76 inference(skolemize,[status(sab)],[631])).
% 0.55/0.76 tff(633,plain,
% 0.55/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[632, 625])).
% 0.55/0.76 tff(634,assumption,(~c1_1(a609)), introduced(assumption)).
% 0.55/0.76 tff(635,plain,
% 0.55/0.76 (^[U: $i] : refl((hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(636,plain,
% 0.55/0.76 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[635])).
% 0.55/0.76 tff(637,plain,
% 0.55/0.76 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(638,plain,
% 0.55/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp5) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp5))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp5) <=> (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp5) <=> (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(639,plain,
% 0.55/0.76 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp5) <=> ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[638])).
% 0.55/0.76 tff(640,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.55/0.76 tff(641,plain,
% 0.55/0.76 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.55/0.76 tff(642,plain,
% 0.55/0.76 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[641, 637])).
% 0.55/0.76 tff(643,plain,(
% 0.55/0.76 ![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.76 inference(skolemize,[status(sab)],[642])).
% 0.55/0.76 tff(644,plain,
% 0.55/0.76 (![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[643, 636])).
% 0.55/0.76 tff(645,plain,
% 0.55/0.76 (((~hskp24) | c3_1(a651)) <=> ((~hskp24) | c3_1(a651))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(646,axiom,((~hskp24) | c3_1(a651)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.55/0.76 tff(647,plain,
% 0.55/0.76 ((~hskp24) | c3_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.55/0.76 tff(648,plain,
% 0.55/0.76 ((~hskp24) | c3_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[647, 645])).
% 0.55/0.76 tff(649,plain,
% 0.55/0.76 ((~hskp24) | c3_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[648, 645])).
% 0.55/0.76 tff(650,plain,
% 0.55/0.76 ((~hskp24) | c3_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[649, 645])).
% 0.55/0.76 tff(651,plain,
% 0.55/0.76 ((~hskp24) | c3_1(a651)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[650, 645])).
% 0.55/0.76 tff(652,plain,
% 0.55/0.76 (c3_1(a651)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[651, 600])).
% 0.55/0.76 tff(653,plain,
% 0.55/0.76 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(654,plain,
% 0.55/0.76 ((hskp10 | hskp5 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651))) <=> (hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(655,plain,
% 0.55/0.76 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[654])).
% 0.55/0.76 tff(656,plain,
% 0.55/0.76 (((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.55/0.76 inference(transitivity,[status(thm)],[655, 653])).
% 0.55/0.76 tff(657,plain,
% 0.55/0.76 ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp10 | hskp5 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(658,plain,
% 0.55/0.76 ((~![U: $i] : (hskp10 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp10 | hskp5 | c2_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[657, 656])).
% 0.55/0.76 tff(659,plain,
% 0.55/0.76 (hskp10 | hskp5),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[658, 66, 614, 652, 606, 644])).
% 0.55/0.76 tff(660,plain,
% 0.55/0.76 (hskp5),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[659, 75])).
% 0.55/0.76 tff(661,plain,
% 0.55/0.76 (((~hskp5) | c3_1(a599)) <=> ((~hskp5) | c3_1(a599))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(662,axiom,((~hskp5) | c3_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.55/0.76 tff(663,plain,
% 0.55/0.76 ((~hskp5) | c3_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.55/0.76 tff(664,plain,
% 0.55/0.76 ((~hskp5) | c3_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[663, 661])).
% 0.55/0.76 tff(665,plain,
% 0.55/0.76 ((~hskp5) | c3_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[664, 661])).
% 0.55/0.76 tff(666,plain,
% 0.55/0.76 ((~hskp5) | c3_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[665, 661])).
% 0.55/0.76 tff(667,plain,
% 0.55/0.76 ((~hskp5) | c3_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[666, 661])).
% 0.55/0.76 tff(668,plain,
% 0.55/0.76 (c3_1(a599)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[667, 660])).
% 0.55/0.76 tff(669,plain,
% 0.55/0.76 (((~hskp5) | c2_1(a599)) <=> ((~hskp5) | c2_1(a599))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(670,axiom,((~hskp5) | c2_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.55/0.76 tff(671,plain,
% 0.55/0.76 ((~hskp5) | c2_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.55/0.76 tff(672,plain,
% 0.55/0.76 ((~hskp5) | c2_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[671, 669])).
% 0.55/0.76 tff(673,plain,
% 0.55/0.76 ((~hskp5) | c2_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[672, 669])).
% 0.55/0.76 tff(674,plain,
% 0.55/0.76 ((~hskp5) | c2_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[673, 669])).
% 0.55/0.76 tff(675,plain,
% 0.55/0.76 ((~hskp5) | c2_1(a599)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[674, 669])).
% 0.55/0.76 tff(676,plain,
% 0.55/0.76 (c2_1(a599)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[675, 660])).
% 0.55/0.76 tff(677,plain,
% 0.55/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(678,plain,
% 0.55/0.76 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651))) <=> (c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(679,plain,
% 0.55/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[678])).
% 0.55/0.76 tff(680,plain,
% 0.55/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651)))),
% 0.55/0.76 inference(transitivity,[status(thm)],[679, 677])).
% 0.55/0.76 tff(681,plain,
% 0.55/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(682,plain,
% 0.55/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | (~c2_1(a609)) | c0_1(a651) | (~c1_1(a651))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[681, 680])).
% 0.55/0.76 tff(683,plain,
% 0.55/0.76 ((~c0_1(a599)) | c0_1(a651)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[682, 66, 614, 616, 676, 668, 606, 634, 615, 633])).
% 0.55/0.76 tff(684,plain,
% 0.55/0.76 (~c0_1(a599)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[683, 1])).
% 0.55/0.76 tff(685,plain,
% 0.55/0.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.55/0.76 inference(bind,[status(th)],[])).
% 0.55/0.76 tff(686,plain,
% 0.55/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.76 inference(quant_intro,[status(thm)],[685])).
% 0.55/0.76 tff(687,plain,
% 0.55/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(688,plain,
% 0.55/0.76 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.55/0.77 inference(bind,[status(th)],[])).
% 0.55/0.77 tff(689,plain,
% 0.55/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.77 inference(quant_intro,[status(thm)],[688])).
% 0.55/0.77 tff(690,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.55/0.77 tff(691,plain,
% 0.55/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.55/0.77 tff(692,plain,
% 0.55/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[691, 687])).
% 0.55/0.77 tff(693,plain,(
% 0.55/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.77 inference(skolemize,[status(sab)],[692])).
% 0.55/0.77 tff(694,plain,
% 0.55/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[693, 686])).
% 0.55/0.77 tff(695,plain,
% 0.55/0.77 (((~hskp5) | (~c1_1(a599))) <=> ((~hskp5) | (~c1_1(a599)))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(696,plain,
% 0.55/0.77 (((~c1_1(a599)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a599)))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(697,axiom,((~c1_1(a599)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.55/0.77 tff(698,plain,
% 0.55/0.77 ((~hskp5) | (~c1_1(a599))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[697, 696])).
% 0.55/0.77 tff(699,plain,
% 0.55/0.77 ((~hskp5) | (~c1_1(a599))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[698, 695])).
% 0.55/0.77 tff(700,plain,
% 0.55/0.77 (~c1_1(a599)),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[699, 660])).
% 0.55/0.77 tff(701,plain,
% 0.55/0.77 (^[U: $i] : refl((hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.55/0.77 inference(bind,[status(th)],[])).
% 0.55/0.77 tff(702,plain,
% 0.55/0.77 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.77 inference(quant_intro,[status(thm)],[701])).
% 0.55/0.77 tff(703,plain,
% 0.55/0.77 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(704,plain,
% 0.55/0.77 (^[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) | hskp8) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp8))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp8) <=> (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp8) <=> (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.55/0.77 inference(bind,[status(th)],[])).
% 0.55/0.77 tff(705,plain,
% 0.55/0.77 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp8) <=> ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.77 inference(quant_intro,[status(thm)],[704])).
% 0.55/0.77 tff(706,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.55/0.77 tff(707,plain,
% 0.55/0.77 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[706, 705])).
% 0.55/0.77 tff(708,plain,
% 0.55/0.77 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[707, 703])).
% 0.55/0.77 tff(709,plain,(
% 0.55/0.77 ![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.77 inference(skolemize,[status(sab)],[708])).
% 0.55/0.77 tff(710,plain,
% 0.55/0.77 (![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[709, 702])).
% 0.55/0.77 tff(711,plain,
% 0.55/0.77 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(712,plain,
% 0.55/0.77 ((hskp14 | hskp8 | (~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c1_1(a651))) <=> (hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(713,plain,
% 0.55/0.77 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651))))),
% 0.55/0.77 inference(monotonicity,[status(thm)],[712])).
% 0.55/0.77 tff(714,plain,
% 0.55/0.77 (((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.55/0.77 inference(transitivity,[status(thm)],[713, 711])).
% 0.55/0.77 tff(715,plain,
% 0.55/0.77 ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp8 | (~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.55/0.77 inference(quant_inst,[status(thm)],[])).
% 0.55/0.77 tff(716,plain,
% 0.55/0.77 ((~![U: $i] : (hskp14 | hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp8 | (~ndr1_0) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[715, 714])).
% 0.55/0.77 tff(717,plain,
% 0.55/0.77 (hskp14 | hskp8 | c0_1(a651)),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[716, 66, 614, 652, 710])).
% 0.55/0.77 tff(718,plain,
% 0.55/0.77 (hskp8),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[717, 1, 2])).
% 0.55/0.77 tff(719,plain,
% 0.55/0.77 (~c2_1(a603)),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[464, 718])).
% 0.55/0.77 tff(720,plain,
% 0.55/0.77 (c0_1(a603)),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[495, 718])).
% 0.55/0.77 tff(721,plain,
% 0.55/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(722,plain,
% 0.55/0.77 (((~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599))) <=> (c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(723,plain,
% 0.55/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603))))),
% 0.55/0.77 inference(monotonicity,[status(thm)],[722])).
% 0.55/0.77 tff(724,plain,
% 0.55/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.55/0.77 inference(transitivity,[status(thm)],[723, 721])).
% 0.55/0.77 tff(725,plain,
% 0.55/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))),
% 0.55/0.77 inference(quant_inst,[status(thm)],[])).
% 0.55/0.77 tff(726,plain,
% 0.55/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a603)) | (~c0_1(a603))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.55/0.77 tff(727,plain,
% 0.55/0.77 (~c3_1(a603)),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[726, 66, 720, 676, 668, 719, 700, 694, 684])).
% 0.55/0.77 tff(728,plain,
% 0.55/0.77 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.55/0.77 inference(bind,[status(th)],[])).
% 0.55/0.77 tff(729,plain,
% 0.55/0.77 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.55/0.77 inference(quant_intro,[status(thm)],[728])).
% 0.55/0.77 tff(730,plain,
% 0.55/0.77 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(731,plain,
% 0.62/0.77 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(732,plain,
% 0.62/0.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[731])).
% 0.62/0.77 tff(733,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.62/0.77 tff(734,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[733, 732])).
% 0.62/0.77 tff(735,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[734, 730])).
% 0.62/0.77 tff(736,plain,(
% 0.62/0.77 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.77 inference(skolemize,[status(sab)],[735])).
% 0.62/0.77 tff(737,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[736, 729])).
% 0.62/0.77 tff(738,plain,
% 0.62/0.77 (~c1_1(a603)),
% 0.62/0.77 inference(unit_resolution,[status(thm)],[470, 718])).
% 0.62/0.77 tff(739,plain,
% 0.62/0.77 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(740,plain,
% 0.62/0.77 ((hskp11 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c0_1(a603)) | c3_1(a609) | c0_1(a609) | (~c2_1(a609))) <=> (hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(741,plain,
% 0.62/0.77 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c0_1(a603)) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609)))),
% 0.62/0.77 inference(monotonicity,[status(thm)],[740])).
% 0.62/0.77 tff(742,plain,
% 0.62/0.77 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c0_1(a603)) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609))),
% 0.62/0.77 inference(transitivity,[status(thm)],[741, 739])).
% 0.62/0.77 tff(743,plain,
% 0.62/0.77 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c0_1(a603)) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)))),
% 0.62/0.77 inference(quant_inst,[status(thm)],[])).
% 0.62/0.77 tff(744,plain,
% 0.62/0.77 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a609) | c1_1(a603) | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a609)) | c0_1(a609)),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.62/0.77 tff(745,plain,
% 0.62/0.77 (hskp11),
% 0.62/0.77 inference(unit_resolution,[status(thm)],[744, 66, 616, 720, 615, 738, 737, 727, 623])).
% 0.62/0.77 tff(746,plain,
% 0.62/0.77 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(747,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[746])).
% 0.62/0.77 tff(748,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(749,plain,
% 0.62/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.62/0.77 inference(bind,[status(th)],[])).
% 0.62/0.77 tff(750,plain,
% 0.62/0.77 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.77 inference(quant_intro,[status(thm)],[749])).
% 0.62/0.77 tff(751,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.62/0.77 tff(752,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[751, 750])).
% 0.62/0.77 tff(753,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[752, 748])).
% 0.62/0.77 tff(754,plain,(
% 0.62/0.77 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.77 inference(skolemize,[status(sab)],[753])).
% 0.62/0.77 tff(755,plain,
% 0.62/0.77 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[754, 747])).
% 0.62/0.77 tff(756,assumption,(hskp11), introduced(assumption)).
% 0.62/0.77 tff(757,plain,
% 0.62/0.77 (((~hskp11) | (~c3_1(a608))) <=> ((~hskp11) | (~c3_1(a608)))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(758,plain,
% 0.62/0.77 (((~c3_1(a608)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a608)))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.77 tff(759,axiom,((~c3_1(a608)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.62/0.77 tff(760,plain,
% 0.62/0.77 ((~hskp11) | (~c3_1(a608))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[759, 758])).
% 0.62/0.77 tff(761,plain,
% 0.62/0.77 ((~hskp11) | (~c3_1(a608))),
% 0.62/0.77 inference(modus_ponens,[status(thm)],[760, 757])).
% 0.62/0.77 tff(762,plain,
% 0.62/0.77 (~c3_1(a608)),
% 0.62/0.77 inference(unit_resolution,[status(thm)],[761, 756])).
% 0.62/0.77 tff(763,plain,
% 0.62/0.77 (((~hskp11) | (~c0_1(a608))) <=> ((~hskp11) | (~c0_1(a608)))),
% 0.62/0.77 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(764,plain,
% 0.62/0.78 (((~c0_1(a608)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a608)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(765,axiom,((~c0_1(a608)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.62/0.78 tff(766,plain,
% 0.62/0.78 ((~hskp11) | (~c0_1(a608))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.62/0.78 tff(767,plain,
% 0.62/0.78 ((~hskp11) | (~c0_1(a608))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[766, 763])).
% 0.62/0.78 tff(768,plain,
% 0.62/0.78 (~c0_1(a608)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[767, 756])).
% 0.62/0.78 tff(769,plain,
% 0.62/0.78 (((~hskp11) | c1_1(a608)) <=> ((~hskp11) | c1_1(a608))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(770,axiom,((~hskp11) | c1_1(a608)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.62/0.78 tff(771,plain,
% 0.62/0.78 ((~hskp11) | c1_1(a608)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[770, 769])).
% 0.62/0.78 tff(772,plain,
% 0.62/0.78 ((~hskp11) | c1_1(a608)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[771, 769])).
% 0.62/0.78 tff(773,plain,
% 0.62/0.78 ((~hskp11) | c1_1(a608)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[772, 769])).
% 0.62/0.78 tff(774,plain,
% 0.62/0.78 ((~hskp11) | c1_1(a608)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[773, 769])).
% 0.62/0.78 tff(775,plain,
% 0.62/0.78 ((~hskp11) | c1_1(a608)),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[774, 769])).
% 0.62/0.78 tff(776,plain,
% 0.62/0.78 (c1_1(a608)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[775, 756])).
% 0.62/0.78 tff(777,assumption,(~hskp28), introduced(assumption)).
% 0.62/0.78 tff(778,plain,
% 0.62/0.78 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(779,plain,
% 0.62/0.78 ((hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a608) | c0_1(a608) | (~c1_1(a608))) <=> (hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(780,plain,
% 0.62/0.78 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a608) | c0_1(a608) | (~c1_1(a608)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651))))),
% 0.62/0.78 inference(monotonicity,[status(thm)],[779])).
% 0.62/0.78 tff(781,plain,
% 0.62/0.78 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a608) | c0_1(a608) | (~c1_1(a608)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.62/0.78 inference(transitivity,[status(thm)],[780, 778])).
% 0.62/0.78 tff(782,plain,
% 0.62/0.78 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a608) | c0_1(a608) | (~c1_1(a608)))),
% 0.62/0.78 inference(quant_inst,[status(thm)],[])).
% 0.62/0.78 tff(783,plain,
% 0.62/0.78 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a608) | c3_1(a608) | (~ndr1_0) | (~c1_1(a608)) | (~c3_1(a651)) | (~c1_1(a651))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.62/0.78 tff(784,plain,
% 0.62/0.78 ($false),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[783, 66, 777, 614, 652, 776, 606, 768, 762, 755])).
% 0.62/0.78 tff(785,plain,((~hskp11) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.62/0.78 tff(786,plain,
% 0.62/0.78 (hskp28),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[785, 745])).
% 0.62/0.78 tff(787,plain,
% 0.62/0.78 (c3_1(a595)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[354, 786])).
% 0.62/0.78 tff(788,plain,
% 0.62/0.78 (c2_1(a595)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[362, 786])).
% 0.62/0.78 tff(789,plain,
% 0.62/0.78 (c1_1(a595)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[370, 786])).
% 0.62/0.78 tff(790,plain,
% 0.62/0.78 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(791,plain,
% 0.62/0.78 ((hskp10 | (~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651))) <=> (hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(792,plain,
% 0.62/0.78 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651))))),
% 0.62/0.78 inference(monotonicity,[status(thm)],[791])).
% 0.62/0.78 tff(793,plain,
% 0.62/0.78 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.78 inference(transitivity,[status(thm)],[792, 790])).
% 0.62/0.78 tff(794,plain,
% 0.62/0.78 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.78 inference(quant_inst,[status(thm)],[])).
% 0.62/0.78 tff(795,plain,
% 0.62/0.78 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a651) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | c0_1(a651) | (~c1_1(a651))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.62/0.78 tff(796,plain,
% 0.62/0.78 ($false),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[795, 66, 75, 789, 788, 787, 614, 606, 106, 1])).
% 0.62/0.78 tff(797,plain,(c0_1(a651) | (~c2_1(a609)) | c3_1(a609) | c1_1(a609) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.62/0.78 tff(798,plain,
% 0.62/0.78 ($false),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[797, 96, 90, 1, 82, 2])).
% 0.62/0.78 tff(799,plain,((~hskp12) | c0_1(a651) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.62/0.78 tff(800,plain,
% 0.62/0.78 (~hskp12),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[799, 2, 1])).
% 0.62/0.78 tff(801,assumption,(~hskp10), introduced(assumption)).
% 0.62/0.78 tff(802,assumption,(~hskp12), introduced(assumption)).
% 0.62/0.78 tff(803,plain,
% 0.62/0.78 ((hskp9 | hskp12 | hskp10) <=> (hskp9 | hskp12 | hskp10)),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(804,plain,
% 0.62/0.78 (((hskp10 | hskp9) | hskp12) <=> (hskp9 | hskp12 | hskp10)),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(805,axiom,((hskp10 | hskp9) | hskp12), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.62/0.78 tff(806,plain,
% 0.62/0.78 (hskp9 | hskp12 | hskp10),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[805, 804])).
% 0.62/0.78 tff(807,plain,
% 0.62/0.78 (hskp9 | hskp12 | hskp10),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[806, 803])).
% 0.62/0.78 tff(808,plain,
% 0.62/0.78 (hskp9 | hskp12 | hskp10),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[807, 803])).
% 0.62/0.78 tff(809,plain,
% 0.62/0.78 (hskp9 | hskp12 | hskp10),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[808, 803])).
% 0.62/0.78 tff(810,plain,
% 0.62/0.78 (hskp9 | hskp12 | hskp10),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[809, 803])).
% 0.62/0.78 tff(811,plain,
% 0.62/0.78 (hskp9),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[810, 802, 801])).
% 0.62/0.78 tff(812,plain,
% 0.62/0.78 (c2_1(a604)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[138, 811])).
% 0.62/0.78 tff(813,assumption,(~c1_1(a604)), introduced(assumption)).
% 0.62/0.78 tff(814,assumption,(~c3_1(a615)), introduced(assumption)).
% 0.62/0.78 tff(815,plain,
% 0.62/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(816,plain,
% 0.62/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[815])).
% 0.62/0.78 tff(817,plain,
% 0.62/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(818,plain,
% 0.62/0.78 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(819,plain,
% 0.62/0.78 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[818])).
% 0.62/0.78 tff(820,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.62/0.78 tff(821,plain,
% 0.62/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[820, 819])).
% 0.62/0.78 tff(822,plain,
% 0.62/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[821, 817])).
% 0.62/0.78 tff(823,plain,(
% 0.62/0.78 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.78 inference(skolemize,[status(sab)],[822])).
% 0.62/0.78 tff(824,plain,
% 0.62/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[823, 816])).
% 0.62/0.78 tff(825,plain,
% 0.62/0.78 (~hskp9),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[146, 813])).
% 0.62/0.78 tff(826,plain,
% 0.62/0.78 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(827,plain,
% 0.62/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[826])).
% 0.62/0.78 tff(828,plain,
% 0.62/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(829,plain,
% 0.62/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.62/0.78 inference(bind,[status(th)],[])).
% 0.62/0.78 tff(830,plain,
% 0.62/0.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.78 inference(quant_intro,[status(thm)],[829])).
% 0.62/0.78 tff(831,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.62/0.78 tff(832,plain,
% 0.62/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.62/0.78 tff(833,plain,
% 0.62/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[832, 828])).
% 0.62/0.78 tff(834,plain,(
% 0.62/0.78 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.78 inference(skolemize,[status(sab)],[833])).
% 0.62/0.78 tff(835,plain,
% 0.62/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[834, 827])).
% 0.62/0.78 tff(836,plain,
% 0.62/0.78 (hskp21),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[556, 539, 339])).
% 0.62/0.78 tff(837,plain,
% 0.62/0.78 (~c1_1(a631)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[521, 836])).
% 0.62/0.78 tff(838,plain,
% 0.62/0.78 (c3_1(a631)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[529, 836])).
% 0.62/0.78 tff(839,plain,
% 0.62/0.78 (c0_1(a631)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[537, 836])).
% 0.62/0.78 tff(840,plain,
% 0.62/0.78 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(841,plain,
% 0.62/0.78 ((hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a604) | c1_1(a604) | (~c2_1(a604))) <=> (hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(842,plain,
% 0.62/0.78 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a604) | c1_1(a604) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631))))),
% 0.62/0.78 inference(monotonicity,[status(thm)],[841])).
% 0.62/0.78 tff(843,plain,
% 0.62/0.78 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a604) | c1_1(a604) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.62/0.78 inference(transitivity,[status(thm)],[842, 840])).
% 0.62/0.78 tff(844,plain,
% 0.62/0.78 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a604) | c1_1(a604) | (~c2_1(a604)))),
% 0.62/0.78 inference(quant_inst,[status(thm)],[])).
% 0.62/0.78 tff(845,plain,
% 0.62/0.78 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a604) | c1_1(a631) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a631)) | (~c0_1(a631))),
% 0.62/0.78 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.62/0.78 tff(846,plain,
% 0.62/0.78 (~c2_1(a604)),
% 0.62/0.78 inference(unit_resolution,[status(thm)],[845, 66, 539, 839, 838, 813, 837, 200, 835])).
% 0.62/0.78 tff(847,plain,
% 0.62/0.78 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(848,plain,
% 0.62/0.78 ((hskp14 | hskp4 | (~ndr1_0) | c3_1(a604) | c2_1(a604) | c1_1(a604)) <=> (hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604))),
% 0.62/0.78 inference(rewrite,[status(thm)],[])).
% 0.62/0.78 tff(849,plain,
% 0.62/0.78 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a604) | c2_1(a604) | c1_1(a604))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604)))),
% 0.62/0.78 inference(monotonicity,[status(thm)],[848])).
% 0.62/0.78 tff(850,plain,
% 0.62/0.78 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a604) | c2_1(a604) | c1_1(a604))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604))),
% 0.62/0.78 inference(transitivity,[status(thm)],[849, 847])).
% 0.62/0.78 tff(851,plain,
% 0.62/0.78 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c3_1(a604) | c2_1(a604) | c1_1(a604))),
% 0.62/0.78 inference(quant_inst,[status(thm)],[])).
% 0.62/0.78 tff(852,plain,
% 0.62/0.78 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp14 | hskp4 | c1_1(a604) | c2_1(a604) | (~ndr1_0) | c3_1(a604)),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[851, 850])).
% 0.62/0.79 tff(853,plain,
% 0.62/0.79 (hskp14 | hskp4 | c2_1(a604) | c3_1(a604)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[852, 66, 813, 441])).
% 0.62/0.79 tff(854,plain,
% 0.62/0.79 (c3_1(a604)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[853, 2, 339, 846])).
% 0.62/0.79 tff(855,assumption,(~hskp8), introduced(assumption)).
% 0.62/0.79 tff(856,plain,
% 0.62/0.79 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(857,plain,
% 0.62/0.79 ((hskp8 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651))) <=> (hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(858,plain,
% 0.62/0.79 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651))))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[857])).
% 0.62/0.79 tff(859,plain,
% 0.62/0.79 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.79 inference(transitivity,[status(thm)],[858, 856])).
% 0.62/0.79 tff(860,plain,
% 0.62/0.79 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(861,plain,
% 0.62/0.79 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp8 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.62/0.79 tff(862,plain,
% 0.62/0.79 (hskp8 | hskp4 | (~c0_1(a651))),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[861, 66, 614, 606, 451])).
% 0.62/0.79 tff(863,plain,
% 0.62/0.79 (~c0_1(a651)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[862, 855, 339])).
% 0.62/0.79 tff(864,plain,
% 0.62/0.79 ($false),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[717, 863, 855, 2])).
% 0.62/0.79 tff(865,plain,(hskp8 | hskp14 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.62/0.79 tff(866,plain,
% 0.62/0.79 (hskp8),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[865, 2, 339])).
% 0.62/0.79 tff(867,plain,
% 0.62/0.79 (~c2_1(a603)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[464, 866])).
% 0.62/0.79 tff(868,plain,
% 0.62/0.79 (~c1_1(a603)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[470, 866])).
% 0.62/0.79 tff(869,plain,
% 0.62/0.79 (c3_1(a603)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[477, 66, 2, 339, 868, 867, 441])).
% 0.62/0.79 tff(870,plain,
% 0.62/0.79 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(871,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[870])).
% 0.62/0.79 tff(872,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(873,plain,
% 0.62/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(874,plain,
% 0.62/0.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[873])).
% 0.62/0.79 tff(875,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.62/0.79 tff(876,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[875, 874])).
% 0.62/0.79 tff(877,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[876, 872])).
% 0.62/0.79 tff(878,plain,(
% 0.62/0.79 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.79 inference(skolemize,[status(sab)],[877])).
% 0.62/0.79 tff(879,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[878, 871])).
% 0.62/0.79 tff(880,plain,
% 0.62/0.79 (c0_1(a603)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[495, 866])).
% 0.62/0.79 tff(881,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(882,plain,
% 0.62/0.79 ((hskp12 | (~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c2_1(a603) | c1_1(a603) | (~c0_1(a603))) <=> (hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(883,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603))))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[882])).
% 0.62/0.79 tff(884,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.62/0.79 inference(transitivity,[status(thm)],[883, 881])).
% 0.62/0.79 tff(885,plain,
% 0.62/0.79 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a603) | (~c3_1(a603)) | (~c0_1(a603)) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(886,plain,
% 0.62/0.79 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a603) | c2_1(a603) | (~ndr1_0) | (~c3_1(a603)) | (~c0_1(a603))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[885, 884])).
% 0.62/0.79 tff(887,plain,
% 0.62/0.79 (hskp12),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[886, 66, 880, 868, 867, 879, 869])).
% 0.62/0.79 tff(888,plain,
% 0.62/0.79 (~c3_1(a609)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[95, 887])).
% 0.62/0.79 tff(889,plain,
% 0.62/0.79 (c2_1(a609)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[89, 887])).
% 0.62/0.79 tff(890,plain,
% 0.62/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(891,plain,
% 0.62/0.79 (((~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a604) | c1_1(a604) | c0_1(a604)) <=> (c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(892,plain,
% 0.62/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609))))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[891])).
% 0.62/0.79 tff(893,plain,
% 0.62/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609)))),
% 0.62/0.79 inference(transitivity,[status(thm)],[892, 890])).
% 0.62/0.79 tff(894,plain,
% 0.62/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c0_1(a609)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a604) | c1_1(a604) | c0_1(a604))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(895,plain,
% 0.62/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c2_1(a604) | c3_1(a609) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a609)) | (~c0_1(a609))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[894, 893])).
% 0.62/0.79 tff(896,plain,
% 0.62/0.79 (~c0_1(a609)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[895, 66, 889, 813, 846, 888, 200, 824, 854])).
% 0.62/0.79 tff(897,plain,
% 0.62/0.79 (~c1_1(a609)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[81, 887])).
% 0.62/0.79 tff(898,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(899,plain,
% 0.62/0.79 ((hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a609) | c1_1(a609) | (~c2_1(a609))) <=> (hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(900,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631))))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[899])).
% 0.62/0.79 tff(901,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.62/0.79 inference(transitivity,[status(thm)],[900, 898])).
% 0.62/0.79 tff(902,plain,
% 0.62/0.79 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c0_1(a609) | c1_1(a609) | (~c2_1(a609)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(903,plain,
% 0.62/0.79 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a631) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | c0_1(a609) | (~c3_1(a631)) | (~c0_1(a631))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.62/0.79 tff(904,plain,
% 0.62/0.79 ($false),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[903, 66, 539, 839, 838, 889, 837, 897, 835, 896])).
% 0.62/0.79 tff(905,plain,(hskp14 | hskp1 | c1_1(a604) | c0_1(a604) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.62/0.79 tff(906,plain,
% 0.62/0.79 (hskp14),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[905, 539, 813, 200, 339])).
% 0.62/0.79 tff(907,plain,
% 0.62/0.79 (c0_1(a615)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[280, 906])).
% 0.62/0.79 tff(908,plain,
% 0.62/0.79 (((~hskp14) | (~c1_1(a615))) <=> ((~hskp14) | (~c1_1(a615)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(909,plain,
% 0.62/0.79 (((~c1_1(a615)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a615)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(910,axiom,((~c1_1(a615)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.62/0.79 tff(911,plain,
% 0.62/0.79 ((~hskp14) | (~c1_1(a615))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.62/0.79 tff(912,plain,
% 0.62/0.79 ((~hskp14) | (~c1_1(a615))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[911, 908])).
% 0.62/0.79 tff(913,plain,
% 0.62/0.79 (~c1_1(a615)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[912, 906])).
% 0.62/0.79 tff(914,plain,
% 0.62/0.79 (c2_1(a615)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[272, 906])).
% 0.62/0.79 tff(915,plain,
% 0.62/0.79 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(916,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[915])).
% 0.62/0.79 tff(917,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(918,plain,
% 0.62/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(919,plain,
% 0.62/0.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[918])).
% 0.62/0.79 tff(920,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.62/0.79 tff(921,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.62/0.79 tff(922,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[921, 917])).
% 0.62/0.79 tff(923,plain,(
% 0.62/0.79 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.79 inference(skolemize,[status(sab)],[922])).
% 0.62/0.79 tff(924,plain,
% 0.62/0.79 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[923, 916])).
% 0.62/0.79 tff(925,assumption,(c2_1(a615)), introduced(assumption)).
% 0.62/0.79 tff(926,assumption,(c0_1(a615)), introduced(assumption)).
% 0.62/0.79 tff(927,assumption,(~hskp9), introduced(assumption)).
% 0.62/0.79 tff(928,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(929,plain,
% 0.62/0.79 ((hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651))) <=> (hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(930,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651))))),
% 0.62/0.79 inference(monotonicity,[status(thm)],[929])).
% 0.62/0.79 tff(931,plain,
% 0.62/0.79 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.79 inference(transitivity,[status(thm)],[930, 928])).
% 0.62/0.79 tff(932,plain,
% 0.62/0.79 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.79 inference(quant_inst,[status(thm)],[])).
% 0.62/0.79 tff(933,plain,
% 0.62/0.79 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a651) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[932, 931])).
% 0.62/0.79 tff(934,plain,
% 0.62/0.79 ((~c3_1(a615)) | c0_1(a651)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[933, 927, 66, 614, 926, 925, 606, 924])).
% 0.62/0.79 tff(935,plain,
% 0.62/0.79 (~c3_1(a615)),
% 0.62/0.79 inference(unit_resolution,[status(thm)],[934, 1])).
% 0.62/0.80 tff(936,assumption,(~c1_1(a615)), introduced(assumption)).
% 0.62/0.80 tff(937,plain,
% 0.62/0.80 (hskp28 | c3_1(a615)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[345, 66, 339, 926, 925, 338])).
% 0.62/0.80 tff(938,plain,
% 0.62/0.80 (hskp28),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[937, 935])).
% 0.62/0.80 tff(939,plain,
% 0.62/0.80 (c3_1(a595)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[354, 938])).
% 0.62/0.80 tff(940,plain,
% 0.62/0.80 (c2_1(a595)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[362, 938])).
% 0.62/0.80 tff(941,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(942,plain,
% 0.62/0.80 (((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c0_1(a595)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651))) <=> (c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(943,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c0_1(a595)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651))))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[942])).
% 0.62/0.80 tff(944,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c0_1(a595)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[943, 941])).
% 0.62/0.80 tff(945,plain,
% 0.62/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c0_1(a595)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a651) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(946,plain,
% 0.62/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c3_1(a595)) | (~c0_1(a595)) | (~c2_1(a595)) | c3_1(a615) | (~c2_1(a615)) | c0_1(a651) | (~c1_1(a651))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.62/0.80 tff(947,plain,
% 0.62/0.80 (~c0_1(a595)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[946, 66, 940, 939, 614, 925, 606, 936, 633, 1, 935])).
% 0.62/0.80 tff(948,plain,
% 0.62/0.80 (hskp25 | c3_1(a615)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[304, 66, 926, 925, 298])).
% 0.62/0.80 tff(949,plain,
% 0.62/0.80 (hskp25),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[948, 935])).
% 0.62/0.80 tff(950,plain,
% 0.62/0.80 (~c0_1(a656)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[311, 949])).
% 0.62/0.80 tff(951,plain,
% 0.62/0.80 (c3_1(a656)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[319, 949])).
% 0.62/0.80 tff(952,plain,
% 0.62/0.80 (c1_1(a656)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[327, 949])).
% 0.62/0.80 tff(953,plain,
% 0.62/0.80 (c1_1(a595)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[370, 938])).
% 0.62/0.80 tff(954,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(955,plain,
% 0.62/0.80 (((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595))) <=> (c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(956,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656))))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[955])).
% 0.62/0.80 tff(957,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[956, 954])).
% 0.62/0.80 tff(958,plain,
% 0.62/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a656) | (~c1_1(a656)) | (~c3_1(a656)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(959,plain,
% 0.62/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a656) | (~ndr1_0) | (~c3_1(a595)) | c0_1(a595) | (~c1_1(a595)) | (~c2_1(a595)) | (~c3_1(a656)) | (~c1_1(a656))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.62/0.80 tff(960,plain,
% 0.62/0.80 ($false),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[959, 66, 953, 940, 939, 952, 951, 950, 116, 947])).
% 0.62/0.80 tff(961,plain,(c0_1(a651) | (~c2_1(a615)) | c1_1(a615) | (~c0_1(a615)) | hskp4 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.62/0.80 tff(962,plain,
% 0.62/0.80 (c0_1(a651)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[961, 914, 913, 907, 339, 825])).
% 0.62/0.80 tff(963,plain,
% 0.62/0.80 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(964,plain,
% 0.62/0.80 ((hskp22 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651))) <=> (hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(965,plain,
% 0.62/0.80 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651))))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[964])).
% 0.62/0.80 tff(966,plain,
% 0.62/0.80 (((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[965, 963])).
% 0.62/0.80 tff(967,plain,
% 0.62/0.80 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp22 | hskp4 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(968,plain,
% 0.62/0.80 ((~![U: $i] : (hskp22 | hskp4 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp22 | hskp4 | c2_1(a651) | (~ndr1_0) | (~c0_1(a651)) | (~c1_1(a651))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[967, 966])).
% 0.62/0.80 tff(969,plain,
% 0.62/0.80 (hskp22 | hskp4 | (~c0_1(a651))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[968, 66, 614, 606, 398])).
% 0.62/0.80 tff(970,plain,
% 0.62/0.80 (hskp22),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[969, 962, 339])).
% 0.62/0.80 tff(971,plain,
% 0.62/0.80 (~c3_1(a644)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[411, 970])).
% 0.62/0.80 tff(972,plain,
% 0.62/0.80 (~c2_1(a644)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[417, 970])).
% 0.62/0.80 tff(973,plain,
% 0.62/0.80 (~c0_1(a644)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[423, 970])).
% 0.62/0.80 tff(974,plain,
% 0.62/0.80 (c1_1(a644)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[430, 66, 973, 972, 971, 174])).
% 0.62/0.80 tff(975,plain,
% 0.62/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(976,plain,
% 0.62/0.80 ((hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644))) <=> (hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(977,plain,
% 0.62/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644))))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[976])).
% 0.62/0.80 tff(978,plain,
% 0.62/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[977, 975])).
% 0.62/0.80 tff(979,plain,
% 0.62/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(980,plain,
% 0.62/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp1 | c0_1(a644) | c3_1(a644) | c1_1(a631) | (~ndr1_0) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.62/0.80 tff(981,plain,
% 0.62/0.80 ($false),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[980, 66, 539, 839, 838, 973, 971, 837, 515, 974])).
% 0.62/0.80 tff(982,plain,(hskp1 | hskp4 | c1_1(a604) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.80 tff(983,plain,
% 0.62/0.80 (hskp1),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[982, 339, 813, 200])).
% 0.62/0.80 tff(984,plain,
% 0.62/0.80 (~c3_1(a594)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[180, 983])).
% 0.62/0.80 tff(985,plain,
% 0.62/0.80 (c0_1(a594)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[196, 983])).
% 0.62/0.80 tff(986,plain,
% 0.62/0.80 (hskp14 | (~c2_1(a594))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[386, 66, 985, 984, 12])).
% 0.62/0.80 tff(987,plain,
% 0.62/0.80 (~c2_1(a594)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[986, 2])).
% 0.62/0.80 tff(988,plain,
% 0.62/0.80 (c1_1(a594)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[188, 983])).
% 0.62/0.80 tff(989,plain,
% 0.62/0.80 (hskp22 | c2_1(a594)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[404, 66, 339, 985, 988, 398])).
% 0.62/0.80 tff(990,plain,
% 0.62/0.80 (hskp22),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[989, 987])).
% 0.62/0.80 tff(991,plain,
% 0.62/0.80 (~c3_1(a644)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[411, 990])).
% 0.62/0.80 tff(992,plain,
% 0.62/0.80 (~c2_1(a644)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[417, 990])).
% 0.62/0.80 tff(993,plain,
% 0.62/0.80 (~c0_1(a644)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[423, 990])).
% 0.62/0.80 tff(994,plain,
% 0.62/0.80 (c1_1(a644)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[430, 66, 993, 992, 991, 174])).
% 0.62/0.80 tff(995,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(996,plain,
% 0.62/0.80 (((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a604) | c0_1(a604) | (~c3_1(a604))) <=> (c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(997,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a604) | c0_1(a604) | (~c3_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644))))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[996])).
% 0.62/0.80 tff(998,plain,
% 0.62/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a604) | c0_1(a604) | (~c3_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[997, 995])).
% 0.62/0.80 tff(999,plain,
% 0.62/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a604) | c0_1(a604) | (~c3_1(a604)))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(1000,plain,
% 0.62/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a604) | c0_1(a644) | c3_1(a644) | c0_1(a604) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a604)) | (~c1_1(a644))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[999, 998])).
% 0.62/0.80 tff(1001,plain,
% 0.62/0.80 (~c3_1(a604)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[1000, 66, 813, 985, 988, 993, 991, 200, 984, 233, 994])).
% 0.62/0.80 tff(1002,plain,
% 0.62/0.80 (c2_1(a604)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[853, 1001, 339, 2])).
% 0.62/0.80 tff(1003,plain,
% 0.62/0.80 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(1004,plain,
% 0.62/0.80 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[1003])).
% 0.62/0.80 tff(1005,plain,
% 0.62/0.80 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(1006,plain,
% 0.62/0.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(1007,plain,
% 0.62/0.80 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[1006])).
% 0.62/0.80 tff(1008,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.62/0.80 tff(1009,plain,
% 0.62/0.80 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 0.62/0.80 tff(1010,plain,
% 0.62/0.80 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[1009, 1005])).
% 0.62/0.80 tff(1011,plain,(
% 0.62/0.80 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(skolemize,[status(sab)],[1010])).
% 0.62/0.80 tff(1012,plain,
% 0.62/0.80 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[1011, 1004])).
% 0.62/0.80 tff(1013,plain,
% 0.62/0.80 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(1014,plain,
% 0.62/0.80 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a604) | c0_1(a604) | (~c2_1(a604))) <=> (hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(1015,plain,
% 0.62/0.80 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604))))),
% 0.62/0.80 inference(monotonicity,[status(thm)],[1014])).
% 0.62/0.80 tff(1016,plain,
% 0.62/0.80 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)))),
% 0.62/0.80 inference(transitivity,[status(thm)],[1015, 1013])).
% 0.62/0.80 tff(1017,plain,
% 0.62/0.80 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(1018,plain,
% 0.62/0.80 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a604) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 0.62/0.80 tff(1019,plain,
% 0.62/0.80 (hskp4 | hskp3 | c1_1(a604) | (~c2_1(a604))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[1018, 66, 200, 1012])).
% 0.62/0.80 tff(1020,plain,
% 0.62/0.80 (hskp3),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[1019, 1002, 813, 339])).
% 0.62/0.80 tff(1021,plain,
% 0.62/0.80 (((~hskp3) | (~c3_1(a597))) <=> ((~hskp3) | (~c3_1(a597)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(1022,plain,
% 0.62/0.80 (((~c3_1(a597)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a597)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(1023,axiom,((~c3_1(a597)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.62/0.80 tff(1024,plain,
% 0.62/0.80 ((~hskp3) | (~c3_1(a597))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.62/0.80 tff(1025,plain,
% 0.62/0.80 ((~hskp3) | (~c3_1(a597))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[1024, 1021])).
% 0.62/0.80 tff(1026,plain,
% 0.62/0.80 (~c3_1(a597)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[1025, 1020])).
% 0.62/0.80 tff(1027,plain,
% 0.62/0.80 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(1028,plain,
% 0.62/0.80 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[1027])).
% 0.62/0.80 tff(1029,plain,
% 0.62/0.80 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(1030,plain,
% 0.62/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(1031,plain,
% 0.62/0.81 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[1030])).
% 0.62/0.81 tff(1032,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.62/0.81 tff(1033,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 0.62/0.81 tff(1034,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1033, 1029])).
% 0.62/0.81 tff(1035,plain,(
% 0.62/0.81 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.62/0.81 inference(skolemize,[status(sab)],[1034])).
% 0.62/0.81 tff(1036,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1035, 1028])).
% 0.62/0.81 tff(1037,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1038,plain,
% 0.62/0.81 ((hskp21 | (~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c1_1(a603) | (~c0_1(a603)) | (~c3_1(a603))) <=> (hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1039,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c1_1(a603) | (~c0_1(a603)) | (~c3_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[1038])).
% 0.62/0.81 tff(1040,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c1_1(a603) | (~c0_1(a603)) | (~c3_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[1039, 1037])).
% 0.62/0.81 tff(1041,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c1_1(a603) | (~c0_1(a603)) | (~c3_1(a603)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(1042,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a603) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a603)) | (~c0_1(a603))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 0.62/0.81 tff(1043,plain,
% 0.62/0.81 (hskp21),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[1042, 66, 880, 985, 988, 868, 984, 1036, 869])).
% 0.62/0.81 tff(1044,plain,
% 0.62/0.81 (~c1_1(a631)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[521, 1043])).
% 0.62/0.81 tff(1045,plain,
% 0.62/0.81 (((~hskp3) | c2_1(a597)) <=> ((~hskp3) | c2_1(a597))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1046,axiom,((~hskp3) | c2_1(a597)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.62/0.81 tff(1047,plain,
% 0.62/0.81 ((~hskp3) | c2_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 0.62/0.81 tff(1048,plain,
% 0.62/0.81 ((~hskp3) | c2_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1047, 1045])).
% 0.62/0.81 tff(1049,plain,
% 0.62/0.81 ((~hskp3) | c2_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1048, 1045])).
% 0.62/0.81 tff(1050,plain,
% 0.62/0.81 ((~hskp3) | c2_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1049, 1045])).
% 0.62/0.81 tff(1051,plain,
% 0.62/0.81 ((~hskp3) | c2_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1050, 1045])).
% 0.62/0.81 tff(1052,plain,
% 0.62/0.81 (c2_1(a597)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[1051, 1020])).
% 0.62/0.81 tff(1053,plain,
% 0.62/0.81 (((~hskp3) | c1_1(a597)) <=> ((~hskp3) | c1_1(a597))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1054,axiom,((~hskp3) | c1_1(a597)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.62/0.81 tff(1055,plain,
% 0.62/0.81 ((~hskp3) | c1_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 0.62/0.81 tff(1056,plain,
% 0.62/0.81 ((~hskp3) | c1_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1055, 1053])).
% 0.62/0.81 tff(1057,plain,
% 0.62/0.81 ((~hskp3) | c1_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1056, 1053])).
% 0.62/0.81 tff(1058,plain,
% 0.62/0.81 ((~hskp3) | c1_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1057, 1053])).
% 0.62/0.81 tff(1059,plain,
% 0.62/0.81 ((~hskp3) | c1_1(a597)),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1058, 1053])).
% 0.62/0.81 tff(1060,plain,
% 0.62/0.81 (c1_1(a597)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[1059, 1020])).
% 0.62/0.81 tff(1061,plain,
% 0.62/0.81 (c3_1(a631)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[529, 1043])).
% 0.62/0.81 tff(1062,plain,
% 0.62/0.81 (c0_1(a631)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[537, 1043])).
% 0.62/0.81 tff(1063,plain,
% 0.62/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1064,plain,
% 0.62/0.81 (((~ndr1_0) | c3_1(a597) | (~c2_1(a597)) | (~c1_1(a597)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631))) <=> (c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1065,plain,
% 0.62/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a597) | (~c2_1(a597)) | (~c1_1(a597)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[1064])).
% 0.62/0.81 tff(1066,plain,
% 0.62/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a597) | (~c2_1(a597)) | (~c1_1(a597)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[1065, 1063])).
% 0.62/0.81 tff(1067,plain,
% 0.62/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a597) | (~c2_1(a597)) | (~c1_1(a597)) | c3_1(a644) | c2_1(a644) | (~c1_1(a644)) | c1_1(a631) | (~c3_1(a631)) | (~c0_1(a631)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(1068,plain,
% 0.62/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c2_1(a644) | c3_1(a644) | c1_1(a631) | c3_1(a597) | (~ndr1_0) | (~c1_1(a597)) | (~c2_1(a597)) | (~c3_1(a631)) | (~c0_1(a631)) | (~c1_1(a644))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 0.62/0.81 tff(1069,plain,
% 0.62/0.81 ($false),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[1068, 66, 1062, 1061, 1060, 1052, 992, 991, 1044, 1026, 488, 994])).
% 0.62/0.81 tff(1070,plain,(hskp14 | c1_1(a604) | hskp4 | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.81 tff(1071,plain,
% 0.62/0.81 (hskp14),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[1070, 339, 813, 200])).
% 0.62/0.81 tff(1072,plain,
% 0.62/0.81 (c0_1(a615)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[280, 1071])).
% 0.62/0.81 tff(1073,plain,
% 0.62/0.81 (~c1_1(a615)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[912, 1071])).
% 0.62/0.81 tff(1074,plain,
% 0.62/0.81 (c2_1(a615)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[272, 1071])).
% 0.62/0.81 tff(1075,plain,
% 0.62/0.81 (c0_1(a651)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[961, 1074, 1073, 1072, 339, 825])).
% 0.62/0.81 tff(1076,plain,
% 0.62/0.81 (hskp22),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[969, 1075, 339])).
% 0.62/0.81 tff(1077,plain,
% 0.62/0.81 (~c3_1(a644)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[411, 1076])).
% 0.62/0.81 tff(1078,plain,
% 0.62/0.81 (~c2_1(a644)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[417, 1076])).
% 0.62/0.81 tff(1079,plain,
% 0.62/0.81 (~c0_1(a644)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[423, 1076])).
% 0.62/0.81 tff(1080,plain,
% 0.62/0.81 (c1_1(a644)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[430, 66, 1079, 1078, 1077, 174])).
% 0.62/0.81 tff(1081,plain,
% 0.62/0.81 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(1082,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[1081])).
% 0.62/0.81 tff(1083,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1084,plain,
% 0.62/0.81 (^[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)) | 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) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(1085,plain,
% 0.62/0.81 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[1084])).
% 0.62/0.81 tff(1086,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.62/0.81 tff(1087,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.62/0.81 tff(1088,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1087, 1083])).
% 0.62/0.81 tff(1089,plain,(
% 0.62/0.81 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.62/0.81 inference(skolemize,[status(sab)],[1088])).
% 0.62/0.81 tff(1090,plain,
% 0.62/0.81 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1089, 1082])).
% 0.62/0.81 tff(1091,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1092,plain,
% 0.62/0.81 ((hskp5 | (~ndr1_0) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c3_1(a644) | c2_1(a644) | c0_1(a644)) <=> (hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1093,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c3_1(a644) | c2_1(a644) | c0_1(a644))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[1092])).
% 0.62/0.81 tff(1094,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c3_1(a644) | c2_1(a644) | c0_1(a644))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[1093, 1091])).
% 0.62/0.81 tff(1095,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c3_1(a644) | c2_1(a644) | c0_1(a644))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(1096,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a644) | c2_1(a644) | c3_1(a644) | (~ndr1_0) | (~c1_1(a644))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 0.62/0.81 tff(1097,plain,
% 0.62/0.81 (hskp5),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[1096, 66, 1079, 1078, 1077, 1090, 1080])).
% 0.62/0.81 tff(1098,plain,
% 0.62/0.81 (~c1_1(a599)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[699, 1097])).
% 0.62/0.81 tff(1099,plain,
% 0.62/0.81 (c3_1(a599)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[667, 1097])).
% 0.62/0.81 tff(1100,plain,
% 0.62/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1101,plain,
% 0.62/0.81 (((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599))) <=> (c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1102,plain,
% 0.62/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[1101])).
% 0.62/0.81 tff(1103,plain,
% 0.62/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[1102, 1100])).
% 0.62/0.81 tff(1104,plain,
% 0.62/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a594) | (~c0_1(a594)) | (~c1_1(a594)) | c3_1(a644) | c0_1(a644) | (~c1_1(a644)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(1105,plain,
% 0.62/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a644) | c3_1(a644) | c1_1(a599) | c3_1(a594) | (~ndr1_0) | (~c0_1(a594)) | (~c1_1(a594)) | (~c3_1(a599)) | c0_1(a599) | (~c1_1(a644))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 0.62/0.81 tff(1106,plain,
% 0.62/0.81 (c0_1(a599)),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[1105, 66, 1099, 985, 988, 1079, 1077, 1098, 984, 233, 1080])).
% 0.62/0.81 tff(1107,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1108,plain,
% 0.62/0.81 ((hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644))) <=> (hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(1109,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[1108])).
% 0.62/0.81 tff(1110,plain,
% 0.62/0.81 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.62/0.81 inference(transitivity,[status(thm)],[1109, 1107])).
% 0.62/0.81 tff(1111,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a615)) | (~c3_1(a615)) | (~c0_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(1112,plain,
% 0.62/0.81 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a644) | c2_1(a644) | (~ndr1_0) | (~c3_1(a615)) | (~c0_1(a615)) | (~c2_1(a615)) | (~c1_1(a644))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 0.62/0.82 tff(1113,plain,
% 0.62/0.82 ((~c3_1(a615)) | (~c1_1(a644))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1112, 825, 66, 1072, 1074, 1079, 1078, 924])).
% 0.62/0.82 tff(1114,plain,
% 0.62/0.82 (~c3_1(a615)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1113, 1080])).
% 0.62/0.82 tff(1115,plain,
% 0.62/0.82 (c2_1(a599)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[675, 1097])).
% 0.62/0.82 tff(1116,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1117,plain,
% 0.62/0.82 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644))) <=> (c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1118,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[1117])).
% 0.62/0.82 tff(1119,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[1118, 1116])).
% 0.62/0.82 tff(1120,plain,
% 0.62/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c3_1(a615) | c1_1(a615) | (~c2_1(a615)) | c2_1(a644) | c0_1(a644) | (~c1_1(a644)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(1121,plain,
% 0.62/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a644) | c2_1(a644) | c1_1(a615) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c2_1(a599)) | c3_1(a615) | (~c2_1(a615)) | (~c1_1(a644))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 0.62/0.82 tff(1122,plain,
% 0.62/0.82 ($false),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1121, 66, 1074, 1115, 1099, 1079, 1078, 1073, 633, 1114, 1080, 1106])).
% 0.62/0.82 tff(1123,plain,(hskp4 | c1_1(a604) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.82 tff(1124,plain,
% 0.62/0.82 (hskp4),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1123, 813, 200])).
% 0.62/0.82 tff(1125,plain,
% 0.62/0.82 (~c2_1(a598)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[209, 1124])).
% 0.62/0.82 tff(1126,plain,
% 0.62/0.82 (~c1_1(a598)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[221, 1124])).
% 0.62/0.82 tff(1127,plain,
% 0.62/0.82 (~c0_1(a598)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[215, 1124])).
% 0.62/0.82 tff(1128,plain,
% 0.62/0.82 (hskp12),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[810, 75, 927])).
% 0.62/0.82 tff(1129,plain,
% 0.62/0.82 (~c1_1(a609)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[81, 1128])).
% 0.62/0.82 tff(1130,plain,
% 0.62/0.82 (~c3_1(a609)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[95, 1128])).
% 0.62/0.82 tff(1131,plain,
% 0.62/0.82 (c2_1(a609)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[89, 1128])).
% 0.62/0.82 tff(1132,plain,
% 0.62/0.82 (c0_1(a651)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[797, 1131, 1130, 1129, 2])).
% 0.62/0.82 tff(1133,plain,
% 0.62/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(1134,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[1133])).
% 0.62/0.82 tff(1135,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1136,plain,
% 0.62/0.82 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(1137,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[1136])).
% 0.62/0.82 tff(1138,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.62/0.82 tff(1139,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 0.62/0.82 tff(1140,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1139, 1135])).
% 0.62/0.82 tff(1141,plain,(
% 0.62/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(skolemize,[status(sab)],[1140])).
% 0.62/0.82 tff(1142,plain,
% 0.62/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1141, 1134])).
% 0.62/0.82 tff(1143,plain,
% 0.62/0.82 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(1144,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[1143])).
% 0.62/0.82 tff(1145,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1146,plain,
% 0.62/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_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) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | 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)) | c3_1(V) | 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) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | 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)) | hskp18) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | 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)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(1147,plain,
% 0.62/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[1146])).
% 0.62/0.82 tff(1148,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)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.62/0.82 tff(1149,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 0.62/0.82 tff(1150,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1149, 1145])).
% 0.62/0.82 tff(1151,plain,(
% 0.62/0.82 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.82 inference(skolemize,[status(sab)],[1150])).
% 0.62/0.82 tff(1152,plain,
% 0.62/0.82 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1151, 1144])).
% 0.62/0.82 tff(1153,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1154,plain,
% 0.62/0.82 ((hskp18 | (~ndr1_0) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609))) <=> (hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1155,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[1154])).
% 0.62/0.82 tff(1156,plain,
% 0.62/0.82 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[1155, 1153])).
% 0.62/0.82 tff(1157,plain,
% 0.62/0.82 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651)) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(1158,plain,
% 0.62/0.82 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp18 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c3_1(a651)) | (~c0_1(a651)) | (~c1_1(a651))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 0.62/0.82 tff(1159,plain,
% 0.62/0.82 (hskp18 | (~c0_1(a651))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1158, 66, 614, 652, 1131, 1129, 1130, 1152])).
% 0.62/0.82 tff(1160,plain,
% 0.62/0.82 (hskp18),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1159, 1132])).
% 0.62/0.82 tff(1161,plain,
% 0.62/0.82 (((~hskp18) | c3_1(a625)) <=> ((~hskp18) | c3_1(a625))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1162,axiom,((~hskp18) | c3_1(a625)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.62/0.82 tff(1163,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a625)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.62/0.82 tff(1164,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a625)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1163, 1161])).
% 0.62/0.82 tff(1165,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a625)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1164, 1161])).
% 0.62/0.82 tff(1166,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a625)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1165, 1161])).
% 0.62/0.82 tff(1167,plain,
% 0.62/0.82 ((~hskp18) | c3_1(a625)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1166, 1161])).
% 0.62/0.82 tff(1168,plain,
% 0.62/0.82 (c3_1(a625)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1167, 1160])).
% 0.62/0.82 tff(1169,plain,
% 0.62/0.82 (((~hskp18) | (~c1_1(a625))) <=> ((~hskp18) | (~c1_1(a625)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1170,plain,
% 0.62/0.82 (((~c1_1(a625)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a625)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1171,axiom,((~c1_1(a625)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.62/0.82 tff(1172,plain,
% 0.62/0.82 ((~hskp18) | (~c1_1(a625))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 0.62/0.82 tff(1173,plain,
% 0.62/0.82 ((~hskp18) | (~c1_1(a625))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1172, 1169])).
% 0.62/0.82 tff(1174,plain,
% 0.62/0.82 (~c1_1(a625)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1173, 1160])).
% 0.62/0.82 tff(1175,plain,
% 0.62/0.82 (((~hskp18) | (~c0_1(a625))) <=> ((~hskp18) | (~c0_1(a625)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1176,plain,
% 0.62/0.82 (((~c0_1(a625)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a625)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1177,axiom,((~c0_1(a625)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.62/0.82 tff(1178,plain,
% 0.62/0.82 ((~hskp18) | (~c0_1(a625))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 0.62/0.82 tff(1179,plain,
% 0.62/0.82 ((~hskp18) | (~c0_1(a625))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1178, 1175])).
% 0.62/0.82 tff(1180,plain,
% 0.62/0.82 (~c0_1(a625)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1179, 1160])).
% 0.62/0.82 tff(1181,assumption,(c0_1(a651)), introduced(assumption)).
% 0.62/0.82 tff(1182,assumption,(hskp7), introduced(assumption)).
% 0.62/0.82 tff(1183,plain,
% 0.62/0.82 (((~hskp7) | (~c0_1(a602))) <=> ((~hskp7) | (~c0_1(a602)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1184,plain,
% 0.62/0.82 (((~c0_1(a602)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a602)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1185,axiom,((~c0_1(a602)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.62/0.82 tff(1186,plain,
% 0.62/0.82 ((~hskp7) | (~c0_1(a602))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 0.62/0.82 tff(1187,plain,
% 0.62/0.82 ((~hskp7) | (~c0_1(a602))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1186, 1183])).
% 0.62/0.82 tff(1188,plain,
% 0.62/0.82 (~c0_1(a602)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1187, 1182])).
% 0.62/0.82 tff(1189,assumption,(~c1_1(a625)), introduced(assumption)).
% 0.62/0.82 tff(1190,assumption,(~c0_1(a625)), introduced(assumption)).
% 0.62/0.82 tff(1191,plain,
% 0.62/0.82 (((~hskp7) | c3_1(a602)) <=> ((~hskp7) | c3_1(a602))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1192,axiom,((~hskp7) | c3_1(a602)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.62/0.82 tff(1193,plain,
% 0.62/0.82 ((~hskp7) | c3_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 0.62/0.82 tff(1194,plain,
% 0.62/0.82 ((~hskp7) | c3_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1193, 1191])).
% 0.62/0.82 tff(1195,plain,
% 0.62/0.82 ((~hskp7) | c3_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1194, 1191])).
% 0.62/0.82 tff(1196,plain,
% 0.62/0.82 ((~hskp7) | c3_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1195, 1191])).
% 0.62/0.82 tff(1197,plain,
% 0.62/0.82 ((~hskp7) | c3_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1196, 1191])).
% 0.62/0.82 tff(1198,plain,
% 0.62/0.82 (c3_1(a602)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1197, 1182])).
% 0.62/0.82 tff(1199,plain,
% 0.62/0.82 (((~hskp7) | c2_1(a602)) <=> ((~hskp7) | c2_1(a602))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1200,axiom,((~hskp7) | c2_1(a602)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.62/0.82 tff(1201,plain,
% 0.62/0.82 ((~hskp7) | c2_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 0.62/0.82 tff(1202,plain,
% 0.62/0.82 ((~hskp7) | c2_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1201, 1199])).
% 0.62/0.82 tff(1203,plain,
% 0.62/0.82 ((~hskp7) | c2_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1202, 1199])).
% 0.62/0.82 tff(1204,plain,
% 0.62/0.82 ((~hskp7) | c2_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1203, 1199])).
% 0.62/0.82 tff(1205,plain,
% 0.62/0.82 ((~hskp7) | c2_1(a602)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1204, 1199])).
% 0.62/0.82 tff(1206,plain,
% 0.62/0.82 (c2_1(a602)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1205, 1182])).
% 0.62/0.82 tff(1207,assumption,(c3_1(a625)), introduced(assumption)).
% 0.62/0.82 tff(1208,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1209,plain,
% 0.62/0.82 (((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a602) | (~c2_1(a602)) | (~c3_1(a602)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1210,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a602) | (~c2_1(a602)) | (~c3_1(a602)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651))))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[1209])).
% 0.62/0.82 tff(1211,plain,
% 0.62/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a602) | (~c2_1(a602)) | (~c3_1(a602)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.82 inference(transitivity,[status(thm)],[1210, 1208])).
% 0.62/0.82 tff(1212,plain,
% 0.62/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a602) | (~c2_1(a602)) | (~c3_1(a602)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(1213,plain,
% 0.62/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | c0_1(a602) | (~ndr1_0) | (~c2_1(a602)) | (~c3_1(a602)) | (~c3_1(a625)) | (~c3_1(a651)) | (~c0_1(a651))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.62/0.82 tff(1214,plain,
% 0.62/0.82 ($false),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1213, 66, 652, 1207, 1206, 1198, 606, 1190, 1189, 1188, 694, 1181])).
% 0.62/0.82 tff(1215,plain,((~hskp7) | (~c3_1(a625)) | c0_1(a625) | c1_1(a625) | (~c0_1(a651))), inference(lemma,lemma(discharge,[]))).
% 0.62/0.82 tff(1216,plain,
% 0.62/0.82 (~hskp7),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[1215, 1180, 1132, 1174, 1168])).
% 0.62/0.82 tff(1217,plain,
% 0.62/0.82 (^[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))))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(1218,plain,
% 0.62/0.82 (![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)))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[1217])).
% 0.62/0.82 tff(1219,plain,
% 0.62/0.82 (![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)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(1220,plain,
% 0.62/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp7) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp7) <=> (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(1221,plain,
% 0.62/0.83 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp7) <=> ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[1220])).
% 0.62/0.83 tff(1222,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.62/0.83 tff(1223,plain,
% 0.62/0.83 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 0.62/0.83 tff(1224,plain,
% 0.62/0.83 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1223, 1219])).
% 0.62/0.83 tff(1225,plain,(
% 0.62/0.83 ![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[1224])).
% 0.62/0.83 tff(1226,plain,
% 0.62/0.83 (![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1225, 1218])).
% 0.62/0.83 tff(1227,plain,
% 0.62/0.83 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1228,plain,
% 0.62/0.83 ((hskp19 | hskp7 | (~ndr1_0) | c3_1(a609) | c1_1(a609) | (~c2_1(a609))) <=> (hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1229,plain,
% 0.62/0.83 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[1228])).
% 0.62/0.83 tff(1230,plain,
% 0.62/0.83 (((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))) <=> ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[1229, 1227])).
% 0.62/0.83 tff(1231,plain,
% 0.62/0.83 ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp7 | (~ndr1_0) | c3_1(a609) | c1_1(a609) | (~c2_1(a609)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(1232,plain,
% 0.62/0.83 ((~![U: $i] : (hskp19 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp7 | c1_1(a609) | c3_1(a609) | (~ndr1_0) | (~c2_1(a609))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 0.62/0.83 tff(1233,plain,
% 0.62/0.83 (hskp19 | hskp7),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1232, 66, 1131, 1129, 1130, 1226])).
% 0.62/0.83 tff(1234,plain,
% 0.62/0.83 (hskp19),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1233, 1216])).
% 0.62/0.83 tff(1235,plain,
% 0.62/0.83 (((~hskp19) | (~c3_1(a627))) <=> ((~hskp19) | (~c3_1(a627)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1236,plain,
% 0.62/0.83 (((~c3_1(a627)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a627)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1237,axiom,((~c3_1(a627)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.62/0.83 tff(1238,plain,
% 0.62/0.83 ((~hskp19) | (~c3_1(a627))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 0.62/0.83 tff(1239,plain,
% 0.62/0.83 ((~hskp19) | (~c3_1(a627))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1238, 1235])).
% 0.62/0.83 tff(1240,plain,
% 0.62/0.83 (~c3_1(a627)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1239, 1234])).
% 0.62/0.83 tff(1241,plain,
% 0.62/0.83 (((~hskp19) | (~c2_1(a627))) <=> ((~hskp19) | (~c2_1(a627)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1242,plain,
% 0.62/0.83 (((~c2_1(a627)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a627)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1243,axiom,((~c2_1(a627)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.62/0.83 tff(1244,plain,
% 0.62/0.83 ((~hskp19) | (~c2_1(a627))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 0.62/0.83 tff(1245,plain,
% 0.62/0.83 ((~hskp19) | (~c2_1(a627))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1244, 1241])).
% 0.62/0.83 tff(1246,plain,
% 0.62/0.83 (~c2_1(a627)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1245, 1234])).
% 0.62/0.83 tff(1247,plain,
% 0.62/0.83 (((~hskp19) | c0_1(a627)) <=> ((~hskp19) | c0_1(a627))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1248,axiom,((~hskp19) | c0_1(a627)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.62/0.83 tff(1249,plain,
% 0.62/0.83 ((~hskp19) | c0_1(a627)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 0.62/0.83 tff(1250,plain,
% 0.62/0.83 ((~hskp19) | c0_1(a627)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1249, 1247])).
% 0.62/0.83 tff(1251,plain,
% 0.62/0.83 ((~hskp19) | c0_1(a627)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1250, 1247])).
% 0.62/0.83 tff(1252,plain,
% 0.62/0.83 ((~hskp19) | c0_1(a627)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1251, 1247])).
% 0.62/0.83 tff(1253,plain,
% 0.62/0.83 ((~hskp19) | c0_1(a627)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1252, 1247])).
% 0.62/0.83 tff(1254,plain,
% 0.62/0.83 (c0_1(a627)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1253, 1234])).
% 0.62/0.83 tff(1255,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1256,plain,
% 0.62/0.83 (((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1257,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[1256])).
% 0.62/0.83 tff(1258,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[1257, 1255])).
% 0.62/0.83 tff(1259,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(1260,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 0.62/0.83 tff(1261,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1260, 66, 652, 1254, 606, 1246, 1240, 223, 234, 243, 1142, 1132])).
% 0.62/0.83 tff(1262,plain,(hskp14 | c0_1(a598) | c1_1(a598) | c2_1(a598) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(1263,plain,
% 0.62/0.83 (hskp14),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1262, 1127, 1126, 1125, 825])).
% 0.62/0.83 tff(1264,plain,
% 0.62/0.83 (c2_1(a615)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[272, 1263])).
% 0.62/0.83 tff(1265,plain,
% 0.62/0.83 (c0_1(a615)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[280, 1263])).
% 0.62/0.83 tff(1266,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1267,plain,
% 0.62/0.83 (((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a598) | c1_1(a598) | (~c3_1(a598)) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1268,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a598) | c1_1(a598) | (~c3_1(a598)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[1267])).
% 0.62/0.83 tff(1269,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a598) | c1_1(a598) | (~c3_1(a598)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[1268, 1266])).
% 0.62/0.83 tff(1270,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a598) | c1_1(a598) | (~c3_1(a598)) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(1271,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a598)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1270, 1269])).
% 0.62/0.83 tff(1272,plain,
% 0.62/0.83 (~c3_1(a598)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1271, 66, 1265, 1264, 1127, 1126, 1125, 824, 814])).
% 0.62/0.83 tff(1273,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1274,plain,
% 0.62/0.83 (((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1275,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[1274])).
% 0.62/0.83 tff(1276,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[1275, 1273])).
% 0.62/0.83 tff(1277,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a615) | (~c2_1(a615)) | (~c0_1(a615)) | c0_1(a604) | c1_1(a604) | (~c3_1(a604)) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(1278,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | (~c3_1(a604)) | c3_1(a615) | (~c0_1(a615)) | (~c2_1(a615))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 0.62/0.83 tff(1279,plain,
% 0.62/0.83 (~c3_1(a604)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1278, 66, 1265, 1264, 813, 200, 1127, 1126, 1125, 824, 814])).
% 0.62/0.83 tff(1280,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1281,plain,
% 0.62/0.83 (((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a604) | c0_1(a604) | c1_1(a604) | c2_1(a598) | c1_1(a598) | c0_1(a598)) <=> (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1282,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a604) | c0_1(a604) | c1_1(a604) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604)))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[1281])).
% 0.62/0.83 tff(1283,plain,
% 0.62/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a604) | c0_1(a604) | c1_1(a604) | c2_1(a598) | c1_1(a598) | c0_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604))),
% 0.62/0.83 inference(transitivity,[status(thm)],[1282, 1280])).
% 0.62/0.83 tff(1284,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a598) | c2_1(a598) | c0_1(a598) | c3_1(a604) | c0_1(a604) | c1_1(a604) | c2_1(a598) | c1_1(a598) | c0_1(a598))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(1285,plain,
% 0.62/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V) | c1_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a604) | c0_1(a604) | c0_1(a598) | c1_1(a598) | c2_1(a598) | (~ndr1_0) | c3_1(a598) | c3_1(a604)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 0.62/0.83 tff(1286,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1285, 66, 813, 200, 1127, 1126, 1125, 174, 1279, 1272])).
% 0.62/0.83 tff(1287,plain,(c3_1(a615) | c1_1(a604) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(1288,plain,
% 0.62/0.83 (c3_1(a615)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1287, 813, 200])).
% 0.62/0.83 tff(1289,plain,
% 0.62/0.83 ((~c3_1(a615)) | c0_1(a651)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[933, 825, 66, 614, 1265, 1264, 606, 924])).
% 0.62/0.83 tff(1290,plain,
% 0.62/0.83 (c0_1(a651)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[1289, 1288])).
% 0.62/0.83 tff(1291,plain,
% 0.62/0.83 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(1292,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[1291])).
% 0.62/0.83 tff(1293,plain,
% 0.62/0.83 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(1294,plain,
% 0.62/0.83 (^[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(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~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(V))) <=> ((~ndr1_0) | (~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(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~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(V))) | c2_1(U)) <=> ((~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(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(1295,plain,
% 0.62/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[1294])).
% 0.62/0.84 tff(1296,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.62/0.84 tff(1297,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 0.62/0.84 tff(1298,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1297, 1293])).
% 0.62/0.84 tff(1299,plain,(
% 0.62/0.84 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.62/0.84 inference(skolemize,[status(sab)],[1298])).
% 0.62/0.84 tff(1300,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1299, 1292])).
% 0.62/0.84 tff(1301,plain,
% 0.62/0.84 (~c1_1(a615)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[912, 1263])).
% 0.62/0.84 tff(1302,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(1303,plain,
% 0.62/0.84 ((hskp12 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)) | c1_1(a615) | (~c2_1(a615)) | (~c0_1(a615))) <=> (hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(1304,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)) | c1_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[1303])).
% 0.62/0.84 tff(1305,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)) | c1_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[1304, 1302])).
% 0.62/0.84 tff(1306,plain,
% 0.62/0.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c0_1(a651)) | (~c1_1(a651)) | c1_1(a615) | (~c2_1(a615)) | (~c0_1(a615)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(1307,plain,
% 0.62/0.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a651) | c1_1(a615) | (~ndr1_0) | (~c0_1(a615)) | (~c2_1(a615)) | (~c0_1(a651)) | (~c1_1(a651))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 0.62/0.84 tff(1308,plain,
% 0.62/0.84 (hskp12 | (~c0_1(a651))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1307, 66, 614, 1265, 1264, 606, 1301, 1300])).
% 0.62/0.84 tff(1309,plain,
% 0.62/0.84 (hskp12),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1308, 1290])).
% 0.62/0.84 tff(1310,plain,
% 0.62/0.84 (~c3_1(a609)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[95, 1309])).
% 0.62/0.84 tff(1311,plain,
% 0.62/0.84 (~c1_1(a609)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[81, 1309])).
% 0.62/0.84 tff(1312,plain,
% 0.62/0.84 (c2_1(a609)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[89, 1309])).
% 0.62/0.84 tff(1313,plain,
% 0.62/0.84 (hskp18),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1158, 66, 614, 652, 1312, 1311, 1310, 1152, 1290])).
% 0.62/0.84 tff(1314,plain,
% 0.62/0.84 (c3_1(a625)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1167, 1313])).
% 0.62/0.84 tff(1315,plain,
% 0.62/0.84 (~c1_1(a625)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1173, 1313])).
% 0.62/0.84 tff(1316,plain,
% 0.62/0.84 (~c0_1(a625)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1179, 1313])).
% 0.62/0.84 tff(1317,plain,
% 0.62/0.84 (~hskp7),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1215, 1316, 1290, 1315, 1314])).
% 0.62/0.84 tff(1318,plain,
% 0.62/0.84 (hskp19 | hskp7),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1232, 66, 1312, 1311, 1310, 1226])).
% 0.62/0.84 tff(1319,plain,
% 0.62/0.84 (hskp19),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1318, 1317])).
% 0.62/0.84 tff(1320,plain,
% 0.62/0.84 (~c3_1(a627)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1239, 1319])).
% 0.62/0.84 tff(1321,plain,
% 0.62/0.84 (~c2_1(a627)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1245, 1319])).
% 0.62/0.84 tff(1322,plain,
% 0.62/0.84 (c0_1(a627)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1253, 1319])).
% 0.62/0.84 tff(1323,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1260, 66, 652, 1322, 606, 1321, 1320, 1127, 1126, 1125, 1142, 1290])).
% 0.62/0.84 tff(1324,plain,(c1_1(a604) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(1325,plain,
% 0.62/0.84 (c1_1(a604)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1324, 200])).
% 0.62/0.84 tff(1326,plain,
% 0.62/0.84 (~c3_1(a604)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[153, 66, 1325, 812, 200, 116])).
% 0.62/0.84 tff(1327,plain,
% 0.62/0.84 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(1328,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[1327])).
% 0.62/0.84 tff(1329,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(1330,plain,
% 0.62/0.84 (^[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)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_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)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.62/0.84 inference(bind,[status(th)],[])).
% 0.62/0.84 tff(1331,plain,
% 0.62/0.84 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.84 inference(quant_intro,[status(thm)],[1330])).
% 0.62/0.84 tff(1332,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.62/0.84 tff(1333,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 0.62/0.84 tff(1334,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1333, 1329])).
% 0.62/0.84 tff(1335,plain,(
% 0.62/0.84 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.84 inference(skolemize,[status(sab)],[1334])).
% 0.62/0.84 tff(1336,plain,
% 0.62/0.84 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1335, 1328])).
% 0.62/0.84 tff(1337,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(1338,plain,
% 0.62/0.84 ((hskp12 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c2_1(a604))) <=> (hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(1339,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[1338])).
% 0.62/0.84 tff(1340,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[1339, 1337])).
% 0.62/0.84 tff(1341,plain,
% 0.62/0.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c2_1(a604)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(1342,plain,
% 0.62/0.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp12 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | c3_1(a604) | (~c3_1(a651)) | (~c1_1(a651))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.62/0.84 tff(1343,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1342, 66, 802, 614, 652, 812, 606, 200, 1336, 1326])).
% 0.62/0.84 tff(1344,plain,(hskp12 | c0_1(a604) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(1345,plain,
% 0.62/0.84 (hskp12),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1344, 75, 200])).
% 0.62/0.84 tff(1346,plain,
% 0.62/0.84 (c0_1(a651)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[799, 1345, 2])).
% 0.62/0.84 tff(1347,plain,
% 0.62/0.84 (~c3_1(a609)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[95, 1345])).
% 0.62/0.84 tff(1348,plain,
% 0.62/0.84 (~c1_1(a609)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[81, 1345])).
% 0.62/0.84 tff(1349,plain,
% 0.62/0.84 (c2_1(a609)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[89, 1345])).
% 0.62/0.84 tff(1350,plain,
% 0.62/0.84 (hskp18),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1158, 66, 614, 652, 1349, 1348, 1347, 1152, 1346])).
% 0.62/0.84 tff(1351,plain,
% 0.62/0.84 (~c1_1(a625)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1173, 1350])).
% 0.62/0.84 tff(1352,plain,
% 0.62/0.84 (~c0_1(a625)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1179, 1350])).
% 0.62/0.84 tff(1353,plain,
% 0.62/0.84 (c3_1(a625)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1167, 1350])).
% 0.62/0.84 tff(1354,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(1355,plain,
% 0.62/0.84 (((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a625) | (~c2_1(a625)) | (~c3_1(a625)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(1356,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a625) | (~c2_1(a625)) | (~c3_1(a625)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[1355])).
% 0.62/0.84 tff(1357,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a625) | (~c2_1(a625)) | (~c3_1(a625)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[1356, 1354])).
% 0.62/0.84 tff(1358,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c0_1(a625) | (~c2_1(a625)) | (~c3_1(a625)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(1359,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a651) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c2_1(a625)) | (~c3_1(a651)) | (~c0_1(a651))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 0.62/0.84 tff(1360,plain,
% 0.62/0.84 (~c2_1(a625)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1359, 66, 652, 1353, 606, 1352, 1351, 694, 1346])).
% 0.62/0.84 tff(1361,plain,
% 0.62/0.84 (~hskp7),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1215, 1352, 1346, 1351, 1353])).
% 0.62/0.84 tff(1362,plain,
% 0.62/0.84 (hskp19 | hskp7),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1232, 66, 1349, 1348, 1347, 1226])).
% 0.62/0.84 tff(1363,plain,
% 0.62/0.84 (hskp19),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1362, 1361])).
% 0.62/0.84 tff(1364,plain,
% 0.62/0.84 (~c3_1(a627)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1239, 1363])).
% 0.62/0.84 tff(1365,plain,
% 0.62/0.84 (~c2_1(a627)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1245, 1363])).
% 0.62/0.84 tff(1366,plain,
% 0.62/0.84 (c0_1(a627)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1253, 1363])).
% 0.62/0.84 tff(1367,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(1368,plain,
% 0.62/0.84 (((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a625) | c1_1(a625) | c0_1(a625)) <=> (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.84 inference(rewrite,[status(thm)],[])).
% 0.62/0.84 tff(1369,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651))))),
% 0.62/0.84 inference(monotonicity,[status(thm)],[1368])).
% 0.62/0.84 tff(1370,plain,
% 0.62/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651)))),
% 0.62/0.84 inference(transitivity,[status(thm)],[1369, 1367])).
% 0.62/0.84 tff(1371,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c0_1(a651)) | c3_1(a627) | c2_1(a627) | (~c0_1(a627)) | c2_1(a625) | c1_1(a625) | c0_1(a625))),
% 0.62/0.84 inference(quant_inst,[status(thm)],[])).
% 0.62/0.84 tff(1372,plain,
% 0.62/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a651) | c2_1(a627) | c3_1(a627) | c0_1(a625) | c1_1(a625) | (~ndr1_0) | c2_1(a625) | (~c0_1(a627)) | (~c3_1(a651)) | (~c0_1(a651))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 0.62/0.84 tff(1373,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1372, 66, 652, 1366, 606, 1365, 1364, 1352, 1351, 1142, 1346, 1360])).
% 0.62/0.84 tff(1374,plain,(hskp14 | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(1375,plain,
% 0.62/0.84 (hskp14),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1374, 200])).
% 0.62/0.84 tff(1376,plain,
% 0.62/0.84 (c0_1(a615)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[280, 1375])).
% 0.62/0.84 tff(1377,plain,
% 0.62/0.84 (~c1_1(a615)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[912, 1375])).
% 0.62/0.84 tff(1378,plain,
% 0.62/0.84 (c2_1(a615)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[272, 1375])).
% 0.62/0.84 tff(1379,plain,
% 0.62/0.84 (hskp9 | (~c3_1(a615)) | c0_1(a651)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[933, 66, 614, 926, 925, 606, 924])).
% 0.62/0.84 tff(1380,plain,
% 0.62/0.84 (~c3_1(a615)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1379, 927, 1])).
% 0.62/0.84 tff(1381,plain,
% 0.62/0.84 (hskp4),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[961, 927, 925, 926, 936, 1])).
% 0.62/0.84 tff(1382,plain,
% 0.62/0.84 (~c2_1(a598)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[209, 1381])).
% 0.62/0.84 tff(1383,plain,
% 0.62/0.84 (~c1_1(a598)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[221, 1381])).
% 0.62/0.84 tff(1384,plain,
% 0.62/0.84 (~c0_1(a598)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[215, 1381])).
% 0.62/0.84 tff(1385,plain,
% 0.62/0.84 (~c3_1(a598)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1271, 66, 926, 925, 1384, 1383, 1382, 824, 1380])).
% 0.62/0.84 tff(1386,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[249, 66, 1384, 1383, 1382, 174, 1385])).
% 0.62/0.84 tff(1387,plain,(hskp9 | (~c0_1(a615)) | (~c2_1(a615)) | c1_1(a615) | c0_1(a651)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.84 tff(1388,plain,
% 0.62/0.84 (hskp9),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[1387, 1, 1378, 1377, 1376])).
% 0.62/0.84 tff(1389,plain,
% 0.62/0.84 (c2_1(a604)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[138, 1388])).
% 0.62/0.84 tff(1390,plain,
% 0.62/0.84 (~c3_1(a604)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[153, 66, 1325, 1389, 200, 116])).
% 0.62/0.84 tff(1391,plain,
% 0.62/0.84 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(1392,plain,
% 0.62/0.85 ((hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(1393,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[1392])).
% 0.62/0.85 tff(1394,plain,
% 0.62/0.85 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[1393, 1391])).
% 0.62/0.85 tff(1395,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a651) | (~c3_1(a651)) | (~c1_1(a651)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(1396,plain,
% 0.62/0.85 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a651) | c0_1(a604) | (~ndr1_0) | c3_1(a604) | (~c1_1(a604)) | (~c3_1(a651)) | (~c1_1(a651))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 0.62/0.85 tff(1397,plain,
% 0.62/0.85 (hskp28),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1396, 66, 614, 652, 1325, 606, 200, 755, 1390])).
% 0.62/0.85 tff(1398,plain,
% 0.62/0.85 (c3_1(a595)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[354, 1397])).
% 0.62/0.85 tff(1399,plain,
% 0.62/0.85 (c2_1(a595)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[362, 1397])).
% 0.62/0.85 tff(1400,plain,
% 0.62/0.85 (c1_1(a595)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[370, 1397])).
% 0.62/0.85 tff(1401,plain,
% 0.62/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(1402,plain,
% 0.62/0.85 (((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a651) | (~c1_1(a651)) | (~c3_1(a651)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.85 inference(rewrite,[status(thm)],[])).
% 0.62/0.85 tff(1403,plain,
% 0.62/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a651) | (~c1_1(a651)) | (~c3_1(a651)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651))))),
% 0.62/0.85 inference(monotonicity,[status(thm)],[1402])).
% 0.62/0.85 tff(1404,plain,
% 0.62/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a651) | (~c1_1(a651)) | (~c3_1(a651)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651)))),
% 0.62/0.85 inference(transitivity,[status(thm)],[1403, 1401])).
% 0.62/0.85 tff(1405,plain,
% 0.62/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a595)) | (~c3_1(a595)) | (~c1_1(a595)) | c0_1(a651) | (~c1_1(a651)) | (~c3_1(a651)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 0.62/0.85 inference(quant_inst,[status(thm)],[])).
% 0.62/0.85 tff(1406,plain,
% 0.62/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | (~ndr1_0) | (~c3_1(a595)) | (~c1_1(a595)) | (~c2_1(a595)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a651)) | c0_1(a651) | (~c1_1(a651))),
% 0.62/0.85 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 0.62/0.85 tff(1407,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1406, 66, 1400, 1399, 1398, 614, 652, 1325, 1389, 200, 116, 1])).
% 0.62/0.85 tff(1408,plain,(c0_1(a651) | c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(1409,plain,
% 0.62/0.85 (c0_1(a651)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1408, 200])).
% 0.62/0.85 tff(1410,plain,
% 0.62/0.85 (hskp12 | (~c0_1(a651))),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1307, 66, 614, 1376, 1378, 606, 1377, 1300])).
% 0.62/0.85 tff(1411,plain,
% 0.62/0.85 (hskp12),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1410, 1409])).
% 0.62/0.85 tff(1412,plain,
% 0.62/0.85 (~c3_1(a609)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[95, 1411])).
% 0.62/0.85 tff(1413,plain,
% 0.62/0.85 (~c1_1(a609)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[81, 1411])).
% 0.62/0.85 tff(1414,plain,
% 0.62/0.85 (c2_1(a609)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[89, 1411])).
% 0.62/0.85 tff(1415,plain,
% 0.62/0.85 (hskp18),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1158, 66, 614, 652, 1414, 1413, 1412, 1152, 1409])).
% 0.62/0.85 tff(1416,plain,
% 0.62/0.85 (~c1_1(a625)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1173, 1415])).
% 0.62/0.85 tff(1417,plain,
% 0.62/0.85 (~c0_1(a625)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1179, 1415])).
% 0.62/0.85 tff(1418,plain,
% 0.62/0.85 (c3_1(a625)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1167, 1415])).
% 0.62/0.85 tff(1419,plain,
% 0.62/0.85 (~c2_1(a625)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1359, 66, 652, 1418, 606, 1417, 1416, 694, 1409])).
% 0.62/0.85 tff(1420,plain,
% 0.62/0.85 (~hskp7),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1215, 1417, 1409, 1416, 1418])).
% 0.62/0.85 tff(1421,plain,
% 0.62/0.85 (hskp19 | hskp7),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1232, 66, 1414, 1413, 1412, 1226])).
% 0.62/0.85 tff(1422,plain,
% 0.62/0.85 (hskp19),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1421, 1420])).
% 0.62/0.85 tff(1423,plain,
% 0.62/0.85 (~c3_1(a627)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1239, 1422])).
% 0.62/0.85 tff(1424,plain,
% 0.62/0.85 (~c2_1(a627)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1245, 1422])).
% 0.62/0.85 tff(1425,plain,
% 0.62/0.85 (c0_1(a627)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1253, 1422])).
% 0.62/0.85 tff(1426,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1372, 66, 652, 1425, 606, 1424, 1423, 1417, 1416, 1142, 1409, 1419])).
% 0.62/0.85 tff(1427,plain,(c0_1(a604)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(1428,plain,
% 0.62/0.85 (~hskp9),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[130, 1427])).
% 0.62/0.85 tff(1429,plain,
% 0.62/0.85 (hskp12 | hskp10),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[810, 1428])).
% 0.62/0.85 tff(1430,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1429, 800, 75])).
% 0.62/0.85 tff(1431,plain,(hskp14 | c0_1(a651)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(1432,plain,
% 0.62/0.85 (hskp14),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1431, 1])).
% 0.62/0.85 tff(1433,plain,
% 0.62/0.85 (c0_1(a615)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[280, 1432])).
% 0.62/0.85 tff(1434,plain,
% 0.62/0.85 (c2_1(a615)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[272, 1432])).
% 0.62/0.85 tff(1435,plain,
% 0.62/0.85 (~c1_1(a615)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[912, 1432])).
% 0.62/0.85 tff(1436,plain,
% 0.62/0.85 ((~c0_1(a615)) | (~c2_1(a615)) | c1_1(a615) | c0_1(a651)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1387, 1428])).
% 0.62/0.85 tff(1437,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1436, 1435, 1434, 1, 1433])).
% 0.62/0.85 tff(1438,plain,(c0_1(a651)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(1439,plain,
% 0.62/0.85 (hskp18),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1158, 66, 614, 652, 90, 82, 96, 1152, 1438])).
% 0.62/0.85 tff(1440,plain,
% 0.62/0.85 (~c1_1(a625)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1173, 1439])).
% 0.62/0.85 tff(1441,plain,
% 0.62/0.85 (~c0_1(a625)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1179, 1439])).
% 0.62/0.85 tff(1442,plain,
% 0.62/0.85 (c3_1(a625)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1167, 1439])).
% 0.62/0.85 tff(1443,plain,
% 0.62/0.85 (~c2_1(a625)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1359, 66, 652, 1442, 606, 1441, 1440, 694, 1438])).
% 0.62/0.85 tff(1444,plain,
% 0.62/0.85 (~hskp7),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1215, 1441, 1438, 1440, 1442])).
% 0.62/0.85 tff(1445,plain,
% 0.62/0.85 (hskp19 | hskp7),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1232, 66, 90, 82, 96, 1226])).
% 0.62/0.85 tff(1446,plain,
% 0.62/0.85 (hskp19),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1445, 1444])).
% 0.62/0.85 tff(1447,plain,
% 0.62/0.85 (~c3_1(a627)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1239, 1446])).
% 0.62/0.85 tff(1448,plain,
% 0.62/0.85 (~c2_1(a627)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1245, 1446])).
% 0.62/0.85 tff(1449,plain,
% 0.62/0.85 (c0_1(a627)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1253, 1446])).
% 0.62/0.85 tff(1450,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1372, 66, 652, 1449, 606, 1448, 1447, 1441, 1440, 1142, 1438, 1443])).
% 0.62/0.85 tff(1451,plain,(~hskp12), inference(lemma,lemma(discharge,[]))).
% 0.62/0.85 tff(1452,plain,
% 0.62/0.85 (hskp10),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1429, 1451])).
% 0.62/0.85 tff(1453,plain,
% 0.62/0.85 (hskp14),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[74, 1452])).
% 0.62/0.85 tff(1454,plain,
% 0.62/0.85 (~c1_1(a615)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[912, 1453])).
% 0.62/0.85 tff(1455,plain,
% 0.62/0.85 (c2_1(a615)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[272, 1453])).
% 0.62/0.85 tff(1456,plain,
% 0.62/0.85 (c0_1(a615)),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[280, 1453])).
% 0.62/0.85 tff(1457,plain,
% 0.62/0.85 ($false),
% 0.62/0.85 inference(unit_resolution,[status(thm)],[1307, 66, 1451, 614, 1456, 1455, 606, 1454, 1300, 1438])).
% 0.62/0.85 % SZS output end Proof
% 0.62/0.85 % E exiting
%------------------------------------------------------------------------------