%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN466-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:39:13 AM UTC 2025
% Result : Unsatisfiable 1.13s 1.31s
% Output : Proof 1.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN466-1 : TPTP v9.0.0. Released v2.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:36:32 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.13/1.31 % SZS status Unsatisfiable
% 1.13/1.31 % SZS output start Proof
% 1.13/1.31 tff(c1_1_type, type, (
% 1.13/1.31 c1_1: $i > $o)).
% 1.13/1.31 tff(a111_type, type, (
% 1.13/1.31 a111: $i)).
% 1.13/1.31 tff(c0_1_type, type, (
% 1.13/1.31 c0_1: $i > $o)).
% 1.13/1.31 tff(a135_type, type, (
% 1.13/1.31 a135: $i)).
% 1.13/1.31 tff(hskp19_type, type, (
% 1.13/1.31 hskp19: $o)).
% 1.13/1.31 tff(c2_1_type, type, (
% 1.13/1.31 c2_1: $i > $o)).
% 1.13/1.31 tff(c3_1_type, type, (
% 1.13/1.31 c3_1: $i > $o)).
% 1.13/1.31 tff(ndr1_0_type, type, (
% 1.13/1.31 ndr1_0: $o)).
% 1.13/1.31 tff(hskp10_type, type, (
% 1.13/1.31 hskp10: $o)).
% 1.13/1.31 tff(a141_type, type, (
% 1.13/1.31 a141: $i)).
% 1.13/1.31 tff(hskp1_type, type, (
% 1.13/1.31 hskp1: $o)).
% 1.13/1.31 tff(hskp24_type, type, (
% 1.13/1.31 hskp24: $o)).
% 1.13/1.31 tff(hskp31_type, type, (
% 1.13/1.31 hskp31: $o)).
% 1.13/1.31 tff(hskp4_type, type, (
% 1.13/1.31 hskp4: $o)).
% 1.13/1.31 tff(a105_type, type, (
% 1.13/1.31 a105: $i)).
% 1.13/1.31 tff(hskp15_type, type, (
% 1.13/1.31 hskp15: $o)).
% 1.13/1.31 tff(hskp28_type, type, (
% 1.13/1.31 hskp28: $o)).
% 1.13/1.31 tff(a131_type, type, (
% 1.13/1.31 a131: $i)).
% 1.13/1.31 tff(hskp30_type, type, (
% 1.13/1.31 hskp30: $o)).
% 1.13/1.31 tff(a163_type, type, (
% 1.13/1.31 a163: $i)).
% 1.13/1.31 tff(a118_type, type, (
% 1.13/1.31 a118: $i)).
% 1.13/1.31 tff(a106_type, type, (
% 1.13/1.31 a106: $i)).
% 1.13/1.31 tff(a126_type, type, (
% 1.13/1.31 a126: $i)).
% 1.13/1.31 tff(a132_type, type, (
% 1.13/1.31 a132: $i)).
% 1.13/1.31 tff(hskp17_type, type, (
% 1.13/1.31 hskp17: $o)).
% 1.13/1.31 tff(hskp16_type, type, (
% 1.13/1.31 hskp16: $o)).
% 1.13/1.31 tff(hskp5_type, type, (
% 1.13/1.31 hskp5: $o)).
% 1.13/1.31 tff(a117_type, type, (
% 1.13/1.31 a117: $i)).
% 1.13/1.31 tff(a108_type, type, (
% 1.13/1.31 a108: $i)).
% 1.13/1.31 tff(a109_type, type, (
% 1.13/1.31 a109: $i)).
% 1.13/1.31 tff(hskp8_type, type, (
% 1.13/1.31 hskp8: $o)).
% 1.13/1.31 tff(hskp2_type, type, (
% 1.13/1.31 hskp2: $o)).
% 1.13/1.31 tff(a103_type, type, (
% 1.13/1.31 a103: $i)).
% 1.13/1.31 tff(hskp9_type, type, (
% 1.13/1.31 hskp9: $o)).
% 1.13/1.31 tff(a110_type, type, (
% 1.13/1.31 a110: $i)).
% 1.13/1.31 tff(hskp7_type, type, (
% 1.13/1.31 hskp7: $o)).
% 1.13/1.31 tff(hskp6_type, type, (
% 1.13/1.31 hskp6: $o)).
% 1.13/1.31 tff(a107_type, type, (
% 1.13/1.31 a107: $i)).
% 1.13/1.31 tff(a114_type, type, (
% 1.13/1.31 a114: $i)).
% 1.13/1.31 tff(hskp13_type, type, (
% 1.13/1.31 hskp13: $o)).
% 1.13/1.31 tff(hskp11_type, type, (
% 1.13/1.31 hskp11: $o)).
% 1.13/1.31 tff(a112_type, type, (
% 1.13/1.31 a112: $i)).
% 1.13/1.31 tff(a102_type, type, (
% 1.13/1.31 a102: $i)).
% 1.13/1.31 tff(a145_type, type, (
% 1.13/1.31 a145: $i)).
% 1.13/1.31 tff(hskp22_type, type, (
% 1.13/1.31 hskp22: $o)).
% 1.13/1.31 tff(a101_type, type, (
% 1.13/1.31 a101: $i)).
% 1.13/1.31 tff(hskp0_type, type, (
% 1.13/1.31 hskp0: $o)).
% 1.13/1.31 tff(a113_type, type, (
% 1.13/1.31 a113: $i)).
% 1.13/1.31 tff(hskp12_type, type, (
% 1.13/1.31 hskp12: $o)).
% 1.13/1.31 tff(a128_type, type, (
% 1.13/1.31 a128: $i)).
% 1.13/1.31 tff(hskp29_type, type, (
% 1.13/1.31 hskp29: $o)).
% 1.13/1.31 tff(a104_type, type, (
% 1.13/1.31 a104: $i)).
% 1.13/1.31 tff(hskp3_type, type, (
% 1.13/1.31 hskp3: $o)).
% 1.13/1.31 tff(1,assumption,(~hskp19), introduced(assumption)).
% 1.13/1.31 tff(2,plain,
% 1.13/1.31 (^[U: $i] : refl((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.13/1.31 inference(bind,[status(th)],[])).
% 1.13/1.31 tff(3,plain,
% 1.13/1.31 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.13/1.31 inference(quant_intro,[status(thm)],[2])).
% 1.13/1.31 tff(4,plain,
% 1.13/1.31 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(5,plain,
% 1.13/1.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.13/1.31 inference(bind,[status(th)],[])).
% 1.13/1.31 tff(6,plain,
% 1.13/1.31 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.13/1.31 inference(quant_intro,[status(thm)],[5])).
% 1.13/1.32 tff(7,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 1.13/1.32 tff(8,plain,
% 1.13/1.32 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.13/1.32 tff(9,plain,
% 1.13/1.32 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.13/1.32 tff(10,plain,(
% 1.13/1.32 ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.13/1.32 inference(skolemize,[status(sab)],[9])).
% 1.13/1.32 tff(11,plain,
% 1.13/1.32 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.13/1.32 tff(12,plain,
% 1.13/1.32 (^[U: $i] : refl((hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(13,plain,
% 1.13/1.32 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[12])).
% 1.13/1.32 tff(14,plain,
% 1.13/1.32 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(15,plain,
% 1.13/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp24) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp24) <=> (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(16,plain,
% 1.13/1.32 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp24) <=> ![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[15])).
% 1.13/1.32 tff(17,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 1.13/1.32 tff(18,plain,
% 1.13/1.32 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.13/1.32 tff(19,plain,
% 1.13/1.32 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.13/1.32 tff(20,plain,(
% 1.13/1.32 ![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(skolemize,[status(sab)],[19])).
% 1.13/1.32 tff(21,plain,
% 1.13/1.32 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.13/1.32 tff(22,assumption,(~hskp10), introduced(assumption)).
% 1.13/1.32 tff(23,assumption,(~hskp31), introduced(assumption)).
% 1.13/1.32 tff(24,plain,
% 1.13/1.32 (^[U: $i] : refl((hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(25,plain,
% 1.13/1.32 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[24])).
% 1.13/1.32 tff(26,plain,
% 1.13/1.32 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(27,plain,
% 1.13/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp28) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp28) <=> (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(28,plain,
% 1.13/1.32 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp28) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[27])).
% 1.13/1.32 tff(29,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 1.13/1.32 tff(30,plain,
% 1.13/1.32 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.13/1.32 tff(31,plain,
% 1.13/1.32 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.13/1.32 tff(32,plain,(
% 1.13/1.32 ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(skolemize,[status(sab)],[31])).
% 1.13/1.32 tff(33,plain,
% 1.13/1.32 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.13/1.32 tff(34,assumption,(hskp4), introduced(assumption)).
% 1.13/1.32 tff(35,plain,
% 1.13/1.32 (((~hskp4) | (~c1_1(a105))) <=> ((~hskp4) | (~c1_1(a105)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(36,plain,
% 1.13/1.32 (((~c1_1(a105)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a105)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(37,axiom,((~c1_1(a105)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.13/1.32 tff(38,plain,
% 1.13/1.32 ((~hskp4) | (~c1_1(a105))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.13/1.32 tff(39,plain,
% 1.13/1.32 ((~hskp4) | (~c1_1(a105))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[38, 35])).
% 1.13/1.32 tff(40,plain,
% 1.13/1.32 (~c1_1(a105)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[39, 34])).
% 1.13/1.32 tff(41,plain,
% 1.13/1.32 (((~hskp4) | c3_1(a105)) <=> ((~hskp4) | c3_1(a105))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(42,axiom,((~hskp4) | c3_1(a105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.13/1.32 tff(43,plain,
% 1.13/1.32 ((~hskp4) | c3_1(a105)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.13/1.32 tff(44,plain,
% 1.13/1.32 ((~hskp4) | c3_1(a105)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[43, 41])).
% 1.13/1.32 tff(45,plain,
% 1.13/1.32 ((~hskp4) | c3_1(a105)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[44, 41])).
% 1.13/1.32 tff(46,plain,
% 1.13/1.32 ((~hskp4) | c3_1(a105)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.13/1.32 tff(47,plain,
% 1.13/1.32 ((~hskp4) | c3_1(a105)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[46, 41])).
% 1.13/1.32 tff(48,plain,
% 1.13/1.32 (c3_1(a105)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[47, 34])).
% 1.13/1.32 tff(49,assumption,(~c1_1(a163)), introduced(assumption)).
% 1.13/1.32 tff(50,assumption,(hskp31), introduced(assumption)).
% 1.13/1.32 tff(51,plain,
% 1.13/1.32 (((~hskp31) | c3_1(a141)) <=> ((~hskp31) | c3_1(a141))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(52,axiom,((~hskp31) | c3_1(a141)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.13/1.32 tff(53,plain,
% 1.13/1.32 ((~hskp31) | c3_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.13/1.32 tff(54,plain,
% 1.13/1.32 ((~hskp31) | c3_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[53, 51])).
% 1.13/1.32 tff(55,plain,
% 1.13/1.32 ((~hskp31) | c3_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[54, 51])).
% 1.13/1.32 tff(56,plain,
% 1.13/1.32 ((~hskp31) | c3_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.13/1.32 tff(57,plain,
% 1.13/1.32 ((~hskp31) | c3_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[56, 51])).
% 1.13/1.32 tff(58,plain,
% 1.13/1.32 (c3_1(a141)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[57, 50])).
% 1.13/1.32 tff(59,plain,
% 1.13/1.32 (((~hskp31) | c1_1(a141)) <=> ((~hskp31) | c1_1(a141))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(60,axiom,((~hskp31) | c1_1(a141)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.13/1.32 tff(61,plain,
% 1.13/1.32 ((~hskp31) | c1_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.13/1.32 tff(62,plain,
% 1.13/1.32 ((~hskp31) | c1_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[61, 59])).
% 1.13/1.32 tff(63,plain,
% 1.13/1.32 ((~hskp31) | c1_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[62, 59])).
% 1.13/1.32 tff(64,plain,
% 1.13/1.32 ((~hskp31) | c1_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[63, 59])).
% 1.13/1.32 tff(65,plain,
% 1.13/1.32 ((~hskp31) | c1_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[64, 59])).
% 1.13/1.32 tff(66,plain,
% 1.13/1.32 (c1_1(a141)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[65, 50])).
% 1.13/1.32 tff(67,plain,
% 1.13/1.32 (((~hskp31) | c0_1(a141)) <=> ((~hskp31) | c0_1(a141))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(68,axiom,((~hskp31) | c0_1(a141)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.13/1.32 tff(69,plain,
% 1.13/1.32 ((~hskp31) | c0_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.13/1.32 tff(70,plain,
% 1.13/1.32 ((~hskp31) | c0_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[69, 67])).
% 1.13/1.32 tff(71,plain,
% 1.13/1.32 ((~hskp31) | c0_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[70, 67])).
% 1.13/1.32 tff(72,plain,
% 1.13/1.32 ((~hskp31) | c0_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[71, 67])).
% 1.13/1.32 tff(73,plain,
% 1.13/1.32 ((~hskp31) | c0_1(a141)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[72, 67])).
% 1.13/1.32 tff(74,plain,
% 1.13/1.32 (c0_1(a141)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[73, 50])).
% 1.13/1.32 tff(75,plain,
% 1.13/1.32 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(76,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[75])).
% 1.13/1.32 tff(77,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(78,plain,
% 1.13/1.32 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(79,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[78])).
% 1.13/1.32 tff(80,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.13/1.32 tff(81,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.13/1.32 tff(82,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[81, 77])).
% 1.13/1.32 tff(83,plain,(
% 1.13/1.32 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.13/1.32 inference(skolemize,[status(sab)],[82])).
% 1.13/1.32 tff(84,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[83, 76])).
% 1.13/1.32 tff(85,assumption,(~c3_1(a163)), introduced(assumption)).
% 1.13/1.32 tff(86,assumption,(~c2_1(a163)), introduced(assumption)).
% 1.13/1.32 tff(87,plain,
% 1.13/1.32 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(88,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[87])).
% 1.13/1.32 tff(89,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(90,plain,
% 1.13/1.32 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c2_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(91,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[90])).
% 1.13/1.32 tff(92,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.13/1.32 tff(93,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.13/1.32 tff(94,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[93, 89])).
% 1.13/1.32 tff(95,plain,(
% 1.13/1.32 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.13/1.32 inference(skolemize,[status(sab)],[94])).
% 1.13/1.32 tff(96,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[95, 88])).
% 1.13/1.32 tff(97,assumption,(~c2_1(a106)), introduced(assumption)).
% 1.13/1.32 tff(98,assumption,(c0_1(a163)), introduced(assumption)).
% 1.13/1.32 tff(99,plain,
% 1.13/1.32 (^[U: $i] : refl((hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(100,plain,
% 1.13/1.32 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[99])).
% 1.13/1.32 tff(101,plain,
% 1.13/1.32 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(102,plain,
% 1.13/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp8))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp8) <=> (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(103,plain,
% 1.13/1.32 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> ![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[102])).
% 1.13/1.32 tff(104,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.13/1.32 tff(105,plain,
% 1.13/1.32 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.13/1.32 tff(106,plain,
% 1.13/1.32 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[105, 101])).
% 1.13/1.32 tff(107,plain,(
% 1.13/1.32 ![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.13/1.32 inference(skolemize,[status(sab)],[106])).
% 1.13/1.32 tff(108,plain,
% 1.13/1.32 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[107, 100])).
% 1.13/1.32 tff(109,assumption,(~ndr1_0), introduced(assumption)).
% 1.13/1.32 tff(110,plain,
% 1.13/1.32 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(111,plain,
% 1.13/1.32 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(112,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause9')).
% 1.13/1.32 tff(113,plain,
% 1.13/1.32 (ndr1_0 | (~hskp24)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.13/1.32 tff(114,plain,
% 1.13/1.32 (ndr1_0 | (~hskp24)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[113, 110])).
% 1.13/1.32 tff(115,plain,
% 1.13/1.32 (~hskp24),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[114, 109])).
% 1.13/1.32 tff(116,plain,
% 1.13/1.32 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(117,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 1.13/1.32 tff(118,plain,
% 1.13/1.32 ((~hskp31) | ndr1_0),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.13/1.32 tff(119,plain,
% 1.13/1.32 ((~hskp31) | ndr1_0),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[118, 116])).
% 1.13/1.32 tff(120,plain,
% 1.13/1.32 ((~hskp31) | ndr1_0),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[119, 116])).
% 1.13/1.32 tff(121,plain,
% 1.13/1.32 ((~hskp31) | ndr1_0),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[120, 116])).
% 1.13/1.32 tff(122,plain,
% 1.13/1.32 ((~hskp31) | ndr1_0),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[121, 116])).
% 1.13/1.32 tff(123,plain,
% 1.13/1.32 (~hskp31),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[122, 109])).
% 1.13/1.32 tff(124,plain,
% 1.13/1.32 ((ndr1_0 | (~hskp30)) <=> (ndr1_0 | (~hskp30))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(125,plain,
% 1.13/1.32 (((~hskp30) | ndr1_0) <=> (ndr1_0 | (~hskp30))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(126,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 1.13/1.32 tff(127,plain,
% 1.13/1.32 (ndr1_0 | (~hskp30)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.13/1.32 tff(128,plain,
% 1.13/1.32 (ndr1_0 | (~hskp30)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[127, 124])).
% 1.13/1.32 tff(129,plain,
% 1.13/1.32 (~hskp30),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[128, 109])).
% 1.13/1.32 tff(130,plain,
% 1.13/1.32 ((hskp31 | hskp30 | hskp24) <=> (hskp31 | hskp30 | hskp24)),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(131,plain,
% 1.13/1.32 (((hskp31 | hskp30) | hskp24) <=> (hskp31 | hskp30 | hskp24)),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(132,plain,
% 1.13/1.32 ((hskp31 | hskp30) <=> (hskp31 | hskp30)),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(133,plain,
% 1.13/1.32 (((hskp31 | hskp30) | hskp24) <=> ((hskp31 | hskp30) | hskp24)),
% 1.13/1.32 inference(monotonicity,[status(thm)],[132])).
% 1.13/1.32 tff(134,plain,
% 1.13/1.32 (((hskp31 | hskp30) | hskp24) <=> (hskp31 | hskp30 | hskp24)),
% 1.13/1.32 inference(transitivity,[status(thm)],[133, 131])).
% 1.13/1.32 tff(135,axiom,((hskp31 | hskp30) | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.13/1.32 tff(136,plain,
% 1.13/1.32 (hskp31 | hskp30 | hskp24),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.13/1.32 tff(137,plain,
% 1.13/1.32 (hskp31 | hskp30 | hskp24),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[136, 130])).
% 1.13/1.32 tff(138,plain,
% 1.13/1.32 (hskp31 | hskp30 | hskp24),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[137, 130])).
% 1.13/1.32 tff(139,plain,
% 1.13/1.32 (hskp31 | hskp30 | hskp24),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[138, 130])).
% 1.13/1.32 tff(140,plain,
% 1.13/1.32 (hskp31 | hskp30 | hskp24),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[139, 130])).
% 1.13/1.32 tff(141,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[140, 129, 123, 115])).
% 1.13/1.32 tff(142,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(143,plain,
% 1.13/1.32 (((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(144,plain,
% 1.13/1.32 ((hskp8 | hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c0_1(a163))) <=> (hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(145,plain,
% 1.13/1.32 (((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[144])).
% 1.13/1.32 tff(146,plain,
% 1.13/1.32 (((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.13/1.32 inference(transitivity,[status(thm)],[145, 143])).
% 1.13/1.32 tff(147,plain,
% 1.13/1.32 ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c0_1(a163)))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(148,plain,
% 1.13/1.32 ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.13/1.32 tff(149,plain,
% 1.13/1.32 (hskp8 | hskp19 | (~c0_1(a163))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[148, 142, 86, 85, 108])).
% 1.13/1.32 tff(150,plain,
% 1.13/1.32 (hskp8),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[149, 1, 98])).
% 1.13/1.32 tff(151,plain,
% 1.13/1.32 (((~hskp8) | (~c3_1(a109))) <=> ((~hskp8) | (~c3_1(a109)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(152,plain,
% 1.13/1.32 (((~c3_1(a109)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a109)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(153,axiom,((~c3_1(a109)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.13/1.32 tff(154,plain,
% 1.13/1.32 ((~hskp8) | (~c3_1(a109))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.13/1.32 tff(155,plain,
% 1.13/1.32 ((~hskp8) | (~c3_1(a109))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[154, 151])).
% 1.13/1.32 tff(156,plain,
% 1.13/1.32 (~c3_1(a109)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[155, 150])).
% 1.13/1.32 tff(157,plain,
% 1.13/1.32 (((~hskp8) | c1_1(a109)) <=> ((~hskp8) | c1_1(a109))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(158,axiom,((~hskp8) | c1_1(a109)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.13/1.32 tff(159,plain,
% 1.13/1.32 ((~hskp8) | c1_1(a109)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.13/1.32 tff(160,plain,
% 1.13/1.32 ((~hskp8) | c1_1(a109)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[159, 157])).
% 1.13/1.32 tff(161,plain,
% 1.13/1.32 ((~hskp8) | c1_1(a109)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[160, 157])).
% 1.13/1.32 tff(162,plain,
% 1.13/1.32 ((~hskp8) | c1_1(a109)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[161, 157])).
% 1.13/1.32 tff(163,plain,
% 1.13/1.32 ((~hskp8) | c1_1(a109)),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[162, 157])).
% 1.13/1.32 tff(164,plain,
% 1.13/1.32 (c1_1(a109)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[163, 150])).
% 1.13/1.32 tff(165,plain,
% 1.13/1.32 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(166,plain,
% 1.13/1.32 ((hskp19 | (~ndr1_0) | c3_1(a109) | c2_1(a109) | (~c1_1(a109))) <=> (hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(167,plain,
% 1.13/1.32 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a109) | c2_1(a109) | (~c1_1(a109)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[166])).
% 1.13/1.32 tff(168,plain,
% 1.13/1.32 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a109) | c2_1(a109) | (~c1_1(a109)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109)))),
% 1.13/1.32 inference(transitivity,[status(thm)],[167, 165])).
% 1.13/1.32 tff(169,plain,
% 1.13/1.32 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a109) | c2_1(a109) | (~c1_1(a109)))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(170,plain,
% 1.13/1.32 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.13/1.32 tff(171,plain,
% 1.13/1.32 (c2_1(a109)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[170, 142, 1, 164, 156, 11])).
% 1.13/1.32 tff(172,plain,
% 1.13/1.32 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.13/1.32 inference(bind,[status(th)],[])).
% 1.13/1.32 tff(173,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.13/1.32 inference(quant_intro,[status(thm)],[172])).
% 1.13/1.32 tff(174,plain,
% 1.13/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(175,plain,
% 1.13/1.32 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.13/1.33 inference(bind,[status(th)],[])).
% 1.13/1.33 tff(176,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.13/1.33 inference(quant_intro,[status(thm)],[175])).
% 1.13/1.33 tff(177,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.13/1.33 tff(178,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.13/1.33 tff(179,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[178, 174])).
% 1.13/1.33 tff(180,plain,(
% 1.13/1.33 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.13/1.33 inference(skolemize,[status(sab)],[179])).
% 1.13/1.33 tff(181,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[180, 173])).
% 1.13/1.33 tff(182,plain,
% 1.13/1.33 (((~hskp8) | (~c0_1(a109))) <=> ((~hskp8) | (~c0_1(a109)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(183,plain,
% 1.13/1.33 (((~c0_1(a109)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a109)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(184,axiom,((~c0_1(a109)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.13/1.33 tff(185,plain,
% 1.13/1.33 ((~hskp8) | (~c0_1(a109))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.13/1.33 tff(186,plain,
% 1.13/1.33 ((~hskp8) | (~c0_1(a109))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[185, 182])).
% 1.13/1.33 tff(187,plain,
% 1.13/1.33 (~c0_1(a109)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[186, 150])).
% 1.13/1.33 tff(188,plain,
% 1.13/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(189,plain,
% 1.13/1.33 (((~ndr1_0) | c3_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109))) <=> (c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(190,plain,
% 1.13/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[189])).
% 1.13/1.33 tff(191,plain,
% 1.13/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163)))),
% 1.13/1.33 inference(transitivity,[status(thm)],[190, 188])).
% 1.13/1.33 tff(192,plain,
% 1.13/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(193,plain,
% 1.13/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[192, 191])).
% 1.13/1.33 tff(194,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[193, 142, 164, 86, 85, 187, 156, 181, 98, 171])).
% 1.13/1.33 tff(195,plain,(hskp19 | c2_1(a163) | c3_1(a163) | (~c0_1(a163))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(196,plain,
% 1.13/1.33 (~c0_1(a163)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[195, 1, 85, 86])).
% 1.13/1.33 tff(197,plain,
% 1.13/1.33 (^[U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.13/1.33 inference(bind,[status(th)],[])).
% 1.13/1.33 tff(198,plain,
% 1.13/1.33 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.33 inference(quant_intro,[status(thm)],[197])).
% 1.13/1.33 tff(199,plain,
% 1.13/1.33 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(200,plain,
% 1.13/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.13/1.33 inference(bind,[status(th)],[])).
% 1.13/1.33 tff(201,plain,
% 1.13/1.33 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp5) <=> ![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.33 inference(quant_intro,[status(thm)],[200])).
% 1.13/1.33 tff(202,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.13/1.33 tff(203,plain,
% 1.13/1.33 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.13/1.33 tff(204,plain,
% 1.13/1.33 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[203, 199])).
% 1.13/1.33 tff(205,plain,(
% 1.13/1.33 ![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.33 inference(skolemize,[status(sab)],[204])).
% 1.13/1.33 tff(206,plain,
% 1.13/1.33 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[205, 198])).
% 1.13/1.33 tff(207,plain,
% 1.13/1.33 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(208,plain,
% 1.13/1.33 ((hskp5 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(209,plain,
% 1.13/1.33 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[208])).
% 1.13/1.33 tff(210,plain,
% 1.13/1.33 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.13/1.33 inference(transitivity,[status(thm)],[209, 207])).
% 1.13/1.33 tff(211,plain,
% 1.13/1.33 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(212,plain,
% 1.13/1.33 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[211, 210])).
% 1.13/1.33 tff(213,plain,
% 1.13/1.33 (hskp5 | c3_1(a163) | c0_1(a163)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[212, 142, 49, 206])).
% 1.13/1.33 tff(214,plain,
% 1.13/1.33 (hskp5),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[213, 196, 85])).
% 1.13/1.33 tff(215,assumption,(c1_1(a106)), introduced(assumption)).
% 1.13/1.33 tff(216,plain,
% 1.13/1.33 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(217,plain,
% 1.13/1.33 ((hskp19 | (~ndr1_0) | c3_1(a106) | c2_1(a106) | (~c1_1(a106))) <=> (hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(218,plain,
% 1.13/1.33 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a106) | c2_1(a106) | (~c1_1(a106)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[217])).
% 1.13/1.33 tff(219,plain,
% 1.13/1.33 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a106) | c2_1(a106) | (~c1_1(a106)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106)))),
% 1.13/1.33 inference(transitivity,[status(thm)],[218, 216])).
% 1.13/1.33 tff(220,plain,
% 1.13/1.33 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a106) | c2_1(a106) | (~c1_1(a106)))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(221,plain,
% 1.13/1.33 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.13/1.33 tff(222,plain,
% 1.13/1.33 (hskp19 | c3_1(a106)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[221, 142, 215, 97, 11])).
% 1.13/1.33 tff(223,plain,
% 1.13/1.33 (c3_1(a106)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[222, 1])).
% 1.13/1.33 tff(224,assumption,(~c0_1(a163)), introduced(assumption)).
% 1.13/1.33 tff(225,plain,
% 1.13/1.33 (hskp5 | c0_1(a163)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[212, 142, 49, 85, 206])).
% 1.13/1.33 tff(226,plain,
% 1.13/1.33 (hskp5),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[225, 224])).
% 1.13/1.33 tff(227,plain,
% 1.13/1.33 (((~hskp5) | c1_1(a106)) <=> ((~hskp5) | c1_1(a106))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(228,axiom,((~hskp5) | c1_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.13/1.33 tff(229,plain,
% 1.13/1.33 ((~hskp5) | c1_1(a106)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.13/1.33 tff(230,plain,
% 1.13/1.33 ((~hskp5) | c1_1(a106)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[229, 227])).
% 1.13/1.33 tff(231,plain,
% 1.13/1.33 ((~hskp5) | c1_1(a106)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[230, 227])).
% 1.13/1.33 tff(232,plain,
% 1.13/1.33 ((~hskp5) | c1_1(a106)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[231, 227])).
% 1.13/1.33 tff(233,plain,
% 1.13/1.33 ((~hskp5) | c1_1(a106)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[232, 227])).
% 1.13/1.33 tff(234,plain,
% 1.13/1.33 (c1_1(a106)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[233, 226])).
% 1.13/1.33 tff(235,plain,
% 1.13/1.33 (hskp19 | c3_1(a106) | (~c1_1(a106))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[221, 142, 97, 11])).
% 1.13/1.33 tff(236,plain,
% 1.13/1.33 (c3_1(a106)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[235, 1, 234])).
% 1.13/1.33 tff(237,plain,
% 1.13/1.33 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.13/1.33 inference(bind,[status(th)],[])).
% 1.13/1.33 tff(238,plain,
% 1.13/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.13/1.33 inference(quant_intro,[status(thm)],[237])).
% 1.13/1.33 tff(239,plain,
% 1.13/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(240,plain,
% 1.13/1.33 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.13/1.33 inference(bind,[status(th)],[])).
% 1.13/1.33 tff(241,plain,
% 1.13/1.33 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.13/1.33 inference(quant_intro,[status(thm)],[240])).
% 1.13/1.33 tff(242,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.13/1.33 tff(243,plain,
% 1.13/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.13/1.33 tff(244,plain,
% 1.13/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[243, 239])).
% 1.13/1.33 tff(245,plain,(
% 1.13/1.33 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.13/1.33 inference(skolemize,[status(sab)],[244])).
% 1.13/1.33 tff(246,plain,
% 1.13/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[245, 238])).
% 1.13/1.33 tff(247,plain,
% 1.13/1.33 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(248,plain,
% 1.13/1.33 ((hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a163) | c1_1(a163) | c0_1(a163)) <=> (hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(249,plain,
% 1.13/1.33 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163)))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[248])).
% 1.13/1.33 tff(250,plain,
% 1.13/1.33 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163))),
% 1.13/1.33 inference(transitivity,[status(thm)],[249, 247])).
% 1.13/1.33 tff(251,plain,
% 1.13/1.33 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a163) | c1_1(a163) | c0_1(a163))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(252,plain,
% 1.13/1.33 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.13/1.33 tff(253,plain,
% 1.13/1.33 (hskp2 | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[252, 142, 49, 86, 97, 246])).
% 1.13/1.33 tff(254,plain,
% 1.13/1.33 (hskp2),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[253, 236, 234, 224])).
% 1.13/1.33 tff(255,plain,
% 1.13/1.33 (((~hskp2) | c1_1(a103)) <=> ((~hskp2) | c1_1(a103))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(256,axiom,((~hskp2) | c1_1(a103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.13/1.33 tff(257,plain,
% 1.13/1.33 ((~hskp2) | c1_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[256, 255])).
% 1.13/1.33 tff(258,plain,
% 1.13/1.33 ((~hskp2) | c1_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[257, 255])).
% 1.13/1.33 tff(259,plain,
% 1.13/1.33 ((~hskp2) | c1_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[258, 255])).
% 1.13/1.33 tff(260,plain,
% 1.13/1.33 ((~hskp2) | c1_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[259, 255])).
% 1.13/1.33 tff(261,plain,
% 1.13/1.33 ((~hskp2) | c1_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[260, 255])).
% 1.13/1.33 tff(262,plain,
% 1.13/1.33 (c1_1(a103)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[261, 254])).
% 1.13/1.33 tff(263,assumption,(~c3_1(a103)), introduced(assumption)).
% 1.13/1.33 tff(264,plain,
% 1.13/1.33 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(265,plain,
% 1.13/1.33 ((hskp19 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103))) <=> (hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(266,plain,
% 1.13/1.33 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[265])).
% 1.13/1.33 tff(267,plain,
% 1.13/1.33 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)))),
% 1.13/1.33 inference(transitivity,[status(thm)],[266, 264])).
% 1.13/1.33 tff(268,plain,
% 1.13/1.33 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(269,plain,
% 1.13/1.33 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.13/1.33 tff(270,plain,
% 1.13/1.33 (hskp19 | c2_1(a103) | (~c1_1(a103))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[269, 142, 263, 11])).
% 1.13/1.33 tff(271,plain,
% 1.13/1.33 (c2_1(a103)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[270, 262, 1])).
% 1.13/1.33 tff(272,plain,
% 1.13/1.33 (((~hskp2) | c0_1(a103)) <=> ((~hskp2) | c0_1(a103))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(273,axiom,((~hskp2) | c0_1(a103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.13/1.33 tff(274,plain,
% 1.13/1.33 ((~hskp2) | c0_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[273, 272])).
% 1.13/1.33 tff(275,plain,
% 1.13/1.33 ((~hskp2) | c0_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[274, 272])).
% 1.13/1.33 tff(276,plain,
% 1.13/1.33 ((~hskp2) | c0_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[275, 272])).
% 1.13/1.33 tff(277,plain,
% 1.13/1.33 ((~hskp2) | c0_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[276, 272])).
% 1.13/1.33 tff(278,plain,
% 1.13/1.33 ((~hskp2) | c0_1(a103)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[277, 272])).
% 1.13/1.33 tff(279,plain,
% 1.13/1.33 (c0_1(a103)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[278, 254])).
% 1.13/1.33 tff(280,assumption,(c3_1(a106)), introduced(assumption)).
% 1.13/1.33 tff(281,plain,
% 1.13/1.33 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_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)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))))),
% 1.13/1.33 inference(bind,[status(th)],[])).
% 1.13/1.33 tff(282,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.13/1.33 inference(quant_intro,[status(thm)],[281])).
% 1.13/1.33 tff(283,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(284,plain,
% 1.13/1.33 (^[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))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | 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(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | 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(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))))),
% 1.13/1.33 inference(bind,[status(th)],[])).
% 1.13/1.33 tff(285,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.13/1.33 inference(quant_intro,[status(thm)],[284])).
% 1.13/1.33 tff(286,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.13/1.33 tff(287,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.13/1.33 tff(288,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[287, 283])).
% 1.13/1.33 tff(289,plain,(
% 1.13/1.33 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.13/1.33 inference(skolemize,[status(sab)],[288])).
% 1.13/1.33 tff(290,plain,
% 1.13/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[289, 282])).
% 1.13/1.33 tff(291,assumption,(hskp9), introduced(assumption)).
% 1.13/1.33 tff(292,plain,
% 1.13/1.33 (((~hskp9) | (~c1_1(a110))) <=> ((~hskp9) | (~c1_1(a110)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(293,plain,
% 1.13/1.33 (((~c1_1(a110)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a110)))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(294,axiom,((~c1_1(a110)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.13/1.33 tff(295,plain,
% 1.13/1.33 ((~hskp9) | (~c1_1(a110))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.13/1.33 tff(296,plain,
% 1.13/1.33 ((~hskp9) | (~c1_1(a110))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[295, 292])).
% 1.13/1.33 tff(297,plain,
% 1.13/1.33 (~c1_1(a110)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[296, 291])).
% 1.13/1.33 tff(298,plain,
% 1.13/1.33 (((~hskp5) | c0_1(a106)) <=> ((~hskp5) | c0_1(a106))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(299,axiom,((~hskp5) | c0_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.13/1.33 tff(300,plain,
% 1.13/1.33 ((~hskp5) | c0_1(a106)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.13/1.33 tff(301,plain,
% 1.13/1.33 ((~hskp5) | c0_1(a106)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[300, 298])).
% 1.13/1.33 tff(302,plain,
% 1.13/1.33 ((~hskp5) | c0_1(a106)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[301, 298])).
% 1.13/1.33 tff(303,plain,
% 1.13/1.33 ((~hskp5) | c0_1(a106)),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[302, 298])).
% 1.13/1.33 tff(304,plain,
% 1.13/1.33 ((~hskp5) | c0_1(a106)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[303, 298])).
% 1.13/1.34 tff(305,plain,
% 1.13/1.34 (c0_1(a106)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[304, 226])).
% 1.13/1.34 tff(306,plain,
% 1.13/1.34 (((~hskp9) | c2_1(a110)) <=> ((~hskp9) | c2_1(a110))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(307,axiom,((~hskp9) | c2_1(a110)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.13/1.34 tff(308,plain,
% 1.13/1.34 ((~hskp9) | c2_1(a110)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[307, 306])).
% 1.13/1.34 tff(309,plain,
% 1.13/1.34 ((~hskp9) | c2_1(a110)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[308, 306])).
% 1.13/1.34 tff(310,plain,
% 1.13/1.34 ((~hskp9) | c2_1(a110)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[309, 306])).
% 1.13/1.34 tff(311,plain,
% 1.13/1.34 ((~hskp9) | c2_1(a110)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[310, 306])).
% 1.13/1.34 tff(312,plain,
% 1.13/1.34 ((~hskp9) | c2_1(a110)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[311, 306])).
% 1.13/1.34 tff(313,plain,
% 1.13/1.34 (c2_1(a110)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[312, 291])).
% 1.13/1.34 tff(314,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(315,plain,
% 1.13/1.34 (((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c1_1(a110) | (~c0_1(a110)) | (~c2_1(a110))) <=> (c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(316,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c1_1(a110) | (~c0_1(a110)) | (~c2_1(a110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[315])).
% 1.13/1.34 tff(317,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c1_1(a110) | (~c0_1(a110)) | (~c2_1(a110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110)))),
% 1.13/1.34 inference(transitivity,[status(thm)],[316, 314])).
% 1.13/1.34 tff(318,plain,
% 1.13/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c1_1(a110) | (~c0_1(a110)) | (~c2_1(a110)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(319,plain,
% 1.13/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.13/1.34 tff(320,plain,
% 1.13/1.34 (~c0_1(a110)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[319, 142, 313, 305, 234, 297, 97, 290, 280])).
% 1.13/1.34 tff(321,assumption,(c2_1(a103)), introduced(assumption)).
% 1.13/1.34 tff(322,plain,
% 1.13/1.34 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(323,plain,
% 1.13/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[322])).
% 1.13/1.34 tff(324,plain,
% 1.13/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(325,plain,
% 1.13/1.34 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_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) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_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) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(326,plain,
% 1.13/1.34 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[325])).
% 1.13/1.34 tff(327,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.13/1.34 tff(328,plain,
% 1.13/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[327, 326])).
% 1.13/1.34 tff(329,plain,
% 1.13/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[328, 324])).
% 1.13/1.34 tff(330,plain,(
% 1.13/1.34 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.13/1.34 inference(skolemize,[status(sab)],[329])).
% 1.13/1.34 tff(331,plain,
% 1.13/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[330, 323])).
% 1.13/1.34 tff(332,plain,
% 1.13/1.34 (((~hskp9) | (~c3_1(a110))) <=> ((~hskp9) | (~c3_1(a110)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(333,plain,
% 1.13/1.34 (((~c3_1(a110)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a110)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(334,axiom,((~c3_1(a110)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.13/1.34 tff(335,plain,
% 1.13/1.34 ((~hskp9) | (~c3_1(a110))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[334, 333])).
% 1.13/1.34 tff(336,plain,
% 1.13/1.34 ((~hskp9) | (~c3_1(a110))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[335, 332])).
% 1.13/1.34 tff(337,plain,
% 1.13/1.34 (~c3_1(a110)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[336, 291])).
% 1.13/1.34 tff(338,assumption,(c0_1(a103)), introduced(assumption)).
% 1.13/1.34 tff(339,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(340,plain,
% 1.13/1.34 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a110) | c3_1(a110) | (~c2_1(a110)) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(341,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a110) | c3_1(a110) | (~c2_1(a110)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163)))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[340])).
% 1.13/1.34 tff(342,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a110) | c3_1(a110) | (~c2_1(a110)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163))),
% 1.13/1.34 inference(transitivity,[status(thm)],[341, 339])).
% 1.13/1.34 tff(343,plain,
% 1.13/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a110) | c3_1(a110) | (~c2_1(a110)) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(344,plain,
% 1.13/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.13/1.34 tff(345,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[344, 142, 313, 338, 49, 85, 337, 263, 331, 224, 321, 320])).
% 1.13/1.34 tff(346,plain,((~hskp9) | (~c0_1(a103)) | c1_1(a163) | c3_1(a163) | c3_1(a103) | c0_1(a163) | (~c2_1(a103)) | c2_1(a106) | (~c3_1(a106))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(347,plain,
% 1.13/1.34 (~hskp9),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[346, 279, 49, 85, 263, 224, 271, 97, 236])).
% 1.13/1.34 tff(348,plain,
% 1.13/1.34 (^[U: $i] : refl((hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(349,plain,
% 1.13/1.34 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[348])).
% 1.13/1.34 tff(350,plain,
% 1.13/1.34 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(351,plain,
% 1.13/1.34 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp9) <=> (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.13/1.34 inference(bind,[status(th)],[])).
% 1.13/1.34 tff(352,plain,
% 1.13/1.34 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.34 inference(quant_intro,[status(thm)],[351])).
% 1.13/1.34 tff(353,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.13/1.34 tff(354,plain,
% 1.13/1.34 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[353, 352])).
% 1.13/1.34 tff(355,plain,
% 1.13/1.34 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[354, 350])).
% 1.13/1.34 tff(356,plain,(
% 1.13/1.34 ![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.34 inference(skolemize,[status(sab)],[355])).
% 1.13/1.34 tff(357,plain,
% 1.13/1.34 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[356, 349])).
% 1.13/1.34 tff(358,plain,
% 1.13/1.34 (((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(359,plain,
% 1.13/1.34 ((hskp8 | hskp9 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(360,plain,
% 1.13/1.34 (((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[359])).
% 1.13/1.34 tff(361,plain,
% 1.13/1.34 (((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.13/1.34 inference(transitivity,[status(thm)],[360, 358])).
% 1.13/1.34 tff(362,plain,
% 1.13/1.34 ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(363,plain,
% 1.13/1.34 ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[362, 361])).
% 1.13/1.34 tff(364,plain,
% 1.13/1.34 (hskp8 | hskp9 | c0_1(a163)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[363, 142, 49, 85, 357])).
% 1.13/1.34 tff(365,plain,
% 1.13/1.34 (hskp8),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[364, 347, 224])).
% 1.13/1.34 tff(366,plain,
% 1.13/1.34 (~c3_1(a109)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[155, 365])).
% 1.13/1.34 tff(367,plain,
% 1.13/1.34 (c1_1(a109)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[163, 365])).
% 1.13/1.34 tff(368,plain,
% 1.13/1.34 (c2_1(a109)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[170, 142, 1, 367, 366, 11])).
% 1.13/1.34 tff(369,plain,
% 1.13/1.34 (~c0_1(a109)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[186, 365])).
% 1.13/1.34 tff(370,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(371,plain,
% 1.13/1.34 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(372,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163)))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[371])).
% 1.13/1.34 tff(373,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 1.13/1.34 inference(transitivity,[status(thm)],[372, 370])).
% 1.13/1.34 tff(374,plain,
% 1.13/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(375,plain,
% 1.13/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.13/1.34 tff(376,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[375, 142, 279, 49, 85, 369, 366, 263, 331, 224, 271, 368])).
% 1.13/1.34 tff(377,plain,(hskp19 | c1_1(a163) | c3_1(a163) | c3_1(a103) | c0_1(a163) | c2_1(a106) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(378,plain,
% 1.13/1.34 (c3_1(a103)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[377, 1, 85, 224, 49, 97, 86])).
% 1.13/1.34 tff(379,plain,
% 1.13/1.34 (((~hskp2) | (~c3_1(a103))) <=> ((~hskp2) | (~c3_1(a103)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(380,plain,
% 1.13/1.34 (((~c3_1(a103)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a103)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(381,axiom,((~c3_1(a103)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.13/1.34 tff(382,plain,
% 1.13/1.34 ((~hskp2) | (~c3_1(a103))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[381, 380])).
% 1.13/1.34 tff(383,plain,
% 1.13/1.34 ((~hskp2) | (~c3_1(a103))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[382, 379])).
% 1.13/1.34 tff(384,plain,
% 1.13/1.34 (~hskp2),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[383, 378])).
% 1.13/1.34 tff(385,plain,
% 1.13/1.34 (hskp2 | (~c3_1(a106))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[252, 142, 215, 49, 86, 97, 246, 224])).
% 1.13/1.34 tff(386,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[385, 384, 223])).
% 1.13/1.34 tff(387,plain,(hskp19 | (~c1_1(a106)) | c1_1(a163) | c2_1(a163) | c2_1(a106) | c0_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(388,plain,
% 1.13/1.34 (~c1_1(a106)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[387, 196, 49, 86, 85, 97, 1])).
% 1.13/1.34 tff(389,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[233, 388, 214])).
% 1.13/1.34 tff(390,plain,(hskp19 | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a106)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(391,plain,
% 1.13/1.34 (hskp19),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[390, 97, 86, 85, 49])).
% 1.13/1.34 tff(392,plain,
% 1.13/1.34 (((~hskp19) | (~c3_1(a135))) <=> ((~hskp19) | (~c3_1(a135)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(393,plain,
% 1.13/1.34 (((~c3_1(a135)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a135)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(394,axiom,((~c3_1(a135)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.13/1.34 tff(395,plain,
% 1.13/1.34 ((~hskp19) | (~c3_1(a135))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.13/1.34 tff(396,plain,
% 1.13/1.34 ((~hskp19) | (~c3_1(a135))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[395, 392])).
% 1.13/1.34 tff(397,plain,
% 1.13/1.34 (~c3_1(a135)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[396, 391])).
% 1.13/1.34 tff(398,plain,
% 1.13/1.34 (((~hskp19) | (~c2_1(a135))) <=> ((~hskp19) | (~c2_1(a135)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(399,plain,
% 1.13/1.34 (((~c2_1(a135)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a135)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(400,axiom,((~c2_1(a135)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.13/1.34 tff(401,plain,
% 1.13/1.34 ((~hskp19) | (~c2_1(a135))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.13/1.34 tff(402,plain,
% 1.13/1.34 ((~hskp19) | (~c2_1(a135))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[401, 398])).
% 1.13/1.34 tff(403,plain,
% 1.13/1.34 (~c2_1(a135)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[402, 391])).
% 1.13/1.34 tff(404,assumption,(hskp19), introduced(assumption)).
% 1.13/1.34 tff(405,assumption,(hskp6), introduced(assumption)).
% 1.13/1.34 tff(406,plain,
% 1.13/1.34 (((~hskp6) | (~c0_1(a107))) <=> ((~hskp6) | (~c0_1(a107)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(407,plain,
% 1.13/1.34 (((~c0_1(a107)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a107)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(408,axiom,((~c0_1(a107)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.13/1.34 tff(409,plain,
% 1.13/1.34 ((~hskp6) | (~c0_1(a107))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[408, 407])).
% 1.13/1.34 tff(410,plain,
% 1.13/1.34 ((~hskp6) | (~c0_1(a107))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[409, 406])).
% 1.13/1.34 tff(411,plain,
% 1.13/1.34 (~c0_1(a107)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[410, 405])).
% 1.13/1.34 tff(412,assumption,(~c0_1(a107)), introduced(assumption)).
% 1.13/1.34 tff(413,plain,
% 1.13/1.34 (~c3_1(a135)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[396, 404])).
% 1.13/1.34 tff(414,plain,
% 1.13/1.34 (((~hskp19) | c0_1(a135)) <=> ((~hskp19) | c0_1(a135))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(415,axiom,((~hskp19) | c0_1(a135)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.13/1.34 tff(416,plain,
% 1.13/1.34 ((~hskp19) | c0_1(a135)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[415, 414])).
% 1.13/1.34 tff(417,plain,
% 1.13/1.34 ((~hskp19) | c0_1(a135)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[416, 414])).
% 1.13/1.34 tff(418,plain,
% 1.13/1.34 ((~hskp19) | c0_1(a135)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[417, 414])).
% 1.13/1.34 tff(419,plain,
% 1.13/1.34 ((~hskp19) | c0_1(a135)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[418, 414])).
% 1.13/1.34 tff(420,plain,
% 1.13/1.34 ((~hskp19) | c0_1(a135)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[419, 414])).
% 1.13/1.34 tff(421,plain,
% 1.13/1.34 (c0_1(a135)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[420, 404])).
% 1.13/1.34 tff(422,plain,
% 1.13/1.34 (~c2_1(a135)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[402, 404])).
% 1.13/1.34 tff(423,assumption,(~c3_1(a135)), introduced(assumption)).
% 1.13/1.34 tff(424,assumption,(~c2_1(a135)), introduced(assumption)).
% 1.13/1.34 tff(425,plain,
% 1.13/1.34 (((~hskp6) | c2_1(a107)) <=> ((~hskp6) | c2_1(a107))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(426,axiom,((~hskp6) | c2_1(a107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.13/1.34 tff(427,plain,
% 1.13/1.34 ((~hskp6) | c2_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[426, 425])).
% 1.13/1.34 tff(428,plain,
% 1.13/1.34 ((~hskp6) | c2_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[427, 425])).
% 1.13/1.34 tff(429,plain,
% 1.13/1.34 ((~hskp6) | c2_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[428, 425])).
% 1.13/1.34 tff(430,plain,
% 1.13/1.34 ((~hskp6) | c2_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[429, 425])).
% 1.13/1.34 tff(431,plain,
% 1.13/1.34 ((~hskp6) | c2_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[430, 425])).
% 1.13/1.34 tff(432,plain,
% 1.13/1.34 (c2_1(a107)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[431, 405])).
% 1.13/1.34 tff(433,plain,
% 1.13/1.34 (((~hskp6) | c1_1(a107)) <=> ((~hskp6) | c1_1(a107))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(434,axiom,((~hskp6) | c1_1(a107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.13/1.34 tff(435,plain,
% 1.13/1.34 ((~hskp6) | c1_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.13/1.34 tff(436,plain,
% 1.13/1.34 ((~hskp6) | c1_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[435, 433])).
% 1.13/1.34 tff(437,plain,
% 1.13/1.34 ((~hskp6) | c1_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[436, 433])).
% 1.13/1.34 tff(438,plain,
% 1.13/1.34 ((~hskp6) | c1_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[437, 433])).
% 1.13/1.34 tff(439,plain,
% 1.13/1.34 ((~hskp6) | c1_1(a107)),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[438, 433])).
% 1.13/1.34 tff(440,plain,
% 1.13/1.34 (c1_1(a107)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[439, 405])).
% 1.13/1.34 tff(441,assumption,(c0_1(a135)), introduced(assumption)).
% 1.13/1.34 tff(442,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(443,plain,
% 1.13/1.34 (((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(444,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[443])).
% 1.13/1.34 tff(445,plain,
% 1.13/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 1.13/1.34 inference(transitivity,[status(thm)],[444, 442])).
% 1.13/1.34 tff(446,plain,
% 1.13/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(447,plain,
% 1.13/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[446, 445])).
% 1.13/1.35 tff(448,plain,
% 1.13/1.35 (~c3_1(a107)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[447, 142, 441, 440, 432, 49, 86, 85, 424, 423, 96])).
% 1.13/1.35 tff(449,plain,
% 1.13/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(450,plain,
% 1.13/1.35 (((~ndr1_0) | c3_1(a107) | (~c1_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a107) | c0_1(a107) | (~c1_1(a107))) <=> (c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(451,plain,
% 1.13/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a107) | (~c1_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a107) | c0_1(a107) | (~c1_1(a107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[450])).
% 1.13/1.35 tff(452,plain,
% 1.13/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a107) | (~c1_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a107) | c0_1(a107) | (~c1_1(a107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[451, 449])).
% 1.13/1.35 tff(453,plain,
% 1.13/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a107) | (~c1_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a107) | c0_1(a107) | (~c1_1(a107)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(454,plain,
% 1.13/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.13/1.35 tff(455,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[454, 142, 441, 440, 432, 424, 423, 412, 181, 448])).
% 1.13/1.35 tff(456,plain,((~hskp6) | (~c0_1(a135)) | c2_1(a135) | c3_1(a135) | c0_1(a107) | c1_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(457,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[456, 422, 421, 405, 413, 412, 49, 86, 85])).
% 1.13/1.35 tff(458,plain,((~hskp19) | (~hskp6) | c0_1(a107) | c1_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(459,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[458, 411, 405, 404, 49, 86, 85])).
% 1.13/1.35 tff(460,plain,((~hskp6) | (~hskp19) | c1_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(461,plain,
% 1.13/1.35 (~hskp6),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[460, 391, 49, 86, 85])).
% 1.13/1.35 tff(462,assumption,(~hskp5), introduced(assumption)).
% 1.13/1.35 tff(463,plain,
% 1.13/1.35 (c0_1(a163)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[213, 462, 85])).
% 1.13/1.35 tff(464,plain,
% 1.13/1.35 (c0_1(a163)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[225, 462])).
% 1.13/1.35 tff(465,plain,
% 1.13/1.35 (hskp19),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[195, 464, 85, 86])).
% 1.13/1.35 tff(466,plain,
% 1.13/1.35 (~c3_1(a135)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[396, 465])).
% 1.13/1.35 tff(467,plain,
% 1.13/1.35 (c0_1(a135)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[420, 465])).
% 1.13/1.35 tff(468,plain,
% 1.13/1.35 (~c2_1(a135)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[402, 465])).
% 1.13/1.35 tff(469,assumption,(hskp28), introduced(assumption)).
% 1.13/1.35 tff(470,plain,
% 1.13/1.35 (((~hskp28) | c3_1(a118)) <=> ((~hskp28) | c3_1(a118))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(471,axiom,((~hskp28) | c3_1(a118)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.13/1.35 tff(472,plain,
% 1.13/1.35 ((~hskp28) | c3_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.13/1.35 tff(473,plain,
% 1.13/1.35 ((~hskp28) | c3_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[472, 470])).
% 1.13/1.35 tff(474,plain,
% 1.13/1.35 ((~hskp28) | c3_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[473, 470])).
% 1.13/1.35 tff(475,plain,
% 1.13/1.35 ((~hskp28) | c3_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[474, 470])).
% 1.13/1.35 tff(476,plain,
% 1.13/1.35 ((~hskp28) | c3_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[475, 470])).
% 1.13/1.35 tff(477,plain,
% 1.13/1.35 (c3_1(a118)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[476, 469])).
% 1.13/1.35 tff(478,plain,
% 1.13/1.35 (((~hskp28) | c2_1(a118)) <=> ((~hskp28) | c2_1(a118))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(479,axiom,((~hskp28) | c2_1(a118)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.13/1.35 tff(480,plain,
% 1.13/1.35 ((~hskp28) | c2_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.13/1.35 tff(481,plain,
% 1.13/1.35 ((~hskp28) | c2_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[480, 478])).
% 1.13/1.35 tff(482,plain,
% 1.13/1.35 ((~hskp28) | c2_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[481, 478])).
% 1.13/1.35 tff(483,plain,
% 1.13/1.35 ((~hskp28) | c2_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[482, 478])).
% 1.13/1.35 tff(484,plain,
% 1.13/1.35 ((~hskp28) | c2_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[483, 478])).
% 1.13/1.35 tff(485,plain,
% 1.13/1.35 (c2_1(a118)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[484, 469])).
% 1.13/1.35 tff(486,plain,
% 1.13/1.35 (((~hskp28) | c1_1(a118)) <=> ((~hskp28) | c1_1(a118))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(487,axiom,((~hskp28) | c1_1(a118)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.13/1.35 tff(488,plain,
% 1.13/1.35 ((~hskp28) | c1_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[487, 486])).
% 1.13/1.35 tff(489,plain,
% 1.13/1.35 ((~hskp28) | c1_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[488, 486])).
% 1.13/1.35 tff(490,plain,
% 1.13/1.35 ((~hskp28) | c1_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[489, 486])).
% 1.13/1.35 tff(491,plain,
% 1.13/1.35 ((~hskp28) | c1_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[490, 486])).
% 1.13/1.35 tff(492,plain,
% 1.13/1.35 ((~hskp28) | c1_1(a118)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[491, 486])).
% 1.13/1.35 tff(493,plain,
% 1.13/1.35 (c1_1(a118)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[492, 469])).
% 1.13/1.35 tff(494,plain,
% 1.13/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(495,plain,
% 1.13/1.35 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(496,plain,
% 1.13/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[495])).
% 1.13/1.35 tff(497,plain,
% 1.13/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[496, 494])).
% 1.13/1.35 tff(498,plain,
% 1.13/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(499,plain,
% 1.13/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[498, 497])).
% 1.13/1.35 tff(500,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[499, 142, 493, 485, 477, 441, 49, 86, 85, 424, 423, 96])).
% 1.13/1.35 tff(501,plain,((~hskp28) | (~c0_1(a135)) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(502,plain,
% 1.13/1.35 (~hskp28),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[501, 468, 49, 86, 85, 467, 466])).
% 1.13/1.35 tff(503,assumption,(~hskp28), introduced(assumption)).
% 1.13/1.35 tff(504,assumption,(hskp15), introduced(assumption)).
% 1.13/1.35 tff(505,plain,
% 1.13/1.35 (((~hskp15) | (~c1_1(a117))) <=> ((~hskp15) | (~c1_1(a117)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(506,plain,
% 1.13/1.35 (((~c1_1(a117)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a117)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(507,axiom,((~c1_1(a117)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.13/1.35 tff(508,plain,
% 1.13/1.35 ((~hskp15) | (~c1_1(a117))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[507, 506])).
% 1.13/1.35 tff(509,plain,
% 1.13/1.35 ((~hskp15) | (~c1_1(a117))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[508, 505])).
% 1.13/1.35 tff(510,plain,
% 1.13/1.35 (~c1_1(a117)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[509, 504])).
% 1.13/1.35 tff(511,plain,
% 1.13/1.35 (((~hskp15) | c0_1(a117)) <=> ((~hskp15) | c0_1(a117))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(512,axiom,((~hskp15) | c0_1(a117)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.13/1.35 tff(513,plain,
% 1.13/1.35 ((~hskp15) | c0_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[512, 511])).
% 1.13/1.35 tff(514,plain,
% 1.13/1.35 ((~hskp15) | c0_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[513, 511])).
% 1.13/1.35 tff(515,plain,
% 1.13/1.35 ((~hskp15) | c0_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[514, 511])).
% 1.13/1.35 tff(516,plain,
% 1.13/1.35 ((~hskp15) | c0_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[515, 511])).
% 1.13/1.35 tff(517,plain,
% 1.13/1.35 ((~hskp15) | c0_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[516, 511])).
% 1.13/1.35 tff(518,plain,
% 1.13/1.35 (c0_1(a117)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[517, 504])).
% 1.13/1.35 tff(519,plain,
% 1.13/1.35 (((~hskp15) | c3_1(a117)) <=> ((~hskp15) | c3_1(a117))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(520,axiom,((~hskp15) | c3_1(a117)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.13/1.35 tff(521,plain,
% 1.13/1.35 ((~hskp15) | c3_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[520, 519])).
% 1.13/1.35 tff(522,plain,
% 1.13/1.35 ((~hskp15) | c3_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[521, 519])).
% 1.13/1.35 tff(523,plain,
% 1.13/1.35 ((~hskp15) | c3_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[522, 519])).
% 1.13/1.35 tff(524,plain,
% 1.13/1.35 ((~hskp15) | c3_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[523, 519])).
% 1.13/1.35 tff(525,plain,
% 1.13/1.35 ((~hskp15) | c3_1(a117)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[524, 519])).
% 1.13/1.35 tff(526,plain,
% 1.13/1.35 (c3_1(a117)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[525, 504])).
% 1.13/1.35 tff(527,plain,
% 1.13/1.35 (^[U: $i] : refl((hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.13/1.35 inference(bind,[status(th)],[])).
% 1.13/1.35 tff(528,plain,
% 1.13/1.35 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.35 inference(quant_intro,[status(thm)],[527])).
% 1.13/1.35 tff(529,plain,
% 1.13/1.35 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(530,plain,
% 1.13/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp31))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp28) <=> ((hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite(((hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp28) <=> (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.13/1.35 inference(bind,[status(th)],[])).
% 1.13/1.35 tff(531,plain,
% 1.13/1.35 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp28) <=> ![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.35 inference(quant_intro,[status(thm)],[530])).
% 1.13/1.35 tff(532,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 1.13/1.35 tff(533,plain,
% 1.13/1.35 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[532, 531])).
% 1.13/1.35 tff(534,plain,
% 1.13/1.35 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[533, 529])).
% 1.13/1.35 tff(535,plain,(
% 1.13/1.35 ![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.35 inference(skolemize,[status(sab)],[534])).
% 1.13/1.35 tff(536,plain,
% 1.13/1.35 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[535, 528])).
% 1.13/1.35 tff(537,assumption,(~c1_1(a117)), introduced(assumption)).
% 1.13/1.35 tff(538,plain,
% 1.13/1.35 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(539,plain,
% 1.13/1.35 ((hskp31 | hskp28 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117))) <=> (hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(540,plain,
% 1.13/1.35 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[539])).
% 1.13/1.35 tff(541,plain,
% 1.13/1.35 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[540, 538])).
% 1.13/1.35 tff(542,plain,
% 1.13/1.35 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(543,plain,
% 1.13/1.35 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[542, 541])).
% 1.13/1.35 tff(544,plain,
% 1.13/1.35 (hskp28 | (~c0_1(a117)) | (~c3_1(a117))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[543, 23, 142, 537, 536])).
% 1.13/1.35 tff(545,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[544, 526, 518, 503])).
% 1.13/1.35 tff(546,plain,((~hskp15) | hskp28 | hskp31 | c1_1(a117)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(547,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[546, 510, 504, 23, 503])).
% 1.13/1.35 tff(548,plain,((~hskp15) | hskp31 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(549,plain,
% 1.13/1.35 (~hskp15),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[548, 502, 23])).
% 1.13/1.35 tff(550,plain,
% 1.13/1.35 ((hskp15 | hskp13 | hskp5) <=> (hskp15 | hskp13 | hskp5)),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(551,plain,
% 1.13/1.35 (((hskp15 | hskp5) | hskp13) <=> (hskp15 | hskp13 | hskp5)),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(552,plain,
% 1.13/1.35 ((hskp5 | hskp15) <=> (hskp15 | hskp5)),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(553,plain,
% 1.13/1.35 (((hskp5 | hskp15) | hskp13) <=> ((hskp15 | hskp5) | hskp13)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[552])).
% 1.13/1.35 tff(554,plain,
% 1.13/1.35 (((hskp5 | hskp15) | hskp13) <=> (hskp15 | hskp13 | hskp5)),
% 1.13/1.35 inference(transitivity,[status(thm)],[553, 551])).
% 1.13/1.35 tff(555,axiom,((hskp5 | hskp15) | hskp13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.13/1.35 tff(556,plain,
% 1.13/1.35 (hskp15 | hskp13 | hskp5),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.13/1.35 tff(557,plain,
% 1.13/1.35 (hskp15 | hskp13 | hskp5),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[556, 550])).
% 1.13/1.35 tff(558,plain,
% 1.13/1.35 (hskp15 | hskp13 | hskp5),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[557, 550])).
% 1.13/1.35 tff(559,plain,
% 1.13/1.35 (hskp15 | hskp13 | hskp5),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[558, 550])).
% 1.13/1.35 tff(560,plain,
% 1.13/1.35 (hskp15 | hskp13 | hskp5),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[559, 550])).
% 1.13/1.35 tff(561,plain,
% 1.13/1.35 (hskp13),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[560, 549, 462])).
% 1.13/1.35 tff(562,plain,
% 1.13/1.35 (((~hskp13) | (~c3_1(a114))) <=> ((~hskp13) | (~c3_1(a114)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(563,plain,
% 1.13/1.35 (((~c3_1(a114)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a114)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(564,axiom,((~c3_1(a114)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.13/1.35 tff(565,plain,
% 1.13/1.35 ((~hskp13) | (~c3_1(a114))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[564, 563])).
% 1.13/1.35 tff(566,plain,
% 1.13/1.35 ((~hskp13) | (~c3_1(a114))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[565, 562])).
% 1.13/1.35 tff(567,plain,
% 1.13/1.35 (~c3_1(a114)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[566, 561])).
% 1.13/1.35 tff(568,plain,
% 1.13/1.35 (((~hskp13) | c2_1(a114)) <=> ((~hskp13) | c2_1(a114))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(569,axiom,((~hskp13) | c2_1(a114)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.13/1.35 tff(570,plain,
% 1.13/1.35 ((~hskp13) | c2_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[569, 568])).
% 1.13/1.35 tff(571,plain,
% 1.13/1.35 ((~hskp13) | c2_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[570, 568])).
% 1.13/1.35 tff(572,plain,
% 1.13/1.35 ((~hskp13) | c2_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[571, 568])).
% 1.13/1.35 tff(573,plain,
% 1.13/1.35 ((~hskp13) | c2_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[572, 568])).
% 1.13/1.35 tff(574,plain,
% 1.13/1.35 ((~hskp13) | c2_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[573, 568])).
% 1.13/1.35 tff(575,plain,
% 1.13/1.35 (c2_1(a114)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[574, 561])).
% 1.13/1.35 tff(576,plain,
% 1.13/1.35 (((~hskp13) | c1_1(a114)) <=> ((~hskp13) | c1_1(a114))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(577,axiom,((~hskp13) | c1_1(a114)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.13/1.35 tff(578,plain,
% 1.13/1.35 ((~hskp13) | c1_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.13/1.35 tff(579,plain,
% 1.13/1.35 ((~hskp13) | c1_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[578, 576])).
% 1.13/1.35 tff(580,plain,
% 1.13/1.35 ((~hskp13) | c1_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[579, 576])).
% 1.13/1.35 tff(581,plain,
% 1.13/1.35 ((~hskp13) | c1_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[580, 576])).
% 1.13/1.35 tff(582,plain,
% 1.13/1.35 ((~hskp13) | c1_1(a114)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[581, 576])).
% 1.13/1.35 tff(583,plain,
% 1.13/1.35 (c1_1(a114)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[582, 561])).
% 1.13/1.35 tff(584,plain,
% 1.13/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(585,plain,
% 1.13/1.35 (((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114))) <=> (c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(586,plain,
% 1.13/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[585])).
% 1.13/1.35 tff(587,plain,
% 1.13/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[586, 584])).
% 1.13/1.35 tff(588,plain,
% 1.13/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(589,plain,
% 1.13/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[588, 587])).
% 1.13/1.35 tff(590,plain,
% 1.13/1.35 (c0_1(a114)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[589, 142, 467, 583, 575, 468, 466, 567, 181])).
% 1.13/1.35 tff(591,plain,
% 1.13/1.35 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.13/1.35 inference(bind,[status(th)],[])).
% 1.13/1.35 tff(592,plain,
% 1.13/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.13/1.35 inference(quant_intro,[status(thm)],[591])).
% 1.13/1.35 tff(593,plain,
% 1.13/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(594,plain,
% 1.13/1.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp7) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.13/1.35 inference(bind,[status(th)],[])).
% 1.13/1.35 tff(595,plain,
% 1.13/1.35 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.13/1.35 inference(quant_intro,[status(thm)],[594])).
% 1.13/1.35 tff(596,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.13/1.35 tff(597,plain,
% 1.13/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[596, 595])).
% 1.13/1.35 tff(598,plain,
% 1.13/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[597, 593])).
% 1.13/1.35 tff(599,plain,(
% 1.13/1.35 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.13/1.35 inference(skolemize,[status(sab)],[598])).
% 1.13/1.35 tff(600,plain,
% 1.13/1.35 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[599, 592])).
% 1.13/1.35 tff(601,plain,
% 1.13/1.35 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(602,plain,
% 1.13/1.35 ((hskp7 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(603,plain,
% 1.13/1.35 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[602])).
% 1.13/1.35 tff(604,plain,
% 1.13/1.35 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163)))),
% 1.13/1.35 inference(transitivity,[status(thm)],[603, 601])).
% 1.13/1.35 tff(605,plain,
% 1.13/1.35 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(606,plain,
% 1.13/1.35 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.13/1.35 tff(607,plain,
% 1.13/1.35 (hskp7),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[606, 142, 583, 575, 49, 86, 600, 464, 590])).
% 1.13/1.35 tff(608,plain,
% 1.13/1.35 (((~hskp7) | (~c0_1(a108))) <=> ((~hskp7) | (~c0_1(a108)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(609,plain,
% 1.13/1.35 (((~c0_1(a108)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a108)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(610,axiom,((~c0_1(a108)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.13/1.35 tff(611,plain,
% 1.13/1.35 ((~hskp7) | (~c0_1(a108))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[610, 609])).
% 1.13/1.35 tff(612,plain,
% 1.13/1.35 ((~hskp7) | (~c0_1(a108))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[611, 608])).
% 1.13/1.35 tff(613,plain,
% 1.13/1.35 (~c0_1(a108)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[612, 607])).
% 1.13/1.35 tff(614,assumption,(~hskp15), introduced(assumption)).
% 1.13/1.35 tff(615,plain,
% 1.13/1.35 (~hskp28),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[501, 441, 49, 86, 85, 424, 423])).
% 1.13/1.35 tff(616,assumption,(hskp7), introduced(assumption)).
% 1.13/1.35 tff(617,plain,
% 1.13/1.35 (((~hskp7) | c3_1(a108)) <=> ((~hskp7) | c3_1(a108))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(618,axiom,((~hskp7) | c3_1(a108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.13/1.35 tff(619,plain,
% 1.13/1.35 ((~hskp7) | c3_1(a108)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[618, 617])).
% 1.13/1.35 tff(620,plain,
% 1.13/1.35 ((~hskp7) | c3_1(a108)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[619, 617])).
% 1.13/1.35 tff(621,plain,
% 1.13/1.35 ((~hskp7) | c3_1(a108)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[620, 617])).
% 1.13/1.35 tff(622,plain,
% 1.13/1.35 ((~hskp7) | c3_1(a108)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[621, 617])).
% 1.13/1.35 tff(623,plain,
% 1.13/1.35 ((~hskp7) | c3_1(a108)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[622, 617])).
% 1.13/1.35 tff(624,plain,
% 1.13/1.35 (c3_1(a108)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[623, 616])).
% 1.13/1.35 tff(625,plain,
% 1.13/1.35 (^[U: $i] : refl((hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 1.13/1.35 inference(bind,[status(th)],[])).
% 1.13/1.35 tff(626,plain,
% 1.13/1.35 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.13/1.35 inference(quant_intro,[status(thm)],[625])).
% 1.13/1.35 tff(627,plain,
% 1.13/1.35 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(628,plain,
% 1.13/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp28) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp28) <=> (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 1.13/1.35 inference(bind,[status(th)],[])).
% 1.13/1.35 tff(629,plain,
% 1.13/1.35 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp28) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.13/1.35 inference(quant_intro,[status(thm)],[628])).
% 1.13/1.35 tff(630,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.13/1.35 tff(631,plain,
% 1.13/1.35 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[630, 629])).
% 1.13/1.35 tff(632,plain,
% 1.13/1.35 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[631, 627])).
% 1.13/1.36 tff(633,plain,(
% 1.13/1.36 ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.13/1.36 inference(skolemize,[status(sab)],[632])).
% 1.13/1.36 tff(634,plain,
% 1.13/1.36 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[633, 626])).
% 1.13/1.36 tff(635,assumption,(~c0_1(a108)), introduced(assumption)).
% 1.13/1.36 tff(636,plain,
% 1.13/1.36 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(637,plain,
% 1.13/1.36 ((hskp28 | hskp15 | (~ndr1_0) | c0_1(a108) | c2_1(a108) | (~c3_1(a108))) <=> (hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(638,plain,
% 1.13/1.36 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a108) | c2_1(a108) | (~c3_1(a108)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[637])).
% 1.13/1.36 tff(639,plain,
% 1.13/1.36 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a108) | c2_1(a108) | (~c3_1(a108)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[638, 636])).
% 1.13/1.36 tff(640,plain,
% 1.13/1.36 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a108) | c2_1(a108) | (~c3_1(a108)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(641,plain,
% 1.13/1.36 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[640, 639])).
% 1.13/1.36 tff(642,plain,
% 1.13/1.36 (hskp28 | hskp15 | c2_1(a108) | (~c3_1(a108))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[641, 142, 635, 634])).
% 1.13/1.36 tff(643,plain,
% 1.13/1.36 (c2_1(a108)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[642, 624, 615, 614])).
% 1.13/1.36 tff(644,plain,
% 1.13/1.36 (((~hskp7) | c1_1(a108)) <=> ((~hskp7) | c1_1(a108))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(645,axiom,((~hskp7) | c1_1(a108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.13/1.36 tff(646,plain,
% 1.13/1.36 ((~hskp7) | c1_1(a108)),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.13/1.36 tff(647,plain,
% 1.13/1.36 ((~hskp7) | c1_1(a108)),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[646, 644])).
% 1.13/1.36 tff(648,plain,
% 1.13/1.36 ((~hskp7) | c1_1(a108)),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[647, 644])).
% 1.13/1.36 tff(649,plain,
% 1.13/1.36 ((~hskp7) | c1_1(a108)),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[648, 644])).
% 1.13/1.36 tff(650,plain,
% 1.13/1.36 ((~hskp7) | c1_1(a108)),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[649, 644])).
% 1.13/1.36 tff(651,plain,
% 1.13/1.36 (c1_1(a108)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[650, 616])).
% 1.13/1.36 tff(652,plain,
% 1.13/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(653,plain,
% 1.13/1.36 (((~ndr1_0) | (~c1_1(a108)) | (~c3_1(a108)) | (~c2_1(a108)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(654,plain,
% 1.13/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a108)) | (~c3_1(a108)) | (~c2_1(a108)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[653])).
% 1.13/1.36 tff(655,plain,
% 1.13/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a108)) | (~c3_1(a108)) | (~c2_1(a108)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[654, 652])).
% 1.13/1.36 tff(656,plain,
% 1.13/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a108)) | (~c3_1(a108)) | (~c2_1(a108)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(657,plain,
% 1.13/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[656, 655])).
% 1.13/1.36 tff(658,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[657, 142, 441, 651, 624, 49, 86, 85, 424, 423, 96, 643])).
% 1.13/1.36 tff(659,plain,((~hskp7) | (~c0_1(a135)) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | hskp15 | c0_1(a108)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(660,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[659, 613, 607, 49, 86, 85, 468, 466, 467, 549])).
% 1.13/1.36 tff(661,plain,(hskp5 | c1_1(a163) | c2_1(a163) | c3_1(a163) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(662,plain,
% 1.13/1.36 (hskp31),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[661, 462, 49, 86, 85])).
% 1.13/1.36 tff(663,plain,
% 1.13/1.36 (c3_1(a141)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[57, 662])).
% 1.13/1.36 tff(664,plain,
% 1.13/1.36 (c1_1(a141)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[65, 662])).
% 1.13/1.36 tff(665,plain,
% 1.13/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(666,plain,
% 1.13/1.36 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(667,plain,
% 1.13/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[666])).
% 1.13/1.36 tff(668,plain,
% 1.13/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[667, 665])).
% 1.13/1.36 tff(669,plain,
% 1.13/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(670,plain,
% 1.13/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[669, 668])).
% 1.13/1.36 tff(671,plain,
% 1.13/1.36 (~c2_1(a141)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[670, 142, 664, 663, 49, 86, 85, 96, 463])).
% 1.13/1.36 tff(672,plain,
% 1.13/1.36 (^[U: $i] : refl((hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.13/1.36 inference(bind,[status(th)],[])).
% 1.13/1.36 tff(673,plain,
% 1.13/1.36 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.36 inference(quant_intro,[status(thm)],[672])).
% 1.13/1.36 tff(674,plain,
% 1.13/1.36 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(675,plain,
% 1.13/1.36 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp16) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp16) <=> (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.13/1.36 inference(bind,[status(th)],[])).
% 1.13/1.36 tff(676,plain,
% 1.13/1.36 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp16) <=> ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.36 inference(quant_intro,[status(thm)],[675])).
% 1.19/1.36 tff(677,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.19/1.36 tff(678,plain,
% 1.19/1.36 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[677, 676])).
% 1.19/1.36 tff(679,plain,
% 1.19/1.36 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[678, 674])).
% 1.19/1.36 tff(680,plain,(
% 1.19/1.36 ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.36 inference(skolemize,[status(sab)],[679])).
% 1.19/1.36 tff(681,plain,
% 1.19/1.36 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[680, 673])).
% 1.19/1.36 tff(682,plain,
% 1.19/1.36 (c0_1(a141)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[73, 662])).
% 1.19/1.36 tff(683,assumption,(~hskp6), introduced(assumption)).
% 1.19/1.36 tff(684,plain,
% 1.19/1.36 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(685,plain,
% 1.19/1.36 ((hskp16 | hskp6 | (~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141))) <=> (hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(686,plain,
% 1.19/1.36 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141)))),
% 1.19/1.36 inference(monotonicity,[status(thm)],[685])).
% 1.19/1.36 tff(687,plain,
% 1.19/1.36 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141))),
% 1.19/1.36 inference(transitivity,[status(thm)],[686, 684])).
% 1.19/1.36 tff(688,plain,
% 1.19/1.36 ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)))),
% 1.19/1.36 inference(quant_inst,[status(thm)],[])).
% 1.19/1.36 tff(689,plain,
% 1.19/1.36 ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[688, 687])).
% 1.19/1.36 tff(690,plain,
% 1.19/1.36 (hskp16 | c2_1(a141)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[689, 142, 683, 682, 663, 681])).
% 1.19/1.36 tff(691,plain,
% 1.19/1.36 (hskp16),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[690, 671])).
% 1.19/1.36 tff(692,plain,
% 1.19/1.36 (((~hskp16) | c1_1(a126)) <=> ((~hskp16) | c1_1(a126))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(693,axiom,((~hskp16) | c1_1(a126)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.19/1.36 tff(694,plain,
% 1.19/1.36 ((~hskp16) | c1_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[693, 692])).
% 1.19/1.36 tff(695,plain,
% 1.19/1.36 ((~hskp16) | c1_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[694, 692])).
% 1.19/1.36 tff(696,plain,
% 1.19/1.36 ((~hskp16) | c1_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[695, 692])).
% 1.19/1.36 tff(697,plain,
% 1.19/1.36 ((~hskp16) | c1_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[696, 692])).
% 1.19/1.36 tff(698,plain,
% 1.19/1.36 ((~hskp16) | c1_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[697, 692])).
% 1.19/1.36 tff(699,plain,
% 1.19/1.36 (c1_1(a126)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[698, 691])).
% 1.19/1.36 tff(700,plain,
% 1.19/1.36 (((~hskp16) | c3_1(a126)) <=> ((~hskp16) | c3_1(a126))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(701,axiom,((~hskp16) | c3_1(a126)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.19/1.36 tff(702,plain,
% 1.19/1.36 ((~hskp16) | c3_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[701, 700])).
% 1.19/1.36 tff(703,plain,
% 1.19/1.36 ((~hskp16) | c3_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[702, 700])).
% 1.19/1.36 tff(704,plain,
% 1.19/1.36 ((~hskp16) | c3_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[703, 700])).
% 1.19/1.36 tff(705,plain,
% 1.19/1.36 ((~hskp16) | c3_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[704, 700])).
% 1.19/1.36 tff(706,plain,
% 1.19/1.36 ((~hskp16) | c3_1(a126)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[705, 700])).
% 1.19/1.36 tff(707,plain,
% 1.19/1.36 (c3_1(a126)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[706, 691])).
% 1.19/1.36 tff(708,plain,
% 1.19/1.36 (((~hskp16) | (~c2_1(a126))) <=> ((~hskp16) | (~c2_1(a126)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(709,plain,
% 1.19/1.36 (((~c2_1(a126)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a126)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(710,axiom,((~c2_1(a126)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.19/1.36 tff(711,plain,
% 1.19/1.36 ((~hskp16) | (~c2_1(a126))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.19/1.36 tff(712,plain,
% 1.19/1.36 ((~hskp16) | (~c2_1(a126))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[711, 708])).
% 1.19/1.36 tff(713,plain,
% 1.19/1.36 (~c2_1(a126)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[712, 691])).
% 1.19/1.36 tff(714,plain,
% 1.19/1.36 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.19/1.36 inference(bind,[status(th)],[])).
% 1.19/1.36 tff(715,plain,
% 1.19/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.36 inference(quant_intro,[status(thm)],[714])).
% 1.19/1.36 tff(716,plain,
% 1.19/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(717,plain,
% 1.19/1.36 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.19/1.36 inference(bind,[status(th)],[])).
% 1.19/1.36 tff(718,plain,
% 1.19/1.36 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.36 inference(quant_intro,[status(thm)],[717])).
% 1.19/1.36 tff(719,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.19/1.36 tff(720,plain,
% 1.19/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[719, 718])).
% 1.19/1.36 tff(721,plain,
% 1.19/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[720, 716])).
% 1.19/1.36 tff(722,plain,(
% 1.19/1.36 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.36 inference(skolemize,[status(sab)],[721])).
% 1.19/1.36 tff(723,plain,
% 1.19/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[722, 715])).
% 1.19/1.36 tff(724,assumption,(~c2_1(a126)), introduced(assumption)).
% 1.19/1.36 tff(725,assumption,(~c2_1(a141)), introduced(assumption)).
% 1.19/1.36 tff(726,plain,
% 1.19/1.36 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.19/1.36 inference(bind,[status(th)],[])).
% 1.19/1.36 tff(727,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(quant_intro,[status(thm)],[726])).
% 1.19/1.36 tff(728,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(729,plain,
% 1.19/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.19/1.36 inference(bind,[status(th)],[])).
% 1.19/1.36 tff(730,plain,
% 1.19/1.36 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(quant_intro,[status(thm)],[729])).
% 1.19/1.36 tff(731,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.19/1.36 tff(732,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[731, 730])).
% 1.19/1.36 tff(733,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[732, 728])).
% 1.19/1.36 tff(734,plain,(
% 1.19/1.36 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(skolemize,[status(sab)],[733])).
% 1.19/1.36 tff(735,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[734, 727])).
% 1.19/1.36 tff(736,assumption,(c1_1(a141)), introduced(assumption)).
% 1.19/1.36 tff(737,assumption,(c0_1(a141)), introduced(assumption)).
% 1.19/1.36 tff(738,plain,
% 1.19/1.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(739,plain,
% 1.19/1.36 ((hskp17 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(740,plain,
% 1.19/1.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163))))),
% 1.19/1.36 inference(monotonicity,[status(thm)],[739])).
% 1.19/1.36 tff(741,plain,
% 1.19/1.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 1.19/1.36 inference(transitivity,[status(thm)],[740, 738])).
% 1.19/1.36 tff(742,plain,
% 1.19/1.36 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 1.19/1.36 inference(quant_inst,[status(thm)],[])).
% 1.19/1.36 tff(743,plain,
% 1.19/1.36 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[742, 741])).
% 1.19/1.36 tff(744,plain,
% 1.19/1.36 (hskp17 | (~c0_1(a163))),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[743, 142, 737, 736, 49, 86, 735, 725])).
% 1.19/1.36 tff(745,plain,
% 1.19/1.36 (hskp17),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[744, 98])).
% 1.19/1.36 tff(746,plain,
% 1.19/1.36 (((~hskp17) | (~c1_1(a132))) <=> ((~hskp17) | (~c1_1(a132)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(747,plain,
% 1.19/1.36 (((~c1_1(a132)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a132)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(748,axiom,((~c1_1(a132)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.19/1.36 tff(749,plain,
% 1.19/1.36 ((~hskp17) | (~c1_1(a132))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[748, 747])).
% 1.19/1.36 tff(750,plain,
% 1.19/1.36 ((~hskp17) | (~c1_1(a132))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[749, 746])).
% 1.19/1.36 tff(751,plain,
% 1.19/1.36 (~c1_1(a132)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[750, 745])).
% 1.19/1.36 tff(752,plain,
% 1.19/1.36 (((~hskp17) | (~c0_1(a132))) <=> ((~hskp17) | (~c0_1(a132)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(753,plain,
% 1.19/1.37 (((~c0_1(a132)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a132)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(754,axiom,((~c0_1(a132)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.19/1.37 tff(755,plain,
% 1.19/1.37 ((~hskp17) | (~c0_1(a132))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[754, 753])).
% 1.19/1.37 tff(756,plain,
% 1.19/1.37 ((~hskp17) | (~c0_1(a132))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[755, 752])).
% 1.19/1.37 tff(757,plain,
% 1.19/1.37 (~c0_1(a132)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[756, 745])).
% 1.19/1.37 tff(758,assumption,(c3_1(a126)), introduced(assumption)).
% 1.19/1.37 tff(759,plain,
% 1.19/1.37 (((~hskp17) | c3_1(a132)) <=> ((~hskp17) | c3_1(a132))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(760,axiom,((~hskp17) | c3_1(a132)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.19/1.37 tff(761,plain,
% 1.19/1.37 ((~hskp17) | c3_1(a132)),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.19/1.37 tff(762,plain,
% 1.19/1.37 ((~hskp17) | c3_1(a132)),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[761, 759])).
% 1.19/1.37 tff(763,plain,
% 1.19/1.37 ((~hskp17) | c3_1(a132)),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[762, 759])).
% 1.19/1.37 tff(764,plain,
% 1.19/1.37 ((~hskp17) | c3_1(a132)),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[763, 759])).
% 1.19/1.37 tff(765,plain,
% 1.19/1.37 ((~hskp17) | c3_1(a132)),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[764, 759])).
% 1.19/1.37 tff(766,plain,
% 1.19/1.37 (c3_1(a132)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[765, 745])).
% 1.19/1.37 tff(767,assumption,(c3_1(a141)), introduced(assumption)).
% 1.19/1.37 tff(768,plain,
% 1.19/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(769,plain,
% 1.19/1.37 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(770,plain,
% 1.19/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[769])).
% 1.19/1.37 tff(771,plain,
% 1.19/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[770, 768])).
% 1.19/1.37 tff(772,plain,
% 1.19/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(773,plain,
% 1.19/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.19/1.37 tff(774,plain,
% 1.19/1.37 (c0_1(a126)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[773, 142, 737, 736, 767, 766, 758, 757, 751, 724, 723])).
% 1.19/1.37 tff(775,plain,
% 1.19/1.37 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.19/1.37 inference(bind,[status(th)],[])).
% 1.19/1.37 tff(776,plain,
% 1.19/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.37 inference(quant_intro,[status(thm)],[775])).
% 1.19/1.37 tff(777,plain,
% 1.19/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(778,plain,
% 1.19/1.37 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.19/1.37 inference(bind,[status(th)],[])).
% 1.19/1.37 tff(779,plain,
% 1.19/1.37 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.37 inference(quant_intro,[status(thm)],[778])).
% 1.19/1.37 tff(780,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.19/1.37 tff(781,plain,
% 1.19/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[780, 779])).
% 1.19/1.37 tff(782,plain,
% 1.19/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[781, 777])).
% 1.19/1.37 tff(783,plain,(
% 1.19/1.37 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.37 inference(skolemize,[status(sab)],[782])).
% 1.19/1.37 tff(784,plain,
% 1.19/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[783, 776])).
% 1.19/1.37 tff(785,assumption,(c1_1(a126)), introduced(assumption)).
% 1.19/1.37 tff(786,plain,
% 1.19/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(787,plain,
% 1.19/1.37 (((~ndr1_0) | c2_1(a126) | (~c1_1(a126)) | (~c0_1(a126)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(788,plain,
% 1.19/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a126) | (~c1_1(a126)) | (~c0_1(a126)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[787])).
% 1.19/1.37 tff(789,plain,
% 1.19/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a126) | (~c1_1(a126)) | (~c0_1(a126)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[788, 786])).
% 1.19/1.37 tff(790,plain,
% 1.19/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a126) | (~c1_1(a126)) | (~c0_1(a126)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(791,plain,
% 1.19/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.19/1.37 tff(792,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[791, 142, 766, 785, 49, 86, 757, 751, 724, 784, 98, 774])).
% 1.19/1.37 tff(793,plain,((~c0_1(a163)) | (~c1_1(a126)) | c1_1(a163) | c2_1(a163) | c2_1(a126) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141)) | (~c3_1(a126)) | c2_1(a141)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(794,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[793, 713, 707, 49, 86, 463, 682, 664, 663, 671, 699])).
% 1.19/1.37 tff(795,plain,(hskp5 | c1_1(a163) | c2_1(a163) | hskp6 | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(796,plain,
% 1.19/1.37 (hskp5),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[795, 461, 86, 49, 85])).
% 1.19/1.37 tff(797,assumption,(hskp5), introduced(assumption)).
% 1.19/1.37 tff(798,plain,
% 1.19/1.37 (c0_1(a106)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[304, 797])).
% 1.19/1.37 tff(799,plain,
% 1.19/1.37 (c1_1(a106)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[233, 797])).
% 1.19/1.37 tff(800,assumption,(c0_1(a106)), introduced(assumption)).
% 1.19/1.37 tff(801,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(802,plain,
% 1.19/1.37 ((hskp17 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(803,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[802])).
% 1.19/1.37 tff(804,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[803, 801])).
% 1.19/1.37 tff(805,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(806,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[805, 804])).
% 1.19/1.37 tff(807,plain,
% 1.19/1.37 (hskp17 | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163))),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[806, 142, 49, 86, 97, 735])).
% 1.19/1.37 tff(808,plain,
% 1.19/1.37 (hskp17),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[807, 98, 800, 215])).
% 1.19/1.37 tff(809,plain,
% 1.19/1.37 (~c1_1(a132)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[750, 808])).
% 1.19/1.37 tff(810,plain,
% 1.19/1.37 (~c0_1(a132)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[756, 808])).
% 1.19/1.37 tff(811,plain,
% 1.19/1.37 (c3_1(a132)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[765, 808])).
% 1.19/1.37 tff(812,plain,
% 1.19/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(813,plain,
% 1.19/1.37 (((~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(814,plain,
% 1.19/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[813])).
% 1.19/1.37 tff(815,plain,
% 1.19/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[814, 812])).
% 1.19/1.37 tff(816,plain,
% 1.19/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(817,plain,
% 1.19/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.19/1.37 tff(818,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[817, 142, 811, 800, 215, 49, 86, 810, 809, 97, 784, 98])).
% 1.19/1.37 tff(819,plain,((~c0_1(a163)) | (~c0_1(a106)) | (~c1_1(a106)) | c1_1(a163) | c2_1(a163) | c2_1(a106)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(820,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[819, 799, 798, 98, 49, 86, 97])).
% 1.19/1.37 tff(821,plain,((~hskp5) | (~c0_1(a163)) | c1_1(a163) | c2_1(a163) | c2_1(a106)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(822,plain,
% 1.19/1.37 (~c0_1(a163)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[821, 796, 49, 86, 97])).
% 1.19/1.37 tff(823,plain,
% 1.19/1.37 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.19/1.37 inference(bind,[status(th)],[])).
% 1.19/1.37 tff(824,plain,
% 1.19/1.37 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.19/1.37 inference(quant_intro,[status(thm)],[823])).
% 1.19/1.37 tff(825,plain,
% 1.19/1.37 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(826,plain,
% 1.19/1.37 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.19/1.37 inference(bind,[status(th)],[])).
% 1.19/1.37 tff(827,plain,
% 1.19/1.37 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.19/1.37 inference(quant_intro,[status(thm)],[826])).
% 1.19/1.37 tff(828,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 1.19/1.37 tff(829,plain,
% 1.19/1.37 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[828, 827])).
% 1.19/1.37 tff(830,plain,
% 1.19/1.37 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[829, 825])).
% 1.19/1.37 tff(831,plain,(
% 1.19/1.37 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.19/1.37 inference(skolemize,[status(sab)],[830])).
% 1.19/1.37 tff(832,plain,
% 1.19/1.37 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[831, 824])).
% 1.19/1.37 tff(833,plain,
% 1.19/1.37 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(834,plain,
% 1.19/1.37 ((hskp7 | hskp6 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(835,plain,
% 1.19/1.37 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[834])).
% 1.19/1.37 tff(836,plain,
% 1.19/1.37 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.19/1.37 inference(transitivity,[status(thm)],[835, 833])).
% 1.19/1.37 tff(837,plain,
% 1.19/1.37 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(838,plain,
% 1.19/1.37 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[837, 836])).
% 1.19/1.37 tff(839,plain,
% 1.19/1.37 (hskp7 | hskp6 | c3_1(a163) | c0_1(a163)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[838, 142, 49, 832])).
% 1.19/1.37 tff(840,plain,
% 1.19/1.37 (hskp7),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[839, 822, 85, 461])).
% 1.19/1.37 tff(841,plain,
% 1.19/1.37 (c3_1(a108)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[623, 840])).
% 1.19/1.37 tff(842,plain,
% 1.19/1.37 (c1_1(a108)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[650, 840])).
% 1.19/1.37 tff(843,plain,
% 1.19/1.37 (c0_1(a135)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[420, 391])).
% 1.19/1.37 tff(844,plain,
% 1.19/1.37 (~c2_1(a108)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[657, 142, 843, 842, 841, 49, 86, 85, 403, 397, 96])).
% 1.19/1.37 tff(845,plain,
% 1.19/1.37 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.19/1.37 inference(bind,[status(th)],[])).
% 1.19/1.37 tff(846,plain,
% 1.19/1.37 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.19/1.37 inference(quant_intro,[status(thm)],[845])).
% 1.19/1.37 tff(847,plain,
% 1.19/1.37 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(848,plain,
% 1.19/1.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.19/1.37 inference(bind,[status(th)],[])).
% 1.19/1.37 tff(849,plain,
% 1.19/1.37 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.19/1.37 inference(quant_intro,[status(thm)],[848])).
% 1.19/1.37 tff(850,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.19/1.37 tff(851,plain,
% 1.19/1.37 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[850, 849])).
% 1.19/1.37 tff(852,plain,
% 1.19/1.37 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[851, 847])).
% 1.19/1.37 tff(853,plain,(
% 1.19/1.37 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.19/1.37 inference(skolemize,[status(sab)],[852])).
% 1.19/1.37 tff(854,plain,
% 1.19/1.37 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[853, 846])).
% 1.19/1.37 tff(855,plain,
% 1.19/1.37 (~c0_1(a108)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[612, 840])).
% 1.19/1.37 tff(856,plain,
% 1.19/1.37 (hskp15),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[659, 855, 49, 86, 85, 403, 397, 843, 840])).
% 1.19/1.37 tff(857,plain,
% 1.19/1.37 (~c1_1(a117)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[509, 856])).
% 1.19/1.37 tff(858,plain,
% 1.19/1.37 (c3_1(a117)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[525, 856])).
% 1.19/1.37 tff(859,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(860,plain,
% 1.19/1.38 ((hskp6 | (~ndr1_0) | c1_1(a117) | c2_1(a117) | (~c3_1(a117)) | c2_1(a108) | c0_1(a108) | (~c1_1(a108))) <=> (hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(861,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a117) | c2_1(a117) | (~c3_1(a117)) | c2_1(a108) | c0_1(a108) | (~c1_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[860])).
% 1.19/1.38 tff(862,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a117) | c2_1(a117) | (~c3_1(a117)) | c2_1(a108) | c0_1(a108) | (~c1_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[861, 859])).
% 1.19/1.38 tff(863,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a117) | c2_1(a117) | (~c3_1(a117)) | c2_1(a108) | c0_1(a108) | (~c1_1(a108)))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(864,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[863, 862])).
% 1.19/1.38 tff(865,plain,
% 1.19/1.38 (c2_1(a117)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[864, 142, 461, 858, 842, 857, 855, 854, 844])).
% 1.19/1.38 tff(866,plain,
% 1.19/1.38 (~hskp28),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[501, 403, 49, 86, 85, 843, 397])).
% 1.19/1.38 tff(867,plain,
% 1.19/1.38 (hskp31),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[548, 856, 866])).
% 1.19/1.38 tff(868,plain,
% 1.19/1.38 (c3_1(a141)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[57, 867])).
% 1.19/1.38 tff(869,plain,
% 1.19/1.38 (c1_1(a141)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[65, 867])).
% 1.19/1.38 tff(870,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(871,plain,
% 1.19/1.38 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(872,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[871])).
% 1.19/1.38 tff(873,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[872, 870])).
% 1.19/1.38 tff(874,plain,
% 1.19/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(875,plain,
% 1.19/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[874, 873])).
% 1.19/1.38 tff(876,plain,
% 1.19/1.38 (~c2_1(a141)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[875, 142, 869, 868, 843, 49, 86, 85, 403, 397, 96])).
% 1.19/1.38 tff(877,plain,
% 1.19/1.38 (c0_1(a117)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[517, 856])).
% 1.19/1.38 tff(878,plain,
% 1.19/1.38 (c0_1(a141)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[73, 867])).
% 1.19/1.38 tff(879,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(880,plain,
% 1.19/1.38 (((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a117) | (~c0_1(a117)) | (~c2_1(a117))) <=> (c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(881,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a117) | (~c0_1(a117)) | (~c2_1(a117)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[880])).
% 1.19/1.38 tff(882,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a117) | (~c0_1(a117)) | (~c2_1(a117)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[881, 879])).
% 1.19/1.38 tff(883,plain,
% 1.19/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a117) | (~c0_1(a117)) | (~c2_1(a117)))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(884,plain,
% 1.19/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.19/1.38 tff(885,plain,
% 1.19/1.38 ($false),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[884, 142, 878, 869, 868, 877, 857, 290, 876, 865])).
% 1.19/1.38 tff(886,plain,(c2_1(a106) | c1_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.38 tff(887,plain,
% 1.19/1.38 (c2_1(a106)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[886, 85, 86, 49])).
% 1.19/1.38 tff(888,plain,
% 1.19/1.38 (((~hskp5) | (~c2_1(a106))) <=> ((~hskp5) | (~c2_1(a106)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(889,plain,
% 1.19/1.38 (((~c2_1(a106)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a106)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(890,axiom,((~c2_1(a106)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.19/1.38 tff(891,plain,
% 1.19/1.38 ((~hskp5) | (~c2_1(a106))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[890, 889])).
% 1.19/1.38 tff(892,plain,
% 1.19/1.38 ((~hskp5) | (~c2_1(a106))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[891, 888])).
% 1.19/1.38 tff(893,plain,
% 1.19/1.38 (~hskp5),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[892, 887])).
% 1.19/1.38 tff(894,plain,
% 1.19/1.38 (c0_1(a163)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[213, 893, 85])).
% 1.19/1.38 tff(895,plain,
% 1.19/1.38 (hskp19),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[195, 894, 85, 86])).
% 1.19/1.38 tff(896,plain,
% 1.19/1.38 (hskp6),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[795, 893, 86, 49, 85])).
% 1.19/1.38 tff(897,plain,
% 1.19/1.38 (~c0_1(a107)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[410, 896])).
% 1.19/1.38 tff(898,plain,
% 1.19/1.38 ($false),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[458, 897, 896, 895, 49, 86, 85])).
% 1.19/1.38 tff(899,plain,(c3_1(a163) | c1_1(a163) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.38 tff(900,plain,
% 1.19/1.38 (c3_1(a163)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[899, 86, 49])).
% 1.19/1.38 tff(901,plain,
% 1.19/1.38 (((~hskp24) | (~c3_1(a163))) <=> ((~hskp24) | (~c3_1(a163)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(902,plain,
% 1.19/1.38 (((~c3_1(a163)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a163)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(903,axiom,((~c3_1(a163)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.19/1.38 tff(904,plain,
% 1.19/1.38 ((~hskp24) | (~c3_1(a163))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[903, 902])).
% 1.19/1.38 tff(905,plain,
% 1.19/1.38 ((~hskp24) | (~c3_1(a163))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[904, 901])).
% 1.19/1.38 tff(906,plain,
% 1.19/1.38 (~hskp24),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[905, 900])).
% 1.19/1.38 tff(907,plain,
% 1.19/1.38 (hskp30),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[140, 23, 906])).
% 1.19/1.38 tff(908,plain,
% 1.19/1.38 (((~hskp30) | c3_1(a131)) <=> ((~hskp30) | c3_1(a131))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(909,axiom,((~hskp30) | c3_1(a131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.19/1.38 tff(910,plain,
% 1.19/1.38 ((~hskp30) | c3_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[909, 908])).
% 1.19/1.38 tff(911,plain,
% 1.19/1.38 ((~hskp30) | c3_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[910, 908])).
% 1.19/1.38 tff(912,plain,
% 1.19/1.38 ((~hskp30) | c3_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[911, 908])).
% 1.19/1.38 tff(913,plain,
% 1.19/1.38 ((~hskp30) | c3_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[912, 908])).
% 1.19/1.38 tff(914,plain,
% 1.19/1.38 ((~hskp30) | c3_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[913, 908])).
% 1.19/1.38 tff(915,plain,
% 1.19/1.38 (c3_1(a131)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[914, 907])).
% 1.19/1.38 tff(916,plain,
% 1.19/1.38 (((~hskp30) | c2_1(a131)) <=> ((~hskp30) | c2_1(a131))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(917,axiom,((~hskp30) | c2_1(a131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.19/1.38 tff(918,plain,
% 1.19/1.38 ((~hskp30) | c2_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[917, 916])).
% 1.19/1.38 tff(919,plain,
% 1.19/1.38 ((~hskp30) | c2_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[918, 916])).
% 1.19/1.38 tff(920,plain,
% 1.19/1.38 ((~hskp30) | c2_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[919, 916])).
% 1.19/1.38 tff(921,plain,
% 1.19/1.38 ((~hskp30) | c2_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[920, 916])).
% 1.19/1.38 tff(922,plain,
% 1.19/1.38 ((~hskp30) | c2_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[921, 916])).
% 1.19/1.38 tff(923,plain,
% 1.19/1.38 (c2_1(a131)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[922, 907])).
% 1.19/1.38 tff(924,plain,
% 1.19/1.38 (((~hskp30) | c0_1(a131)) <=> ((~hskp30) | c0_1(a131))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(925,axiom,((~hskp30) | c0_1(a131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.19/1.38 tff(926,plain,
% 1.19/1.38 ((~hskp30) | c0_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[925, 924])).
% 1.19/1.38 tff(927,plain,
% 1.19/1.38 ((~hskp30) | c0_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[926, 924])).
% 1.19/1.38 tff(928,plain,
% 1.19/1.38 ((~hskp30) | c0_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[927, 924])).
% 1.19/1.38 tff(929,plain,
% 1.19/1.38 ((~hskp30) | c0_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[928, 924])).
% 1.19/1.38 tff(930,plain,
% 1.19/1.38 ((~hskp30) | c0_1(a131)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[929, 924])).
% 1.19/1.38 tff(931,plain,
% 1.19/1.38 (c0_1(a131)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[930, 907])).
% 1.19/1.38 tff(932,plain,
% 1.19/1.38 (^[U: $i] : refl((hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(933,plain,
% 1.19/1.38 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[932])).
% 1.19/1.38 tff(934,plain,
% 1.19/1.38 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(935,plain,
% 1.19/1.38 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp11) <=> ((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp11) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(936,plain,
% 1.19/1.38 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp11) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[935])).
% 1.19/1.38 tff(937,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.19/1.38 tff(938,plain,
% 1.19/1.38 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[937, 936])).
% 1.19/1.38 tff(939,plain,
% 1.19/1.38 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[938, 934])).
% 1.19/1.38 tff(940,plain,(
% 1.19/1.38 ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(skolemize,[status(sab)],[939])).
% 1.19/1.38 tff(941,plain,
% 1.19/1.38 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[940, 933])).
% 1.19/1.38 tff(942,assumption,(hskp30), introduced(assumption)).
% 1.19/1.38 tff(943,plain,
% 1.19/1.38 (c3_1(a131)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[914, 942])).
% 1.19/1.38 tff(944,plain,
% 1.19/1.38 (c2_1(a131)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[922, 942])).
% 1.19/1.38 tff(945,plain,
% 1.19/1.38 (c0_1(a131)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[930, 942])).
% 1.19/1.38 tff(946,assumption,(hskp11), introduced(assumption)).
% 1.19/1.38 tff(947,plain,
% 1.19/1.38 (((~hskp11) | (~c3_1(a112))) <=> ((~hskp11) | (~c3_1(a112)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(948,plain,
% 1.19/1.38 (((~c3_1(a112)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a112)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(949,axiom,((~c3_1(a112)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.19/1.38 tff(950,plain,
% 1.19/1.38 ((~hskp11) | (~c3_1(a112))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[949, 948])).
% 1.19/1.38 tff(951,plain,
% 1.19/1.38 ((~hskp11) | (~c3_1(a112))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[950, 947])).
% 1.19/1.38 tff(952,plain,
% 1.19/1.38 (~c3_1(a112)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[951, 946])).
% 1.19/1.38 tff(953,plain,
% 1.19/1.38 (((~hskp11) | (~c2_1(a112))) <=> ((~hskp11) | (~c2_1(a112)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(954,plain,
% 1.19/1.38 (((~c2_1(a112)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a112)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(955,axiom,((~c2_1(a112)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.19/1.38 tff(956,plain,
% 1.19/1.38 ((~hskp11) | (~c2_1(a112))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[955, 954])).
% 1.19/1.38 tff(957,plain,
% 1.19/1.38 ((~hskp11) | (~c2_1(a112))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[956, 953])).
% 1.19/1.38 tff(958,plain,
% 1.19/1.38 (~c2_1(a112)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[957, 946])).
% 1.19/1.38 tff(959,plain,
% 1.19/1.38 (((~hskp11) | c1_1(a112)) <=> ((~hskp11) | c1_1(a112))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(960,axiom,((~hskp11) | c1_1(a112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.19/1.38 tff(961,plain,
% 1.19/1.38 ((~hskp11) | c1_1(a112)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[960, 959])).
% 1.19/1.38 tff(962,plain,
% 1.19/1.38 ((~hskp11) | c1_1(a112)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[961, 959])).
% 1.19/1.38 tff(963,plain,
% 1.19/1.38 ((~hskp11) | c1_1(a112)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[962, 959])).
% 1.19/1.38 tff(964,plain,
% 1.19/1.38 ((~hskp11) | c1_1(a112)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[963, 959])).
% 1.19/1.38 tff(965,plain,
% 1.19/1.38 ((~hskp11) | c1_1(a112)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[964, 959])).
% 1.19/1.38 tff(966,plain,
% 1.19/1.38 (c1_1(a112)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[965, 946])).
% 1.19/1.38 tff(967,plain,
% 1.19/1.38 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(968,plain,
% 1.19/1.38 ((hskp19 | (~ndr1_0) | c3_1(a112) | c2_1(a112) | (~c1_1(a112))) <=> (hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(969,plain,
% 1.19/1.38 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a112) | c2_1(a112) | (~c1_1(a112)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[968])).
% 1.19/1.38 tff(970,plain,
% 1.19/1.38 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a112) | c2_1(a112) | (~c1_1(a112)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[969, 967])).
% 1.19/1.38 tff(971,plain,
% 1.19/1.38 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a112) | c2_1(a112) | (~c1_1(a112)))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(972,plain,
% 1.19/1.38 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[971, 970])).
% 1.19/1.38 tff(973,plain,
% 1.19/1.38 ($false),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[972, 142, 1, 966, 958, 952, 11])).
% 1.19/1.38 tff(974,plain,((~hskp11) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.19/1.38 tff(975,plain,
% 1.19/1.38 (~hskp11),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[974, 1])).
% 1.19/1.38 tff(976,plain,
% 1.19/1.38 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(977,plain,
% 1.19/1.38 ((hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131))) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(978,plain,
% 1.19/1.38 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[977])).
% 1.19/1.38 tff(979,plain,
% 1.19/1.38 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[978, 976])).
% 1.19/1.38 tff(980,plain,
% 1.19/1.38 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(981,plain,
% 1.19/1.38 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[980, 979])).
% 1.19/1.38 tff(982,plain,
% 1.19/1.38 ($false),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[981, 142, 1, 975, 945, 944, 943, 941])).
% 1.19/1.38 tff(983,plain,((~hskp30) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.19/1.38 tff(984,plain,
% 1.19/1.38 (~hskp30),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[983, 1])).
% 1.19/1.38 tff(985,assumption,(~hskp30), introduced(assumption)).
% 1.19/1.38 tff(986,plain,
% 1.19/1.38 (hskp24),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[140, 23, 985])).
% 1.19/1.38 tff(987,plain,
% 1.19/1.38 (~c3_1(a163)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[905, 986])).
% 1.19/1.38 tff(988,plain,
% 1.19/1.38 (((~hskp24) | (~c2_1(a163))) <=> ((~hskp24) | (~c2_1(a163)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(989,plain,
% 1.19/1.38 (((~c2_1(a163)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a163)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(990,axiom,((~c2_1(a163)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.19/1.38 tff(991,plain,
% 1.19/1.38 ((~hskp24) | (~c2_1(a163))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[990, 989])).
% 1.19/1.38 tff(992,plain,
% 1.19/1.38 ((~hskp24) | (~c2_1(a163))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[991, 988])).
% 1.19/1.38 tff(993,plain,
% 1.19/1.38 (~c2_1(a163)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[992, 986])).
% 1.19/1.38 tff(994,plain,
% 1.19/1.38 (((~hskp24) | (~c1_1(a163))) <=> ((~hskp24) | (~c1_1(a163)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(995,plain,
% 1.19/1.38 (((~c1_1(a163)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a163)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(996,axiom,((~c1_1(a163)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.19/1.38 tff(997,plain,
% 1.19/1.38 ((~hskp24) | (~c1_1(a163))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[996, 995])).
% 1.19/1.38 tff(998,plain,
% 1.19/1.38 ((~hskp24) | (~c1_1(a163))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[997, 994])).
% 1.19/1.38 tff(999,plain,
% 1.19/1.38 (~c1_1(a163)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[998, 986])).
% 1.19/1.38 tff(1000,plain,
% 1.19/1.38 (hskp5),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[661, 999, 993, 987, 23])).
% 1.19/1.38 tff(1001,plain,
% 1.19/1.38 (~c2_1(a106)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[892, 1000])).
% 1.19/1.38 tff(1002,plain,
% 1.19/1.38 (~c0_1(a163)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[821, 1000, 999, 993, 1001])).
% 1.19/1.38 tff(1003,plain,
% 1.19/1.38 (c1_1(a106)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[233, 1000])).
% 1.19/1.38 tff(1004,plain,
% 1.19/1.38 (hskp19),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[387, 1003, 999, 993, 1001, 1002, 987])).
% 1.19/1.38 tff(1005,plain,
% 1.19/1.38 (~c3_1(a135)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[396, 1004])).
% 1.19/1.38 tff(1006,plain,
% 1.19/1.38 (c0_1(a135)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[420, 1004])).
% 1.19/1.38 tff(1007,plain,
% 1.19/1.38 (~c2_1(a135)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[402, 1004])).
% 1.19/1.38 tff(1008,plain,
% 1.19/1.38 (~hskp28),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[501, 1007, 999, 993, 987, 1006, 1005])).
% 1.19/1.38 tff(1009,plain,
% 1.19/1.38 (~hskp15),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[548, 1008, 23])).
% 1.19/1.38 tff(1010,plain,
% 1.19/1.38 (~hskp6),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[460, 1004, 999, 993, 987])).
% 1.19/1.38 tff(1011,plain,
% 1.19/1.38 (hskp7 | hskp6 | c0_1(a163)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[838, 142, 999, 987, 832])).
% 1.19/1.38 tff(1012,plain,
% 1.19/1.38 (hskp7),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1011, 1010, 1002])).
% 1.19/1.38 tff(1013,plain,
% 1.19/1.38 (~c0_1(a108)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[612, 1012])).
% 1.19/1.38 tff(1014,plain,
% 1.19/1.38 ($false),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[659, 1013, 1012, 999, 993, 987, 1007, 1005, 1006, 1009])).
% 1.19/1.38 tff(1015,plain,(hskp31 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.19/1.38 tff(1016,plain,
% 1.19/1.38 (hskp31),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1015, 984])).
% 1.19/1.38 tff(1017,plain,
% 1.19/1.38 (c3_1(a141)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[57, 1016])).
% 1.19/1.38 tff(1018,plain,
% 1.19/1.38 (c1_1(a141)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[65, 1016])).
% 1.19/1.38 tff(1019,plain,
% 1.19/1.38 (c0_1(a141)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[73, 1016])).
% 1.19/1.38 tff(1020,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(1021,plain,
% 1.19/1.38 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(1022,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[1021])).
% 1.19/1.38 tff(1023,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.19/1.38 inference(transitivity,[status(thm)],[1022, 1020])).
% 1.19/1.38 tff(1024,plain,
% 1.19/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(1025,plain,
% 1.19/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 1.19/1.38 tff(1026,plain,
% 1.19/1.38 (c0_1(a163)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1025, 142, 1019, 1018, 1017, 49, 86, 900, 723])).
% 1.19/1.38 tff(1027,plain,
% 1.19/1.38 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(1028,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[1027])).
% 1.19/1.38 tff(1029,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(1030,plain,
% 1.19/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(1031,plain,
% 1.19/1.38 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[1030])).
% 1.19/1.38 tff(1032,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.19/1.38 tff(1033,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 1.19/1.38 tff(1034,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[1033, 1029])).
% 1.19/1.38 tff(1035,plain,(
% 1.19/1.38 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.38 inference(skolemize,[status(sab)],[1034])).
% 1.19/1.38 tff(1036,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[1035, 1028])).
% 1.19/1.38 tff(1037,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(1038,plain,
% 1.19/1.38 ((hskp16 | (~ndr1_0) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(1039,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[1038])).
% 1.19/1.38 tff(1040,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[1039, 1037])).
% 1.19/1.38 tff(1041,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(1042,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 1.19/1.39 tff(1043,plain,
% 1.19/1.39 (hskp16 | (~c3_1(a163)) | (~c0_1(a163))),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1042, 142, 49, 86, 1036])).
% 1.19/1.39 tff(1044,plain,
% 1.19/1.39 (hskp16),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1043, 1026, 900])).
% 1.19/1.39 tff(1045,plain,
% 1.19/1.39 (c1_1(a126)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[698, 1044])).
% 1.19/1.39 tff(1046,plain,
% 1.19/1.39 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1047,plain,
% 1.19/1.39 ((hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141))) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1048,plain,
% 1.19/1.39 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[1047])).
% 1.19/1.39 tff(1049,plain,
% 1.19/1.39 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[1048, 1046])).
% 1.19/1.39 tff(1050,plain,
% 1.19/1.39 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(1051,plain,
% 1.19/1.39 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 1.19/1.39 tff(1052,plain,
% 1.19/1.39 (~c2_1(a141)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1051, 142, 1, 975, 1019, 1017, 941])).
% 1.19/1.39 tff(1053,plain,
% 1.19/1.39 (c3_1(a126)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[706, 1044])).
% 1.19/1.39 tff(1054,plain,
% 1.19/1.39 (~c2_1(a126)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[712, 1044])).
% 1.19/1.39 tff(1055,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[793, 1054, 1053, 49, 86, 1026, 1019, 1018, 1017, 1052, 1045])).
% 1.19/1.39 tff(1056,plain,(hskp19 | c1_1(a163) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(1057,plain,
% 1.19/1.39 (hskp19),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1056, 86, 49])).
% 1.19/1.39 tff(1058,plain,
% 1.19/1.39 (~c3_1(a135)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[396, 1057])).
% 1.19/1.39 tff(1059,plain,
% 1.19/1.39 (~c2_1(a135)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[402, 1057])).
% 1.19/1.39 tff(1060,plain,
% 1.19/1.39 (c0_1(a135)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[420, 1057])).
% 1.19/1.39 tff(1061,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1062,plain,
% 1.19/1.39 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135)) <=> (c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1063,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[1062])).
% 1.19/1.39 tff(1064,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[1063, 1061])).
% 1.19/1.39 tff(1065,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(1066,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 1.19/1.39 tff(1067,plain,
% 1.19/1.39 (c1_1(a135)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1066, 142, 493, 485, 477, 1060, 1059, 1058, 96])).
% 1.19/1.39 tff(1068,assumption,(c3_1(a131)), introduced(assumption)).
% 1.19/1.39 tff(1069,assumption,(c2_1(a131)), introduced(assumption)).
% 1.19/1.39 tff(1070,assumption,(c0_1(a131)), introduced(assumption)).
% 1.19/1.39 tff(1071,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1072,plain,
% 1.19/1.39 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1073,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[1072])).
% 1.19/1.39 tff(1074,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[1073, 1071])).
% 1.19/1.39 tff(1075,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(1076,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 1.19/1.39 tff(1077,plain,
% 1.19/1.39 (c0_1(a163)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1076, 142, 1070, 1069, 1068, 493, 485, 477, 49, 900, 84])).
% 1.19/1.39 tff(1078,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1079,plain,
% 1.19/1.39 ((hskp17 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1080,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[1079])).
% 1.19/1.39 tff(1081,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[1080, 1078])).
% 1.19/1.39 tff(1082,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(1083,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 1.19/1.39 tff(1084,plain,
% 1.19/1.39 (hskp17 | (~c1_1(a135)) | (~c0_1(a163))),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1083, 142, 1060, 49, 86, 1059, 735])).
% 1.19/1.39 tff(1085,plain,
% 1.19/1.39 (hskp17),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1084, 1077, 1067])).
% 1.19/1.39 tff(1086,plain,
% 1.19/1.39 (~c1_1(a132)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[750, 1085])).
% 1.19/1.39 tff(1087,plain,
% 1.19/1.39 (~c0_1(a132)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[756, 1085])).
% 1.19/1.39 tff(1088,plain,
% 1.19/1.39 (c3_1(a132)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[765, 1085])).
% 1.19/1.39 tff(1089,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1090,plain,
% 1.19/1.39 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1091,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[1090])).
% 1.19/1.39 tff(1092,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[1091, 1089])).
% 1.19/1.39 tff(1093,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(1094,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 1.19/1.39 tff(1095,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1094, 142, 1070, 1069, 1068, 493, 485, 477, 1088, 1087, 1086, 84])).
% 1.19/1.39 tff(1096,plain,((~hskp28) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a163) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(1097,plain,
% 1.19/1.39 (~hskp28),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1096, 931, 923, 915, 49, 86])).
% 1.19/1.39 tff(1098,plain,
% 1.19/1.39 (~hskp15),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[548, 1097, 23])).
% 1.19/1.39 tff(1099,plain,
% 1.19/1.39 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1100,plain,
% 1.19/1.39 ((hskp28 | hskp15 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1101,plain,
% 1.19/1.39 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[1100])).
% 1.19/1.39 tff(1102,plain,
% 1.19/1.39 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[1101, 1099])).
% 1.19/1.39 tff(1103,plain,
% 1.19/1.39 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(1104,plain,
% 1.19/1.39 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 1.19/1.39 tff(1105,plain,
% 1.19/1.39 (hskp28 | hskp15 | (~c3_1(a163)) | (~c0_1(a163))),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1104, 142, 49, 33])).
% 1.19/1.39 tff(1106,plain,
% 1.19/1.39 (~c0_1(a163)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1105, 503, 900, 614])).
% 1.19/1.39 tff(1107,plain,
% 1.19/1.39 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1108,plain,
% 1.19/1.39 ((hskp28 | hskp15 | (~ndr1_0) | c0_1(a163) | c2_1(a163) | (~c3_1(a163))) <=> (hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1109,plain,
% 1.19/1.39 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a163) | c2_1(a163) | (~c3_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163)))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[1108])).
% 1.19/1.39 tff(1110,plain,
% 1.19/1.39 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a163) | c2_1(a163) | (~c3_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163))),
% 1.19/1.39 inference(transitivity,[status(thm)],[1109, 1107])).
% 1.19/1.39 tff(1111,plain,
% 1.19/1.39 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a163) | c2_1(a163) | (~c3_1(a163)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(1112,plain,
% 1.19/1.39 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 1.19/1.39 tff(1113,plain,
% 1.19/1.39 (hskp28 | hskp15 | (~c3_1(a163)) | c0_1(a163)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1112, 142, 86, 634])).
% 1.19/1.39 tff(1114,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1113, 1106, 503, 900, 614])).
% 1.19/1.39 tff(1115,plain,(hskp28 | hskp15 | c2_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(1116,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1115, 1098, 1097, 86, 49])).
% 1.19/1.39 tff(1117,plain,(hskp31 | c2_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(1118,plain,
% 1.19/1.39 (hskp31),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1117, 86, 49])).
% 1.19/1.39 tff(1119,plain,
% 1.19/1.39 (c3_1(a141)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[57, 1118])).
% 1.19/1.39 tff(1120,plain,
% 1.19/1.39 (c1_1(a141)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[65, 1118])).
% 1.19/1.39 tff(1121,plain,
% 1.19/1.39 (c0_1(a141)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[73, 1118])).
% 1.19/1.39 tff(1122,plain,
% 1.19/1.39 (c0_1(a163)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1025, 142, 1121, 1120, 1119, 49, 86, 900, 723])).
% 1.19/1.39 tff(1123,plain,
% 1.19/1.39 (hskp16),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1043, 1122, 900])).
% 1.19/1.39 tff(1124,plain,
% 1.19/1.39 (c1_1(a126)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[698, 1123])).
% 1.19/1.39 tff(1125,plain,
% 1.19/1.39 (c3_1(a126)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[706, 1123])).
% 1.19/1.39 tff(1126,plain,
% 1.19/1.39 (~c2_1(a126)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[712, 1123])).
% 1.19/1.39 tff(1127,plain,
% 1.19/1.39 (c2_1(a141)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[793, 1126, 49, 86, 1121, 1120, 1122, 1119, 1125, 1124])).
% 1.19/1.39 tff(1128,plain,
% 1.19/1.39 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(1129,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[1128])).
% 1.19/1.39 tff(1130,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1131,plain,
% 1.19/1.39 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(1132,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[1131])).
% 1.19/1.39 tff(1133,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.19/1.39 tff(1134,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.19/1.39 tff(1135,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1134, 1130])).
% 1.19/1.39 tff(1136,plain,(
% 1.19/1.39 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.19/1.39 inference(skolemize,[status(sab)],[1135])).
% 1.19/1.39 tff(1137,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1136, 1129])).
% 1.19/1.39 tff(1138,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1139,plain,
% 1.19/1.39 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135)) <=> (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1140,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[1139])).
% 1.19/1.39 tff(1141,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[1140, 1138])).
% 1.19/1.39 tff(1142,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(1143,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 1.19/1.39 tff(1144,plain,
% 1.19/1.39 ((~c2_1(a141)) | c1_1(a135)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1143, 142, 1120, 1119, 1060, 1059, 1058, 96])).
% 1.19/1.39 tff(1145,plain,
% 1.19/1.39 (c1_1(a135)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1144, 1127])).
% 1.19/1.39 tff(1146,plain,
% 1.19/1.39 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1147,plain,
% 1.19/1.39 ((hskp24 | hskp1 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135))) <=> (hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(1148,plain,
% 1.19/1.39 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135))))),
% 1.19/1.40 inference(monotonicity,[status(thm)],[1147])).
% 1.19/1.40 tff(1149,plain,
% 1.19/1.40 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.19/1.40 inference(transitivity,[status(thm)],[1148, 1146])).
% 1.19/1.40 tff(1150,plain,
% 1.19/1.40 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.19/1.40 inference(quant_inst,[status(thm)],[])).
% 1.19/1.40 tff(1151,plain,
% 1.19/1.40 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 1.19/1.40 tff(1152,plain,
% 1.19/1.40 (hskp1 | (~c1_1(a135))),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1151, 142, 906, 1060, 1059, 21])).
% 1.19/1.40 tff(1153,plain,
% 1.19/1.40 (hskp1),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1152, 1145])).
% 1.19/1.40 tff(1154,plain,
% 1.19/1.40 (((~hskp1) | (~c1_1(a102))) <=> ((~hskp1) | (~c1_1(a102)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1155,plain,
% 1.19/1.40 (((~c1_1(a102)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a102)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1156,axiom,((~c1_1(a102)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.19/1.40 tff(1157,plain,
% 1.19/1.40 ((~hskp1) | (~c1_1(a102))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 1.19/1.40 tff(1158,plain,
% 1.19/1.40 ((~hskp1) | (~c1_1(a102))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1157, 1154])).
% 1.19/1.40 tff(1159,plain,
% 1.19/1.40 (~c1_1(a102)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1158, 1153])).
% 1.19/1.40 tff(1160,plain,
% 1.19/1.40 (((~hskp1) | (~c0_1(a102))) <=> ((~hskp1) | (~c0_1(a102)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1161,plain,
% 1.19/1.40 (((~c0_1(a102)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a102)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1162,axiom,((~c0_1(a102)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.19/1.40 tff(1163,plain,
% 1.19/1.40 ((~hskp1) | (~c0_1(a102))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 1.19/1.40 tff(1164,plain,
% 1.19/1.40 ((~hskp1) | (~c0_1(a102))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1163, 1160])).
% 1.19/1.40 tff(1165,plain,
% 1.19/1.40 (~c0_1(a102)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1164, 1153])).
% 1.19/1.40 tff(1166,plain,
% 1.19/1.40 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(1167,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[1166])).
% 1.19/1.40 tff(1168,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1169,plain,
% 1.19/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_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) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_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) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(1170,plain,
% 1.19/1.40 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[1169])).
% 1.19/1.40 tff(1171,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)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.19/1.40 tff(1172,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 1.19/1.40 tff(1173,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1172, 1168])).
% 1.19/1.40 tff(1174,plain,(
% 1.19/1.40 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.40 inference(skolemize,[status(sab)],[1173])).
% 1.19/1.40 tff(1175,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1174, 1167])).
% 1.19/1.40 tff(1176,plain,
% 1.19/1.40 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1177,plain,
% 1.19/1.40 ((hskp22 | (~ndr1_0) | c3_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1178,plain,
% 1.19/1.40 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163))))),
% 1.19/1.40 inference(monotonicity,[status(thm)],[1177])).
% 1.19/1.40 tff(1179,plain,
% 1.19/1.40 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 1.19/1.40 inference(transitivity,[status(thm)],[1178, 1176])).
% 1.19/1.40 tff(1180,plain,
% 1.19/1.40 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 1.19/1.40 inference(quant_inst,[status(thm)],[])).
% 1.19/1.40 tff(1181,plain,
% 1.19/1.40 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 1.19/1.40 tff(1182,plain,
% 1.19/1.40 (hskp22 | (~c1_1(a135)) | (~c0_1(a163))),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1181, 142, 1060, 49, 900, 1058, 1175])).
% 1.19/1.40 tff(1183,plain,
% 1.19/1.40 (hskp22),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1182, 1145, 1122])).
% 1.19/1.40 tff(1184,plain,
% 1.19/1.40 (((~hskp22) | (~c2_1(a145))) <=> ((~hskp22) | (~c2_1(a145)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1185,plain,
% 1.19/1.40 (((~c2_1(a145)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a145)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1186,axiom,((~c2_1(a145)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.19/1.40 tff(1187,plain,
% 1.19/1.40 ((~hskp22) | (~c2_1(a145))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 1.19/1.40 tff(1188,plain,
% 1.19/1.40 ((~hskp22) | (~c2_1(a145))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1187, 1184])).
% 1.19/1.40 tff(1189,plain,
% 1.19/1.40 (~c2_1(a145)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1188, 1183])).
% 1.19/1.40 tff(1190,plain,
% 1.19/1.40 (((~hskp22) | (~c1_1(a145))) <=> ((~hskp22) | (~c1_1(a145)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1191,plain,
% 1.19/1.40 (((~c1_1(a145)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a145)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1192,axiom,((~c1_1(a145)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.19/1.40 tff(1193,plain,
% 1.19/1.40 ((~hskp22) | (~c1_1(a145))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 1.19/1.40 tff(1194,plain,
% 1.19/1.40 ((~hskp22) | (~c1_1(a145))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1193, 1190])).
% 1.19/1.40 tff(1195,plain,
% 1.19/1.40 (~c1_1(a145)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1194, 1183])).
% 1.19/1.40 tff(1196,plain,
% 1.19/1.40 (((~hskp22) | (~c0_1(a145))) <=> ((~hskp22) | (~c0_1(a145)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1197,plain,
% 1.19/1.40 (((~c0_1(a145)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a145)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1198,axiom,((~c0_1(a145)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.19/1.40 tff(1199,plain,
% 1.19/1.40 ((~hskp22) | (~c0_1(a145))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 1.19/1.40 tff(1200,plain,
% 1.19/1.40 ((~hskp22) | (~c0_1(a145))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1199, 1196])).
% 1.19/1.40 tff(1201,plain,
% 1.19/1.40 (~c0_1(a145)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1200, 1183])).
% 1.19/1.40 tff(1202,plain,
% 1.19/1.40 (((~hskp1) | c2_1(a102)) <=> ((~hskp1) | c2_1(a102))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1203,axiom,((~hskp1) | c2_1(a102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.19/1.40 tff(1204,plain,
% 1.19/1.40 ((~hskp1) | c2_1(a102)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 1.19/1.40 tff(1205,plain,
% 1.19/1.40 ((~hskp1) | c2_1(a102)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1204, 1202])).
% 1.19/1.40 tff(1206,plain,
% 1.19/1.40 ((~hskp1) | c2_1(a102)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1205, 1202])).
% 1.19/1.40 tff(1207,plain,
% 1.19/1.40 ((~hskp1) | c2_1(a102)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1206, 1202])).
% 1.19/1.40 tff(1208,plain,
% 1.19/1.40 ((~hskp1) | c2_1(a102)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1207, 1202])).
% 1.19/1.40 tff(1209,plain,
% 1.19/1.40 (c2_1(a102)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1208, 1153])).
% 1.19/1.40 tff(1210,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1211,plain,
% 1.19/1.40 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a145) | c0_1(a145) | c2_1(a145)) <=> (c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1212,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102))))),
% 1.19/1.40 inference(monotonicity,[status(thm)],[1211])).
% 1.19/1.40 tff(1213,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 1.19/1.40 inference(transitivity,[status(thm)],[1212, 1210])).
% 1.19/1.40 tff(1214,plain,
% 1.19/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a145) | c0_1(a145) | c2_1(a145))),
% 1.19/1.40 inference(quant_inst,[status(thm)],[])).
% 1.19/1.40 tff(1215,plain,
% 1.19/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 1.19/1.40 tff(1216,plain,
% 1.19/1.40 ($false),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1215, 142, 1120, 1119, 1209, 1201, 1195, 1189, 1165, 1159, 1137, 1127])).
% 1.19/1.40 tff(1217,plain,(c2_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.40 tff(1218,plain,
% 1.19/1.40 (c2_1(a163)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1217, 49])).
% 1.19/1.40 tff(1219,plain,
% 1.19/1.40 (~hskp24),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[992, 1218])).
% 1.19/1.40 tff(1220,plain,
% 1.19/1.40 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(1221,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[1220])).
% 1.19/1.40 tff(1222,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1223,plain,
% 1.19/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp13))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(1224,plain,
% 1.19/1.40 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[1223])).
% 1.19/1.40 tff(1225,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.19/1.40 tff(1226,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 1.19/1.40 tff(1227,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1226, 1222])).
% 1.19/1.40 tff(1228,plain,(
% 1.19/1.40 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.19/1.40 inference(skolemize,[status(sab)],[1227])).
% 1.19/1.40 tff(1229,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1228, 1221])).
% 1.19/1.40 tff(1230,assumption,(hskp10), introduced(assumption)).
% 1.19/1.40 tff(1231,plain,
% 1.19/1.40 (((~hskp10) | (~c3_1(a111))) <=> ((~hskp10) | (~c3_1(a111)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1232,plain,
% 1.19/1.40 (((~c3_1(a111)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a111)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1233,axiom,((~c3_1(a111)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.19/1.40 tff(1234,plain,
% 1.19/1.40 ((~hskp10) | (~c3_1(a111))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 1.19/1.40 tff(1235,plain,
% 1.19/1.40 ((~hskp10) | (~c3_1(a111))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1234, 1231])).
% 1.19/1.40 tff(1236,plain,
% 1.19/1.40 (~c3_1(a111)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1235, 1230])).
% 1.19/1.40 tff(1237,plain,
% 1.19/1.40 (((~hskp10) | (~c2_1(a111))) <=> ((~hskp10) | (~c2_1(a111)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1238,plain,
% 1.19/1.40 (((~c2_1(a111)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a111)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1239,axiom,((~c2_1(a111)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.19/1.40 tff(1240,plain,
% 1.19/1.40 ((~hskp10) | (~c2_1(a111))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 1.19/1.40 tff(1241,plain,
% 1.19/1.40 ((~hskp10) | (~c2_1(a111))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1240, 1237])).
% 1.19/1.40 tff(1242,plain,
% 1.19/1.40 (~c2_1(a111)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1241, 1230])).
% 1.19/1.40 tff(1243,plain,
% 1.19/1.40 (((~hskp10) | (~c0_1(a111))) <=> ((~hskp10) | (~c0_1(a111)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1244,plain,
% 1.19/1.40 (((~c0_1(a111)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a111)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1245,axiom,((~c0_1(a111)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.19/1.40 tff(1246,plain,
% 1.19/1.40 ((~hskp10) | (~c0_1(a111))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 1.19/1.40 tff(1247,plain,
% 1.19/1.40 ((~hskp10) | (~c0_1(a111))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1246, 1243])).
% 1.19/1.40 tff(1248,plain,
% 1.19/1.40 (~c0_1(a111)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1247, 1230])).
% 1.19/1.40 tff(1249,plain,
% 1.19/1.40 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1250,plain,
% 1.19/1.40 ((hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a111) | c0_1(a111) | c3_1(a111)) <=> (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1251,plain,
% 1.19/1.40 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a111) | c0_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141))))),
% 1.19/1.40 inference(monotonicity,[status(thm)],[1250])).
% 1.19/1.40 tff(1252,plain,
% 1.19/1.40 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a111) | c0_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 1.19/1.40 inference(transitivity,[status(thm)],[1251, 1249])).
% 1.19/1.40 tff(1253,plain,
% 1.19/1.40 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a111) | c0_1(a111) | c3_1(a111))),
% 1.19/1.40 inference(quant_inst,[status(thm)],[])).
% 1.19/1.40 tff(1254,plain,
% 1.19/1.40 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 1.19/1.40 tff(1255,plain,
% 1.19/1.40 (hskp13),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1254, 142, 737, 736, 767, 1248, 1242, 1236, 1229])).
% 1.19/1.40 tff(1256,plain,
% 1.19/1.40 (~c3_1(a114)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[566, 1255])).
% 1.19/1.40 tff(1257,plain,
% 1.19/1.40 (^[U: $i] : refl((hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(1258,plain,
% 1.19/1.40 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[1257])).
% 1.19/1.40 tff(1259,plain,
% 1.19/1.40 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1260,plain,
% 1.19/1.40 (^[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) | hskp17) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp17))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp17) <=> (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp17) <=> (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(1261,plain,
% 1.19/1.40 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp17) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[1260])).
% 1.19/1.40 tff(1262,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.19/1.40 tff(1263,plain,
% 1.19/1.40 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 1.19/1.40 tff(1264,plain,
% 1.19/1.40 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1263, 1259])).
% 1.19/1.40 tff(1265,plain,(
% 1.19/1.40 ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.40 inference(skolemize,[status(sab)],[1264])).
% 1.19/1.40 tff(1266,plain,
% 1.19/1.40 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1265, 1258])).
% 1.19/1.40 tff(1267,plain,
% 1.19/1.40 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1268,plain,
% 1.19/1.40 ((hskp19 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163))) <=> (hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1269,plain,
% 1.19/1.40 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)))),
% 1.19/1.40 inference(monotonicity,[status(thm)],[1268])).
% 1.19/1.40 tff(1270,plain,
% 1.19/1.40 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 1.19/1.40 inference(transitivity,[status(thm)],[1269, 1267])).
% 1.19/1.40 tff(1271,plain,
% 1.19/1.40 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))),
% 1.19/1.40 inference(quant_inst,[status(thm)],[])).
% 1.19/1.40 tff(1272,plain,
% 1.19/1.40 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 1.19/1.40 tff(1273,plain,
% 1.19/1.40 (hskp19 | hskp17 | (~c2_1(a163)) | c3_1(a163)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1272, 142, 49, 1266])).
% 1.19/1.40 tff(1274,plain,
% 1.19/1.40 (hskp17),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[1273, 1, 1218, 85])).
% 1.19/1.40 tff(1275,plain,
% 1.19/1.40 (~c1_1(a132)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[750, 1274])).
% 1.19/1.40 tff(1276,plain,
% 1.19/1.40 (~c0_1(a132)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[756, 1274])).
% 1.19/1.40 tff(1277,plain,
% 1.19/1.40 (c3_1(a132)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[765, 1274])).
% 1.19/1.40 tff(1278,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1279,plain,
% 1.19/1.40 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(1280,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132))))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[1279])).
% 1.19/1.41 tff(1281,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132)))),
% 1.19/1.41 inference(transitivity,[status(thm)],[1280, 1278])).
% 1.19/1.41 tff(1282,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(1283,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 1.19/1.41 tff(1284,plain,
% 1.19/1.41 (~c2_1(a141)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1283, 142, 1019, 1018, 1017, 1277, 1276, 1275, 84])).
% 1.19/1.41 tff(1285,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1286,plain,
% 1.19/1.41 (((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163))) <=> (c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1287,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163))))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[1286])).
% 1.19/1.41 tff(1288,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 1.19/1.41 inference(transitivity,[status(thm)],[1287, 1285])).
% 1.19/1.41 tff(1289,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(1290,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 1.19/1.41 tff(1291,plain,
% 1.19/1.41 (~c0_1(a163)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1290, 142, 1019, 1018, 1017, 49, 1218, 290, 1284])).
% 1.19/1.41 tff(1292,plain,
% 1.19/1.41 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(1293,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[1292])).
% 1.19/1.41 tff(1294,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1295,plain,
% 1.19/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | 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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(1296,plain,
% 1.19/1.41 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[1295])).
% 1.19/1.41 tff(1297,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.19/1.41 tff(1298,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 1.19/1.41 tff(1299,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1298, 1294])).
% 1.19/1.41 tff(1300,plain,(
% 1.19/1.41 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.41 inference(skolemize,[status(sab)],[1299])).
% 1.19/1.41 tff(1301,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1300, 1293])).
% 1.19/1.41 tff(1302,plain,
% 1.19/1.41 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1303,plain,
% 1.19/1.41 ((hskp24 | hskp1 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141))) <=> (hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1304,plain,
% 1.19/1.41 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141))))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[1303])).
% 1.19/1.41 tff(1305,plain,
% 1.19/1.41 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 1.19/1.41 inference(transitivity,[status(thm)],[1304, 1302])).
% 1.19/1.41 tff(1306,plain,
% 1.19/1.41 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(1307,plain,
% 1.19/1.41 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 1.19/1.41 tff(1308,plain,
% 1.19/1.41 (hskp1),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1307, 142, 1219, 1019, 1018, 21, 1284])).
% 1.19/1.41 tff(1309,plain,
% 1.19/1.41 (~c1_1(a102)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1158, 1308])).
% 1.19/1.41 tff(1310,plain,
% 1.19/1.41 (~c0_1(a102)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1164, 1308])).
% 1.19/1.41 tff(1311,plain,
% 1.19/1.41 (c2_1(a102)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1208, 1308])).
% 1.19/1.41 tff(1312,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1313,plain,
% 1.19/1.41 ((hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102))) <=> (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1314,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102))))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[1313])).
% 1.19/1.41 tff(1315,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 1.19/1.41 inference(transitivity,[status(thm)],[1314, 1312])).
% 1.19/1.41 tff(1316,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(1317,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 1.19/1.41 tff(1318,plain,
% 1.19/1.41 (hskp10),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1317, 142, 1019, 1018, 1017, 1311, 1310, 1309, 1301])).
% 1.19/1.41 tff(1319,plain,
% 1.19/1.41 (~c3_1(a111)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1235, 1318])).
% 1.19/1.41 tff(1320,plain,
% 1.19/1.41 (~c2_1(a111)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1241, 1318])).
% 1.19/1.41 tff(1321,plain,
% 1.19/1.41 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1322,plain,
% 1.19/1.41 ((hskp19 | (~ndr1_0) | c3_1(a111) | c2_1(a111) | (~c1_1(a111))) <=> (hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1323,plain,
% 1.19/1.41 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a111) | c2_1(a111) | (~c1_1(a111)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111))))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[1322])).
% 1.19/1.41 tff(1324,plain,
% 1.19/1.41 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a111) | c2_1(a111) | (~c1_1(a111)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)))),
% 1.19/1.41 inference(transitivity,[status(thm)],[1323, 1321])).
% 1.19/1.41 tff(1325,plain,
% 1.19/1.41 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a111) | c2_1(a111) | (~c1_1(a111)))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(1326,plain,
% 1.19/1.41 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 1.19/1.41 tff(1327,plain,
% 1.19/1.41 (~c1_1(a111)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1326, 142, 1, 1320, 1319, 11])).
% 1.19/1.41 tff(1328,plain,
% 1.19/1.41 (hskp5),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[213, 1291, 85])).
% 1.19/1.41 tff(1329,plain,
% 1.19/1.41 (~c2_1(a106)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[892, 1328])).
% 1.19/1.41 tff(1330,plain,
% 1.19/1.41 (c1_1(a106)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[233, 1328])).
% 1.19/1.41 tff(1331,plain,
% 1.19/1.41 (c3_1(a106)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[221, 142, 1, 1330, 1329, 11])).
% 1.19/1.41 tff(1332,plain,
% 1.19/1.41 (~c0_1(a111)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1247, 1318])).
% 1.19/1.41 tff(1333,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1334,plain,
% 1.19/1.41 ((hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a111) | c1_1(a111) | c0_1(a111)) <=> (hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1335,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111)))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[1334])).
% 1.19/1.41 tff(1336,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111))),
% 1.19/1.41 inference(transitivity,[status(thm)],[1335, 1333])).
% 1.19/1.41 tff(1337,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a111) | c1_1(a111) | c0_1(a111))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(1338,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 1.19/1.41 tff(1339,plain,
% 1.19/1.41 (hskp2 | c1_1(a111)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1338, 142, 1330, 1332, 1320, 1329, 246, 1331])).
% 1.19/1.41 tff(1340,plain,
% 1.19/1.41 (hskp2),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1339, 1327])).
% 1.19/1.41 tff(1341,plain,
% 1.19/1.41 (~c3_1(a103)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[383, 1340])).
% 1.19/1.41 tff(1342,plain,
% 1.19/1.41 (c0_1(a103)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[278, 1340])).
% 1.19/1.41 tff(1343,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1344,plain,
% 1.19/1.41 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1345,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163)))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[1344])).
% 1.19/1.41 tff(1346,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 1.19/1.41 inference(transitivity,[status(thm)],[1345, 1343])).
% 1.19/1.41 tff(1347,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(1348,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 1.19/1.41 tff(1349,plain,
% 1.19/1.41 (~c2_1(a103)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1348, 142, 1342, 49, 1218, 85, 1341, 331, 1291])).
% 1.19/1.41 tff(1350,plain,
% 1.19/1.41 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(1351,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[1350])).
% 1.19/1.41 tff(1352,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1353,plain,
% 1.19/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(1354,plain,
% 1.19/1.41 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[1353])).
% 1.19/1.41 tff(1355,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.19/1.41 tff(1356,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 1.19/1.41 tff(1357,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1356, 1352])).
% 1.19/1.41 tff(1358,plain,(
% 1.19/1.41 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.41 inference(skolemize,[status(sab)],[1357])).
% 1.19/1.41 tff(1359,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1358, 1351])).
% 1.19/1.41 tff(1360,plain,
% 1.19/1.41 (c1_1(a103)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[261, 1340])).
% 1.19/1.41 tff(1361,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1362,plain,
% 1.19/1.41 ((hskp11 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1363,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132))))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[1362])).
% 1.19/1.41 tff(1364,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132)))),
% 1.19/1.41 inference(transitivity,[status(thm)],[1363, 1361])).
% 1.19/1.41 tff(1365,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(1366,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 1.19/1.41 tff(1367,plain,
% 1.19/1.41 ($false),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1366, 142, 975, 1277, 1360, 1276, 1275, 1341, 1359, 1349])).
% 1.19/1.41 tff(1368,plain,(hskp19 | c1_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.41 tff(1369,plain,
% 1.19/1.41 (hskp19),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[1368, 85, 49])).
% 1.19/1.41 tff(1370,plain,
% 1.19/1.41 (~c3_1(a135)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[396, 1369])).
% 1.19/1.41 tff(1371,plain,
% 1.19/1.41 (~c2_1(a135)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[402, 1369])).
% 1.19/1.41 tff(1372,plain,
% 1.19/1.41 (c2_1(a114)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[574, 1255])).
% 1.19/1.41 tff(1373,plain,
% 1.19/1.41 (c1_1(a114)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[582, 1255])).
% 1.19/1.41 tff(1374,plain,
% 1.19/1.41 (c0_1(a135)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[420, 1369])).
% 1.19/1.41 tff(1375,plain,
% 1.19/1.41 (c0_1(a114)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[589, 142, 1374, 1373, 1372, 1371, 1370, 1256, 181])).
% 1.19/1.41 tff(1376,assumption,(c1_1(a111)), introduced(assumption)).
% 1.19/1.41 tff(1377,assumption,(~c3_1(a111)), introduced(assumption)).
% 1.19/1.41 tff(1378,assumption,(~c0_1(a111)), introduced(assumption)).
% 1.19/1.41 tff(1379,assumption,(hskp13), introduced(assumption)).
% 1.19/1.41 tff(1380,plain,
% 1.19/1.41 (~c3_1(a114)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[566, 1379])).
% 1.19/1.41 tff(1381,plain,
% 1.19/1.41 (c2_1(a114)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[574, 1379])).
% 1.19/1.41 tff(1382,plain,
% 1.19/1.41 (c1_1(a114)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[582, 1379])).
% 1.19/1.41 tff(1383,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1384,plain,
% 1.19/1.41 (((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111))) <=> (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(1385,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[1384])).
% 1.19/1.42 tff(1386,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[1385, 1383])).
% 1.19/1.42 tff(1387,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(1388,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 1.19/1.42 tff(1389,plain,
% 1.19/1.42 ($false),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1388, 142, 441, 1382, 1381, 424, 423, 1380, 1378, 1377, 181, 1376])).
% 1.19/1.42 tff(1390,plain,((~hskp13) | (~c0_1(a135)) | c2_1(a135) | c3_1(a135) | c0_1(a111) | c3_1(a111) | (~c1_1(a111))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.42 tff(1391,plain,
% 1.19/1.42 (~c1_1(a111)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1390, 1255, 1371, 1370, 1248, 1236, 1374])).
% 1.19/1.42 tff(1392,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1393,plain,
% 1.19/1.42 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1394,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[1393])).
% 1.19/1.42 tff(1395,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[1394, 1392])).
% 1.19/1.42 tff(1396,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(1397,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 1.19/1.42 tff(1398,plain,
% 1.19/1.42 ((~c2_1(a141)) | c1_1(a111)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1397, 142, 736, 767, 1374, 1371, 1370, 1242, 1236, 96])).
% 1.19/1.42 tff(1399,plain,
% 1.19/1.42 (~c2_1(a141)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1398, 1391])).
% 1.19/1.42 tff(1400,plain,
% 1.19/1.42 (~c0_1(a163)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1290, 142, 737, 736, 767, 49, 1218, 290, 1399])).
% 1.19/1.42 tff(1401,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1402,plain,
% 1.19/1.42 (((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1403,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163)))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[1402])).
% 1.19/1.42 tff(1404,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163))),
% 1.19/1.42 inference(transitivity,[status(thm)],[1403, 1401])).
% 1.19/1.42 tff(1405,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(1406,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 1.19/1.42 tff(1407,plain,
% 1.19/1.42 ($false),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1406, 142, 1372, 49, 1218, 85, 1256, 331, 1400, 1375])).
% 1.19/1.42 tff(1408,plain,((~hskp10) | c1_1(a163) | c3_1(a163) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.42 tff(1409,plain,
% 1.19/1.42 (~hskp10),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1408, 74, 85, 49, 66, 58])).
% 1.19/1.42 tff(1410,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1411,plain,
% 1.19/1.42 ((hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163))) <=> (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1412,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[1411])).
% 1.19/1.42 tff(1413,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.19/1.42 inference(transitivity,[status(thm)],[1412, 1410])).
% 1.19/1.42 tff(1414,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(1415,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.19/1.42 tff(1416,plain,
% 1.19/1.42 (hskp10 | c0_1(a163)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1415, 142, 74, 66, 58, 49, 1218, 1301])).
% 1.19/1.42 tff(1417,plain,
% 1.19/1.42 (c0_1(a163)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1416, 1409])).
% 1.19/1.42 tff(1418,plain,
% 1.19/1.42 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.19/1.42 inference(bind,[status(th)],[])).
% 1.19/1.42 tff(1419,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(quant_intro,[status(thm)],[1418])).
% 1.19/1.42 tff(1420,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1421,plain,
% 1.19/1.42 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.19/1.42 inference(bind,[status(th)],[])).
% 1.19/1.42 tff(1422,plain,
% 1.19/1.42 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(quant_intro,[status(thm)],[1421])).
% 1.19/1.42 tff(1423,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.19/1.42 tff(1424,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 1.19/1.42 tff(1425,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1424, 1420])).
% 1.19/1.42 tff(1426,plain,(
% 1.19/1.42 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(skolemize,[status(sab)],[1425])).
% 1.19/1.42 tff(1427,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1426, 1419])).
% 1.19/1.42 tff(1428,plain,
% 1.19/1.42 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.19/1.42 inference(bind,[status(th)],[])).
% 1.19/1.42 tff(1429,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(quant_intro,[status(thm)],[1428])).
% 1.19/1.42 tff(1430,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1431,plain,
% 1.19/1.42 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.19/1.42 inference(bind,[status(th)],[])).
% 1.19/1.42 tff(1432,plain,
% 1.19/1.42 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(quant_intro,[status(thm)],[1431])).
% 1.19/1.42 tff(1433,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.19/1.42 tff(1434,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 1.19/1.42 tff(1435,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1434, 1430])).
% 1.19/1.42 tff(1436,plain,(
% 1.19/1.42 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(skolemize,[status(sab)],[1435])).
% 1.19/1.42 tff(1437,plain,
% 1.19/1.42 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1436, 1429])).
% 1.19/1.42 tff(1438,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1439,plain,
% 1.19/1.42 ((hskp17 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163))) <=> (hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1440,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[1439])).
% 1.19/1.42 tff(1441,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[1440, 1438])).
% 1.19/1.42 tff(1442,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(1443,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 1.19/1.42 tff(1444,plain,
% 1.19/1.42 (hskp17 | (~c0_1(a163))),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1443, 142, 49, 1218, 85, 1437])).
% 1.19/1.42 tff(1445,plain,
% 1.19/1.42 (hskp17),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1444, 1417])).
% 1.19/1.42 tff(1446,plain,
% 1.19/1.42 (~c0_1(a132)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[756, 1445])).
% 1.19/1.42 tff(1447,plain,
% 1.19/1.42 (c3_1(a132)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[765, 1445])).
% 1.19/1.42 tff(1448,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1449,plain,
% 1.19/1.42 ((hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132))) <=> (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1450,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[1449])).
% 1.19/1.42 tff(1451,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[1450, 1448])).
% 1.19/1.42 tff(1452,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(1453,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 1.19/1.42 tff(1454,plain,
% 1.19/1.42 (~c2_1(a132)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1453, 142, 1409, 1447, 1218, 85, 1446, 1427, 1417])).
% 1.19/1.42 tff(1455,plain,
% 1.19/1.42 (~c1_1(a132)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[750, 1445])).
% 1.19/1.42 tff(1456,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1457,plain,
% 1.19/1.42 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1458,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[1457])).
% 1.19/1.42 tff(1459,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[1458, 1456])).
% 1.19/1.42 tff(1460,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(1461,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[1460, 1459])).
% 1.19/1.42 tff(1462,plain,
% 1.19/1.42 ($false),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1461, 142, 74, 66, 58, 1447, 1446, 1455, 723, 1454])).
% 1.19/1.42 tff(1463,plain,((~hskp31) | c3_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.42 tff(1464,plain,
% 1.19/1.42 (~hskp31),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[1463, 85, 49])).
% 1.19/1.42 tff(1465,plain,
% 1.19/1.42 (hskp30),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[140, 1464, 1219])).
% 1.19/1.42 tff(1466,plain,
% 1.19/1.42 (c3_1(a131)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[914, 1465])).
% 1.19/1.42 tff(1467,plain,
% 1.19/1.42 (c2_1(a131)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[922, 1465])).
% 1.19/1.42 tff(1468,plain,
% 1.19/1.42 (c0_1(a131)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[930, 1465])).
% 1.19/1.42 tff(1469,plain,
% 1.19/1.42 (hskp30),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[140, 23, 1219])).
% 1.19/1.42 tff(1470,plain,
% 1.19/1.42 (c3_1(a131)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[914, 1469])).
% 1.19/1.42 tff(1471,plain,
% 1.19/1.42 (c0_1(a131)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[930, 1469])).
% 1.19/1.42 tff(1472,plain,
% 1.19/1.42 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1473,plain,
% 1.19/1.42 ((hskp31 | hskp28 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131))) <=> (hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(1474,plain,
% 1.19/1.42 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131)))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[1473])).
% 1.19/1.42 tff(1475,plain,
% 1.19/1.42 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 1.19/1.43 inference(transitivity,[status(thm)],[1474, 1472])).
% 1.19/1.43 tff(1476,plain,
% 1.19/1.43 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(1477,plain,
% 1.19/1.43 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 1.19/1.43 tff(1478,plain,
% 1.19/1.43 (hskp28 | c1_1(a131)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1477, 23, 142, 1471, 1470, 536])).
% 1.19/1.43 tff(1479,plain,
% 1.19/1.43 (c1_1(a131)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1478, 503])).
% 1.19/1.43 tff(1480,plain,
% 1.19/1.43 (^[U: $i] : refl((hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(1481,plain,
% 1.19/1.43 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[1480])).
% 1.19/1.43 tff(1482,plain,
% 1.19/1.43 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1483,plain,
% 1.19/1.43 (^[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)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp17) <=> ((hskp28 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp17))), rewrite(((hskp28 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp17) <=> (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp17) <=> (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(1484,plain,
% 1.19/1.43 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp17) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[1483])).
% 1.19/1.43 tff(1485,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.19/1.43 tff(1486,plain,
% 1.19/1.43 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 1.19/1.43 tff(1487,plain,
% 1.19/1.43 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1486, 1482])).
% 1.19/1.43 tff(1488,plain,(
% 1.19/1.43 ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.43 inference(skolemize,[status(sab)],[1487])).
% 1.19/1.43 tff(1489,plain,
% 1.19/1.43 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1488, 1481])).
% 1.19/1.43 tff(1490,plain,
% 1.19/1.43 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1491,plain,
% 1.19/1.43 ((hskp28 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163))) <=> (hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1492,plain,
% 1.19/1.43 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)))),
% 1.19/1.43 inference(monotonicity,[status(thm)],[1491])).
% 1.19/1.43 tff(1493,plain,
% 1.19/1.43 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 1.19/1.43 inference(transitivity,[status(thm)],[1492, 1490])).
% 1.19/1.43 tff(1494,plain,
% 1.19/1.43 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(1495,plain,
% 1.19/1.43 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.19/1.43 tff(1496,plain,
% 1.19/1.43 (hskp28 | hskp17 | (~c2_1(a163)) | c3_1(a163)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1495, 142, 49, 1489])).
% 1.19/1.43 tff(1497,plain,
% 1.19/1.43 (hskp17),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1496, 503, 1218, 85])).
% 1.19/1.43 tff(1498,plain,
% 1.19/1.43 (~c1_1(a132)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[750, 1497])).
% 1.19/1.43 tff(1499,plain,
% 1.19/1.43 (~c0_1(a132)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[756, 1497])).
% 1.19/1.43 tff(1500,plain,
% 1.19/1.43 (c3_1(a132)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[765, 1497])).
% 1.19/1.43 tff(1501,plain,
% 1.19/1.43 (c2_1(a131)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[922, 1469])).
% 1.19/1.43 tff(1502,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1503,plain,
% 1.19/1.43 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1504,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132))))),
% 1.19/1.43 inference(monotonicity,[status(thm)],[1503])).
% 1.19/1.43 tff(1505,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132)))),
% 1.19/1.43 inference(transitivity,[status(thm)],[1504, 1502])).
% 1.19/1.43 tff(1506,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(1507,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 1.19/1.43 tff(1508,plain,
% 1.19/1.43 ($false),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1507, 142, 1471, 1501, 1470, 1500, 1499, 1498, 84, 1479])).
% 1.19/1.43 tff(1509,plain,(hskp28 | hskp31 | c3_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.43 tff(1510,plain,
% 1.19/1.43 (hskp28),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1509, 23, 85, 49])).
% 1.19/1.43 tff(1511,plain,
% 1.19/1.43 (c3_1(a118)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[476, 1510])).
% 1.19/1.43 tff(1512,plain,
% 1.19/1.43 (c2_1(a118)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[484, 1510])).
% 1.19/1.43 tff(1513,plain,
% 1.19/1.43 (c1_1(a118)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[492, 1510])).
% 1.19/1.43 tff(1514,assumption,(c3_1(a118)), introduced(assumption)).
% 1.19/1.43 tff(1515,assumption,(c2_1(a118)), introduced(assumption)).
% 1.19/1.43 tff(1516,assumption,(c1_1(a118)), introduced(assumption)).
% 1.19/1.43 tff(1517,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1518,plain,
% 1.19/1.43 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105))) <=> (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1519,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 1.19/1.43 inference(monotonicity,[status(thm)],[1518])).
% 1.19/1.43 tff(1520,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.43 inference(transitivity,[status(thm)],[1519, 1517])).
% 1.19/1.43 tff(1521,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(1522,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 1.19/1.43 tff(1523,plain,
% 1.19/1.43 (c0_1(a105)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1522, 142, 1070, 1069, 1068, 1516, 1515, 1514, 48, 40, 84])).
% 1.19/1.43 tff(1524,plain,
% 1.19/1.43 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(1525,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[1524])).
% 1.19/1.43 tff(1526,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1527,plain,
% 1.19/1.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(1528,plain,
% 1.19/1.43 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[1527])).
% 1.19/1.43 tff(1529,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.19/1.43 tff(1530,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 1.19/1.43 tff(1531,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1530, 1526])).
% 1.19/1.43 tff(1532,plain,(
% 1.19/1.43 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.43 inference(skolemize,[status(sab)],[1531])).
% 1.19/1.43 tff(1533,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1532, 1525])).
% 1.19/1.43 tff(1534,plain,
% 1.19/1.43 (((~hskp4) | c2_1(a105)) <=> ((~hskp4) | c2_1(a105))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1535,axiom,((~hskp4) | c2_1(a105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.19/1.43 tff(1536,plain,
% 1.19/1.43 ((~hskp4) | c2_1(a105)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1535, 1534])).
% 1.19/1.43 tff(1537,plain,
% 1.19/1.43 ((~hskp4) | c2_1(a105)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1536, 1534])).
% 1.19/1.43 tff(1538,plain,
% 1.19/1.43 ((~hskp4) | c2_1(a105)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1537, 1534])).
% 1.19/1.43 tff(1539,plain,
% 1.19/1.43 ((~hskp4) | c2_1(a105)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1538, 1534])).
% 1.19/1.43 tff(1540,plain,
% 1.19/1.43 ((~hskp4) | c2_1(a105)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1539, 1534])).
% 1.19/1.43 tff(1541,plain,
% 1.19/1.43 (c2_1(a105)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1540, 34])).
% 1.19/1.43 tff(1542,assumption,(~hskp17), introduced(assumption)).
% 1.19/1.43 tff(1543,plain,
% 1.19/1.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1544,plain,
% 1.19/1.43 ((hskp17 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c2_1(a105)) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105))) <=> (hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1545,plain,
% 1.19/1.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c2_1(a105)) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105))))),
% 1.19/1.43 inference(monotonicity,[status(thm)],[1544])).
% 1.19/1.43 tff(1546,plain,
% 1.19/1.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c2_1(a105)) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)))),
% 1.19/1.43 inference(transitivity,[status(thm)],[1545, 1543])).
% 1.19/1.43 tff(1547,plain,
% 1.19/1.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c2_1(a105)) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(1548,plain,
% 1.19/1.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.19/1.43 tff(1549,plain,
% 1.19/1.43 ($false),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1548, 142, 1542, 1541, 48, 40, 1533, 1523])).
% 1.19/1.43 tff(1550,plain,((~hskp4) | hskp17 | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a118)) | (~c2_1(a118)) | (~c3_1(a118))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.43 tff(1551,plain,
% 1.19/1.43 (hskp17),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1550, 34, 1070, 1069, 1068, 1516, 1515, 1514])).
% 1.19/1.43 tff(1552,plain,
% 1.19/1.43 (~c1_1(a132)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[750, 1551])).
% 1.19/1.43 tff(1553,plain,
% 1.19/1.43 (~c0_1(a132)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[756, 1551])).
% 1.19/1.43 tff(1554,plain,
% 1.19/1.43 (c3_1(a132)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[765, 1551])).
% 1.19/1.43 tff(1555,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1556,plain,
% 1.19/1.43 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1557,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 1.19/1.43 inference(monotonicity,[status(thm)],[1556])).
% 1.19/1.43 tff(1558,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.43 inference(transitivity,[status(thm)],[1557, 1555])).
% 1.19/1.43 tff(1559,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(1560,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 1.19/1.43 tff(1561,plain,
% 1.19/1.43 (~c0_1(a105)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1560, 142, 1516, 1515, 1514, 1554, 1541, 48, 1553, 1552, 84])).
% 1.19/1.43 tff(1562,plain,
% 1.19/1.43 ($false),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1522, 142, 1070, 1069, 1068, 1516, 1515, 1514, 48, 40, 84, 1561])).
% 1.19/1.43 tff(1563,plain,((~hskp4) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a118)) | (~c2_1(a118)) | (~c3_1(a118))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.43 tff(1564,plain,
% 1.19/1.43 (~hskp4),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1563, 1471, 1501, 1470, 1513, 1512, 1511])).
% 1.19/1.43 tff(1565,plain,
% 1.19/1.43 (hskp17),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[1444, 463])).
% 1.19/1.43 tff(1566,plain,
% 1.19/1.43 (~c1_1(a132)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[750, 1565])).
% 1.19/1.43 tff(1567,plain,
% 1.19/1.43 (~c0_1(a132)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[756, 1565])).
% 1.19/1.43 tff(1568,plain,
% 1.19/1.43 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(1569,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[1568])).
% 1.19/1.43 tff(1570,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(1571,plain,
% 1.19/1.43 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(1572,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[1571])).
% 1.19/1.43 tff(1573,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.19/1.43 tff(1574,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 1.19/1.43 tff(1575,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1574, 1570])).
% 1.19/1.43 tff(1576,plain,(
% 1.19/1.43 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.43 inference(skolemize,[status(sab)],[1575])).
% 1.19/1.43 tff(1577,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[1576, 1569])).
% 1.19/1.43 tff(1578,plain,
% 1.19/1.43 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(1579,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[1578])).
% 1.19/1.44 tff(1580,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1581,plain,
% 1.19/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | 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)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.19/1.44 inference(bind,[status(th)],[])).
% 1.19/1.44 tff(1582,plain,
% 1.19/1.44 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[1581])).
% 1.19/1.44 tff(1583,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.19/1.44 tff(1584,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.19/1.44 tff(1585,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1584, 1580])).
% 1.19/1.44 tff(1586,plain,(
% 1.19/1.44 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.44 inference(skolemize,[status(sab)],[1585])).
% 1.19/1.44 tff(1587,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1586, 1579])).
% 1.19/1.44 tff(1588,plain,
% 1.19/1.44 (c3_1(a132)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[765, 1565])).
% 1.19/1.44 tff(1589,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1590,plain,
% 1.19/1.44 ((hskp12 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1591,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[1590])).
% 1.19/1.44 tff(1592,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[1591, 1589])).
% 1.19/1.44 tff(1593,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(1594,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 1.19/1.44 tff(1595,plain,
% 1.19/1.44 (hskp12),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1594, 142, 1588, 1218, 85, 1567, 1566, 1587, 463])).
% 1.19/1.44 tff(1596,plain,
% 1.19/1.44 (((~hskp12) | (~c2_1(a113))) <=> ((~hskp12) | (~c2_1(a113)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1597,plain,
% 1.19/1.44 (((~c2_1(a113)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a113)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1598,axiom,((~c2_1(a113)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.19/1.44 tff(1599,plain,
% 1.19/1.44 ((~hskp12) | (~c2_1(a113))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 1.19/1.44 tff(1600,plain,
% 1.19/1.44 ((~hskp12) | (~c2_1(a113))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1599, 1596])).
% 1.19/1.44 tff(1601,plain,
% 1.19/1.44 (~c2_1(a113)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1600, 1595])).
% 1.19/1.44 tff(1602,plain,
% 1.19/1.44 (((~hskp12) | c3_1(a113)) <=> ((~hskp12) | c3_1(a113))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1603,axiom,((~hskp12) | c3_1(a113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.19/1.44 tff(1604,plain,
% 1.19/1.44 ((~hskp12) | c3_1(a113)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.19/1.44 tff(1605,plain,
% 1.19/1.44 ((~hskp12) | c3_1(a113)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1604, 1602])).
% 1.19/1.44 tff(1606,plain,
% 1.19/1.44 ((~hskp12) | c3_1(a113)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1605, 1602])).
% 1.19/1.44 tff(1607,plain,
% 1.19/1.44 ((~hskp12) | c3_1(a113)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1606, 1602])).
% 1.19/1.44 tff(1608,plain,
% 1.19/1.44 ((~hskp12) | c3_1(a113)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1607, 1602])).
% 1.19/1.44 tff(1609,plain,
% 1.19/1.44 (c3_1(a113)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1608, 1595])).
% 1.19/1.44 tff(1610,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1611,plain,
% 1.19/1.44 (((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a113) | (~c3_1(a113)) | (~c1_1(a113)) | c3_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1612,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a113) | (~c3_1(a113)) | (~c1_1(a113)) | c3_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[1611])).
% 1.19/1.44 tff(1613,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a113) | (~c3_1(a113)) | (~c1_1(a113)) | c3_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[1612, 1610])).
% 1.19/1.44 tff(1614,plain,
% 1.19/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a113) | (~c3_1(a113)) | (~c1_1(a113)) | c3_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(1615,plain,
% 1.19/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.19/1.44 tff(1616,plain,
% 1.19/1.44 (~c1_1(a113)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1615, 142, 1070, 1069, 1068, 1609, 49, 85, 1601, 1577, 463])).
% 1.19/1.44 tff(1617,plain,
% 1.19/1.44 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.19/1.44 inference(bind,[status(th)],[])).
% 1.19/1.44 tff(1618,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[1617])).
% 1.19/1.44 tff(1619,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1620,plain,
% 1.19/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.19/1.44 inference(bind,[status(th)],[])).
% 1.19/1.44 tff(1621,plain,
% 1.19/1.44 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[1620])).
% 1.19/1.44 tff(1622,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.19/1.44 tff(1623,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 1.19/1.44 tff(1624,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1623, 1619])).
% 1.19/1.44 tff(1625,plain,(
% 1.19/1.44 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.44 inference(skolemize,[status(sab)],[1624])).
% 1.19/1.44 tff(1626,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1625, 1618])).
% 1.19/1.44 tff(1627,plain,
% 1.19/1.44 (((~hskp12) | (~c0_1(a113))) <=> ((~hskp12) | (~c0_1(a113)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1628,plain,
% 1.19/1.44 (((~c0_1(a113)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a113)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1629,axiom,((~c0_1(a113)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.19/1.44 tff(1630,plain,
% 1.19/1.44 ((~hskp12) | (~c0_1(a113))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 1.19/1.44 tff(1631,plain,
% 1.19/1.44 ((~hskp12) | (~c0_1(a113))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1630, 1627])).
% 1.19/1.44 tff(1632,plain,
% 1.19/1.44 (~c0_1(a113)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1631, 1595])).
% 1.19/1.44 tff(1633,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1634,plain,
% 1.19/1.44 ((hskp0 | (~ndr1_0) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a113) | c1_1(a113) | c0_1(a113)) <=> (hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1635,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a113) | c1_1(a113) | c0_1(a113))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[1634])).
% 1.19/1.44 tff(1636,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a113) | c1_1(a113) | c0_1(a113))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[1635, 1633])).
% 1.19/1.44 tff(1637,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a113) | c1_1(a113) | c0_1(a113))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(1638,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 1.19/1.44 tff(1639,plain,
% 1.19/1.44 (hskp0),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1638, 142, 1588, 1567, 1566, 1632, 1601, 1626, 1616])).
% 1.19/1.44 tff(1640,plain,
% 1.19/1.44 (((~hskp0) | (~c0_1(a101))) <=> ((~hskp0) | (~c0_1(a101)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1641,plain,
% 1.19/1.44 (((~c0_1(a101)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a101)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1642,axiom,((~c0_1(a101)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.19/1.44 tff(1643,plain,
% 1.19/1.44 ((~hskp0) | (~c0_1(a101))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.19/1.44 tff(1644,plain,
% 1.19/1.44 ((~hskp0) | (~c0_1(a101))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1643, 1640])).
% 1.19/1.44 tff(1645,plain,
% 1.19/1.44 (~c0_1(a101)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1644, 1639])).
% 1.19/1.44 tff(1646,plain,
% 1.19/1.44 (((~hskp0) | c3_1(a101)) <=> ((~hskp0) | c3_1(a101))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1647,axiom,((~hskp0) | c3_1(a101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.19/1.44 tff(1648,plain,
% 1.19/1.44 ((~hskp0) | c3_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1647, 1646])).
% 1.19/1.44 tff(1649,plain,
% 1.19/1.44 ((~hskp0) | c3_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1648, 1646])).
% 1.19/1.44 tff(1650,plain,
% 1.19/1.44 ((~hskp0) | c3_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1649, 1646])).
% 1.19/1.44 tff(1651,plain,
% 1.19/1.44 ((~hskp0) | c3_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1650, 1646])).
% 1.19/1.44 tff(1652,plain,
% 1.19/1.44 ((~hskp0) | c3_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1651, 1646])).
% 1.19/1.44 tff(1653,plain,
% 1.19/1.44 (c3_1(a101)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1652, 1639])).
% 1.19/1.44 tff(1654,plain,
% 1.19/1.44 (((~hskp0) | c2_1(a101)) <=> ((~hskp0) | c2_1(a101))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1655,axiom,((~hskp0) | c2_1(a101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.19/1.44 tff(1656,plain,
% 1.19/1.44 ((~hskp0) | c2_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 1.19/1.44 tff(1657,plain,
% 1.19/1.44 ((~hskp0) | c2_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1656, 1654])).
% 1.19/1.44 tff(1658,plain,
% 1.19/1.44 ((~hskp0) | c2_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1657, 1654])).
% 1.19/1.44 tff(1659,plain,
% 1.19/1.44 ((~hskp0) | c2_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1658, 1654])).
% 1.19/1.44 tff(1660,plain,
% 1.19/1.44 ((~hskp0) | c2_1(a101)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1659, 1654])).
% 1.19/1.44 tff(1661,plain,
% 1.19/1.44 (c2_1(a101)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1660, 1639])).
% 1.19/1.44 tff(1662,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1663,plain,
% 1.19/1.44 ((hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a101) | (~c3_1(a101)) | (~c2_1(a101))) <=> (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1664,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a101) | (~c3_1(a101)) | (~c2_1(a101)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[1663])).
% 1.19/1.44 tff(1665,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a101) | (~c3_1(a101)) | (~c2_1(a101)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[1664, 1662])).
% 1.19/1.44 tff(1666,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a101) | (~c3_1(a101)) | (~c2_1(a101)))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(1667,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 1.19/1.44 tff(1668,plain,
% 1.19/1.44 (hskp10),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1667, 142, 1661, 1653, 1218, 85, 1645, 1427, 463])).
% 1.19/1.44 tff(1669,plain,
% 1.19/1.44 (~c3_1(a111)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1235, 1668])).
% 1.19/1.44 tff(1670,plain,
% 1.19/1.44 (~c0_1(a111)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1247, 1668])).
% 1.19/1.44 tff(1671,plain,
% 1.19/1.44 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1672,plain,
% 1.19/1.44 ((hskp5 | (~ndr1_0) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> (hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1673,plain,
% 1.19/1.44 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111)))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[1672])).
% 1.19/1.44 tff(1674,plain,
% 1.19/1.44 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111))),
% 1.19/1.44 inference(transitivity,[status(thm)],[1673, 1671])).
% 1.19/1.44 tff(1675,plain,
% 1.19/1.44 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(1676,plain,
% 1.19/1.44 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1675, 1674])).
% 1.19/1.44 tff(1677,plain,
% 1.19/1.44 (c1_1(a111)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1676, 142, 462, 1670, 1669, 206])).
% 1.19/1.44 tff(1678,plain,
% 1.19/1.44 (~c2_1(a111)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1241, 1668])).
% 1.19/1.44 tff(1679,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1680,plain,
% 1.19/1.44 ((hskp6 | (~ndr1_0) | c1_1(a113) | c2_1(a113) | (~c3_1(a113)) | c2_1(a111) | c0_1(a111) | (~c1_1(a111))) <=> (hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1681,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a113) | c2_1(a113) | (~c3_1(a113)) | c2_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113)))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[1680])).
% 1.19/1.44 tff(1682,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a113) | c2_1(a113) | (~c3_1(a113)) | c2_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113))),
% 1.19/1.44 inference(transitivity,[status(thm)],[1681, 1679])).
% 1.19/1.44 tff(1683,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a113) | c2_1(a113) | (~c3_1(a113)) | c2_1(a111) | c0_1(a111) | (~c1_1(a111)))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(1684,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 1.19/1.44 tff(1685,plain,
% 1.19/1.44 (hskp6 | (~c1_1(a111))),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1684, 142, 1609, 1601, 1670, 1678, 854, 1616])).
% 1.19/1.44 tff(1686,plain,
% 1.19/1.44 (hskp6),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1685, 1677])).
% 1.19/1.44 tff(1687,plain,
% 1.19/1.44 (c2_1(a107)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[431, 1686])).
% 1.19/1.44 tff(1688,plain,
% 1.19/1.44 (c1_1(a107)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[439, 1686])).
% 1.19/1.44 tff(1689,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1690,plain,
% 1.19/1.44 (((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(1691,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[1690])).
% 1.19/1.44 tff(1692,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[1691, 1689])).
% 1.19/1.44 tff(1693,plain,
% 1.19/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(1694,plain,
% 1.19/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 1.19/1.44 tff(1695,plain,
% 1.19/1.44 (~c3_1(a107)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[1694, 142, 1070, 1069, 1068, 1588, 1688, 1687, 1567, 1566, 84])).
% 1.19/1.44 tff(1696,plain,
% 1.19/1.44 (~c0_1(a107)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[410, 1686])).
% 1.19/1.44 tff(1697,plain,
% 1.19/1.44 ($false),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[454, 142, 1374, 1688, 1687, 1371, 1370, 1696, 181, 1695])).
% 1.19/1.45 tff(1698,plain,(hskp5 | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c3_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.45 tff(1699,plain,
% 1.19/1.45 (hskp5),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1698, 1471, 1501, 1470, 85, 49])).
% 1.19/1.45 tff(1700,plain,
% 1.19/1.45 (c1_1(a106)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[233, 1699])).
% 1.19/1.45 tff(1701,plain,
% 1.19/1.45 (c0_1(a106)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[304, 1699])).
% 1.19/1.45 tff(1702,plain,
% 1.19/1.45 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1703,plain,
% 1.19/1.45 ((hskp24 | hskp1 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106))) <=> (hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1704,plain,
% 1.19/1.45 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106))))),
% 1.19/1.45 inference(monotonicity,[status(thm)],[1703])).
% 1.19/1.45 tff(1705,plain,
% 1.19/1.45 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 1.19/1.45 inference(transitivity,[status(thm)],[1704, 1702])).
% 1.19/1.45 tff(1706,plain,
% 1.19/1.45 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))),
% 1.19/1.45 inference(quant_inst,[status(thm)],[])).
% 1.19/1.45 tff(1707,plain,
% 1.19/1.45 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 1.19/1.45 tff(1708,plain,
% 1.19/1.45 (hskp1 | (~c0_1(a106)) | (~c1_1(a106))),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1707, 142, 1219, 97, 21])).
% 1.19/1.45 tff(1709,plain,
% 1.19/1.45 (hskp1),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1708, 1701, 1700])).
% 1.19/1.45 tff(1710,plain,
% 1.19/1.45 (~c1_1(a102)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1158, 1709])).
% 1.19/1.45 tff(1711,plain,
% 1.19/1.45 (~c0_1(a102)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1164, 1709])).
% 1.19/1.45 tff(1712,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1713,plain,
% 1.19/1.45 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102))) <=> (c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1714,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 1.19/1.45 inference(monotonicity,[status(thm)],[1713])).
% 1.19/1.45 tff(1715,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.45 inference(transitivity,[status(thm)],[1714, 1712])).
% 1.19/1.45 tff(1716,plain,
% 1.19/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))),
% 1.19/1.45 inference(quant_inst,[status(thm)],[])).
% 1.19/1.45 tff(1717,plain,
% 1.19/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 1.19/1.45 tff(1718,plain,
% 1.19/1.45 (~c3_1(a102)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1717, 142, 1471, 1501, 1470, 1513, 1512, 1511, 1711, 1710, 84])).
% 1.19/1.45 tff(1719,plain,
% 1.19/1.45 (c2_1(a102)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1208, 1709])).
% 1.19/1.45 tff(1720,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1721,plain,
% 1.19/1.45 (((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102)) <=> ((~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1722,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163))))),
% 1.19/1.45 inference(monotonicity,[status(thm)],[1721])).
% 1.19/1.45 tff(1723,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163)))),
% 1.19/1.45 inference(transitivity,[status(thm)],[1722, 1720])).
% 1.19/1.45 tff(1724,plain,
% 1.19/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))),
% 1.19/1.45 inference(quant_inst,[status(thm)],[])).
% 1.19/1.45 tff(1725,plain,
% 1.19/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 1.19/1.45 tff(1726,plain,
% 1.19/1.45 (~c0_1(a163)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1725, 142, 1719, 1218, 85, 1711, 1710, 331, 1718])).
% 1.19/1.45 tff(1727,assumption,(~hskp4), introduced(assumption)).
% 1.19/1.45 tff(1728,plain,
% 1.19/1.45 (^[U: $i] : refl((hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.19/1.45 inference(bind,[status(th)],[])).
% 1.19/1.45 tff(1729,plain,
% 1.19/1.45 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(quant_intro,[status(thm)],[1728])).
% 1.19/1.45 tff(1730,plain,
% 1.19/1.45 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1731,plain,
% 1.19/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp10) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp10) <=> (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.19/1.45 inference(bind,[status(th)],[])).
% 1.19/1.45 tff(1732,plain,
% 1.19/1.45 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp10) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(quant_intro,[status(thm)],[1731])).
% 1.19/1.45 tff(1733,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.19/1.45 tff(1734,plain,
% 1.19/1.45 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 1.19/1.45 tff(1735,plain,
% 1.19/1.45 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1734, 1730])).
% 1.19/1.45 tff(1736,plain,(
% 1.19/1.45 ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(skolemize,[status(sab)],[1735])).
% 1.19/1.45 tff(1737,plain,
% 1.19/1.45 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1736, 1729])).
% 1.19/1.45 tff(1738,plain,
% 1.19/1.45 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1739,plain,
% 1.19/1.45 ((hskp10 | hskp4 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131))) <=> (hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1740,plain,
% 1.19/1.45 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131)))),
% 1.19/1.45 inference(monotonicity,[status(thm)],[1739])).
% 1.19/1.45 tff(1741,plain,
% 1.19/1.45 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 1.19/1.45 inference(transitivity,[status(thm)],[1740, 1738])).
% 1.19/1.45 tff(1742,plain,
% 1.19/1.45 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))),
% 1.19/1.45 inference(quant_inst,[status(thm)],[])).
% 1.19/1.45 tff(1743,plain,
% 1.19/1.45 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 1.19/1.45 tff(1744,plain,
% 1.19/1.45 (hskp10 | hskp4 | c1_1(a131)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1743, 142, 1070, 1068, 1737])).
% 1.19/1.45 tff(1745,plain,
% 1.19/1.45 (c1_1(a131)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1744, 22, 1727])).
% 1.19/1.45 tff(1746,plain,
% 1.19/1.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1747,plain,
% 1.19/1.45 ((hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163))) <=> (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1748,plain,
% 1.19/1.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)))),
% 1.19/1.45 inference(monotonicity,[status(thm)],[1747])).
% 1.19/1.45 tff(1749,plain,
% 1.19/1.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 1.19/1.45 inference(transitivity,[status(thm)],[1748, 1746])).
% 1.19/1.45 tff(1750,plain,
% 1.19/1.45 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))),
% 1.19/1.45 inference(quant_inst,[status(thm)],[])).
% 1.19/1.45 tff(1751,plain,
% 1.19/1.45 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 1.19/1.45 tff(1752,plain,
% 1.19/1.45 ($false),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1751, 142, 22, 1070, 1068, 49, 1218, 1301, 224, 1745])).
% 1.19/1.45 tff(1753,plain,(hskp10 | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a163) | c0_1(a163) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.19/1.45 tff(1754,plain,
% 1.19/1.45 (hskp10),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1753, 1471, 1470, 49, 1726, 1564])).
% 1.19/1.45 tff(1755,plain,
% 1.19/1.45 (~c0_1(a111)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1247, 1754])).
% 1.19/1.45 tff(1756,plain,
% 1.19/1.45 (~c3_1(a111)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1235, 1754])).
% 1.19/1.45 tff(1757,assumption,(~c2_1(a111)), introduced(assumption)).
% 1.19/1.45 tff(1758,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1759,plain,
% 1.19/1.45 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1760,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 1.19/1.45 inference(monotonicity,[status(thm)],[1759])).
% 1.19/1.45 tff(1761,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 1.19/1.45 inference(transitivity,[status(thm)],[1760, 1758])).
% 1.19/1.45 tff(1762,plain,
% 1.19/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 1.19/1.45 inference(quant_inst,[status(thm)],[])).
% 1.19/1.45 tff(1763,plain,
% 1.19/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.19/1.45 tff(1764,plain,
% 1.19/1.45 (c2_1(a111) | c1_1(a111)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1763, 142, 1516, 1515, 1514, 441, 424, 423, 1377, 96])).
% 1.19/1.45 tff(1765,plain,
% 1.19/1.45 (c1_1(a111)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1764, 1757])).
% 1.19/1.45 tff(1766,plain,
% 1.19/1.45 (c1_1(a135)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1066, 142, 1516, 1515, 1514, 441, 424, 423, 96])).
% 1.19/1.45 tff(1767,assumption,(c1_1(a135)), introduced(assumption)).
% 1.19/1.45 tff(1768,plain,
% 1.19/1.45 (^[U: $i] : refl((hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.19/1.45 inference(bind,[status(th)],[])).
% 1.19/1.45 tff(1769,plain,
% 1.19/1.45 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(quant_intro,[status(thm)],[1768])).
% 1.19/1.45 tff(1770,plain,
% 1.19/1.45 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1771,plain,
% 1.19/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp4) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp4) <=> (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.19/1.45 inference(bind,[status(th)],[])).
% 1.19/1.45 tff(1772,plain,
% 1.19/1.45 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp4) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(quant_intro,[status(thm)],[1771])).
% 1.19/1.45 tff(1773,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 1.19/1.45 tff(1774,plain,
% 1.19/1.45 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 1.19/1.45 tff(1775,plain,
% 1.19/1.45 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1774, 1770])).
% 1.19/1.45 tff(1776,plain,(
% 1.19/1.45 ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(skolemize,[status(sab)],[1775])).
% 1.19/1.45 tff(1777,plain,
% 1.19/1.45 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1776, 1769])).
% 1.19/1.45 tff(1778,plain,
% 1.19/1.45 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1779,plain,
% 1.19/1.45 ((hskp29 | hskp4 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135))) <=> (hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1780,plain,
% 1.19/1.45 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135))))),
% 1.19/1.45 inference(monotonicity,[status(thm)],[1779])).
% 1.19/1.45 tff(1781,plain,
% 1.19/1.45 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.19/1.45 inference(transitivity,[status(thm)],[1780, 1778])).
% 1.19/1.45 tff(1782,plain,
% 1.19/1.45 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.19/1.45 inference(quant_inst,[status(thm)],[])).
% 1.19/1.45 tff(1783,plain,
% 1.19/1.45 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 1.19/1.45 tff(1784,plain,
% 1.19/1.45 (hskp29 | hskp4 | (~c1_1(a135))),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1783, 142, 441, 424, 1777])).
% 1.19/1.45 tff(1785,plain,
% 1.19/1.45 (hskp29),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1784, 1727, 1767])).
% 1.19/1.45 tff(1786,plain,
% 1.19/1.45 (((~hskp29) | c0_1(a128)) <=> ((~hskp29) | c0_1(a128))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1787,axiom,((~hskp29) | c0_1(a128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.19/1.45 tff(1788,plain,
% 1.19/1.45 ((~hskp29) | c0_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1787, 1786])).
% 1.19/1.45 tff(1789,plain,
% 1.19/1.45 ((~hskp29) | c0_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1788, 1786])).
% 1.19/1.45 tff(1790,plain,
% 1.19/1.45 ((~hskp29) | c0_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1789, 1786])).
% 1.19/1.45 tff(1791,plain,
% 1.19/1.45 ((~hskp29) | c0_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1790, 1786])).
% 1.19/1.45 tff(1792,plain,
% 1.19/1.45 ((~hskp29) | c0_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1791, 1786])).
% 1.19/1.45 tff(1793,plain,
% 1.19/1.45 (c0_1(a128)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1792, 1785])).
% 1.19/1.45 tff(1794,assumption,(~hskp13), introduced(assumption)).
% 1.19/1.45 tff(1795,plain,
% 1.19/1.45 (((~hskp29) | c1_1(a128)) <=> ((~hskp29) | c1_1(a128))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1796,axiom,((~hskp29) | c1_1(a128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.19/1.45 tff(1797,plain,
% 1.19/1.45 ((~hskp29) | c1_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 1.19/1.45 tff(1798,plain,
% 1.19/1.45 ((~hskp29) | c1_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1797, 1795])).
% 1.19/1.45 tff(1799,plain,
% 1.19/1.45 ((~hskp29) | c1_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1798, 1795])).
% 1.19/1.45 tff(1800,plain,
% 1.19/1.45 ((~hskp29) | c1_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1799, 1795])).
% 1.19/1.45 tff(1801,plain,
% 1.19/1.45 ((~hskp29) | c1_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1800, 1795])).
% 1.19/1.45 tff(1802,plain,
% 1.19/1.45 (c1_1(a128)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1801, 1785])).
% 1.19/1.45 tff(1803,plain,
% 1.19/1.45 (((~hskp29) | c2_1(a128)) <=> ((~hskp29) | c2_1(a128))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(1804,axiom,((~hskp29) | c2_1(a128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.19/1.45 tff(1805,plain,
% 1.19/1.45 ((~hskp29) | c2_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 1.19/1.45 tff(1806,plain,
% 1.19/1.45 ((~hskp29) | c2_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1805, 1803])).
% 1.19/1.45 tff(1807,plain,
% 1.19/1.45 ((~hskp29) | c2_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1806, 1803])).
% 1.19/1.45 tff(1808,plain,
% 1.19/1.45 ((~hskp29) | c2_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1807, 1803])).
% 1.19/1.45 tff(1809,plain,
% 1.19/1.45 ((~hskp29) | c2_1(a128)),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[1808, 1803])).
% 1.19/1.45 tff(1810,plain,
% 1.19/1.45 (c2_1(a128)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[1809, 1785])).
% 1.19/1.45 tff(1811,assumption,(c1_1(a128)), introduced(assumption)).
% 1.19/1.45 tff(1812,assumption,(c0_1(a128)), introduced(assumption)).
% 1.19/1.45 tff(1813,plain,
% 1.19/1.46 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)))),
% 1.19/1.46 inference(rewrite,[status(thm)],[])).
% 1.19/1.46 tff(1814,plain,
% 1.19/1.46 ((hskp13 | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)) | c2_1(a111) | c0_1(a111) | c3_1(a111)) <=> (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)))),
% 1.19/1.46 inference(rewrite,[status(thm)],[])).
% 1.19/1.46 tff(1815,plain,
% 1.19/1.46 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)) | c2_1(a111) | c0_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128))))),
% 1.19/1.46 inference(monotonicity,[status(thm)],[1814])).
% 1.19/1.46 tff(1816,plain,
% 1.19/1.46 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)) | c2_1(a111) | c0_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)))),
% 1.19/1.46 inference(transitivity,[status(thm)],[1815, 1813])).
% 1.19/1.46 tff(1817,plain,
% 1.19/1.46 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)) | c2_1(a111) | c0_1(a111) | c3_1(a111))),
% 1.19/1.46 inference(quant_inst,[status(thm)],[])).
% 1.19/1.46 tff(1818,plain,
% 1.19/1.46 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128))),
% 1.19/1.46 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 1.19/1.46 tff(1819,plain,
% 1.19/1.46 (hskp13 | (~c3_1(a128))),
% 1.19/1.46 inference(unit_resolution,[status(thm)],[1818, 142, 1812, 1811, 1378, 1757, 1377, 1229])).
% 1.19/1.46 tff(1820,plain,
% 1.19/1.46 (~c3_1(a128)),
% 1.19/1.46 inference(unit_resolution,[status(thm)],[1819, 1794])).
% 1.19/1.46 tff(1821,plain,
% 1.19/1.46 (^[U: $i] : refl((hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.19/1.46 inference(bind,[status(th)],[])).
% 1.19/1.46 tff(1822,plain,
% 1.19/1.46 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.19/1.46 inference(quant_intro,[status(thm)],[1821])).
% 1.19/1.46 tff(1823,plain,
% 1.19/1.46 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.19/1.46 inference(rewrite,[status(thm)],[])).
% 1.19/1.46 tff(1824,plain,
% 1.19/1.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) | hskp4) <=> ((hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) | hskp4) <=> (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.19/1.46 inference(bind,[status(th)],[])).
% 1.19/1.46 tff(1825,plain,
% 1.19/1.46 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) | hskp4) <=> ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.19/1.46 inference(quant_intro,[status(thm)],[1824])).
% 1.19/1.46 tff(1826,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 1.19/1.46 tff(1827,plain,
% 1.19/1.46 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.19/1.46 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 1.19/1.46 tff(1828,plain,
% 1.19/1.46 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.19/1.46 inference(modus_ponens,[status(thm)],[1827, 1823])).
% 1.19/1.46 tff(1829,plain,(
% 1.19/1.46 ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.19/1.46 inference(skolemize,[status(sab)],[1828])).
% 1.19/1.46 tff(1830,plain,
% 1.19/1.46 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.19/1.46 inference(modus_ponens,[status(thm)],[1829, 1822])).
% 1.19/1.46 tff(1831,assumption,(c2_1(a128)), introduced(assumption)).
% 1.19/1.46 tff(1832,plain,
% 1.19/1.46 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128)))),
% 1.19/1.46 inference(rewrite,[status(thm)],[])).
% 1.19/1.46 tff(1833,plain,
% 1.19/1.46 ((hskp13 | hskp4 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c2_1(a128))) <=> (hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128)))),
% 1.19/1.46 inference(rewrite,[status(thm)],[])).
% 1.19/1.46 tff(1834,plain,
% 1.19/1.46 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c2_1(a128)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128))))),
% 1.19/1.46 inference(monotonicity,[status(thm)],[1833])).
% 1.19/1.46 tff(1835,plain,
% 1.19/1.46 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c2_1(a128)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128)))),
% 1.19/1.46 inference(transitivity,[status(thm)],[1834, 1832])).
% 1.19/1.46 tff(1836,plain,
% 1.19/1.46 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c2_1(a128)))),
% 1.19/1.46 inference(quant_inst,[status(thm)],[])).
% 1.19/1.46 tff(1837,plain,
% 1.19/1.46 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128))),
% 1.19/1.46 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 1.19/1.46 tff(1838,plain,
% 1.19/1.46 (hskp13 | c3_1(a128)),
% 1.19/1.46 inference(unit_resolution,[status(thm)],[1837, 142, 1727, 1811, 1831, 1830])).
% 1.19/1.46 tff(1839,plain,
% 1.19/1.46 ($false),
% 1.19/1.46 inference(unit_resolution,[status(thm)],[1838, 1820, 1794])).
% 1.19/1.46 tff(1840,plain,(hskp13 | hskp4 | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c0_1(a111) | c2_1(a111) | c3_1(a111)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.46 tff(1841,plain,
% 1.19/1.46 ($false),
% 1.19/1.46 inference(unit_resolution,[status(thm)],[1840, 1810, 1802, 1794, 1727, 1793, 1378, 1757, 1377])).
% 1.19/1.46 tff(1842,plain,(hskp4 | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a135)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1843,plain,
% 1.29/1.46 (hskp13),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1842, 1757, 1378, 1727, 1377, 1766, 441, 424])).
% 1.29/1.46 tff(1844,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1390, 1843, 1765, 424, 423, 1378, 1377, 441])).
% 1.29/1.46 tff(1845,plain,(c2_1(a111) | c2_1(a135) | c3_1(a135) | c0_1(a111) | c3_1(a111) | (~c0_1(a135)) | hskp4 | (~c1_1(a118)) | (~c2_1(a118)) | (~c3_1(a118))), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1846,plain,
% 1.29/1.46 (c2_1(a111)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1845, 1727, 423, 1378, 1377, 441, 424, 1516, 1515, 1514])).
% 1.29/1.46 tff(1847,plain,
% 1.29/1.46 (~hskp10),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1241, 1846])).
% 1.29/1.46 tff(1848,plain,
% 1.29/1.46 (c1_1(a131)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1744, 1847, 1727])).
% 1.29/1.46 tff(1849,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1751, 142, 1847, 1070, 1068, 49, 1218, 1301, 224, 1848])).
% 1.29/1.46 tff(1850,plain,(hskp4 | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a163) | c0_1(a163) | c3_1(a135) | c0_1(a111) | c3_1(a111) | (~c0_1(a135)) | c2_1(a135) | (~c1_1(a118)) | (~c2_1(a118)) | (~c3_1(a118))), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1851,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1850, 1756, 1755, 1470, 49, 1726, 1370, 1564, 1471, 1374, 1371, 1513, 1512, 1511])).
% 1.29/1.46 tff(1852,plain,(hskp31 | c1_1(a163) | c3_1(a163) | c2_1(a106)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1853,plain,
% 1.29/1.46 (c2_1(a106)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1852, 1464, 85, 49])).
% 1.29/1.46 tff(1854,plain,
% 1.29/1.46 (~hskp5),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[892, 1853])).
% 1.29/1.46 tff(1855,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1698, 1854, 1468, 1467, 1466, 85, 49])).
% 1.29/1.46 tff(1856,plain,(c3_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1857,plain,
% 1.29/1.46 (c3_1(a163)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1856, 49])).
% 1.29/1.46 tff(1858,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1859,plain,
% 1.29/1.46 ((hskp17 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1860,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1859])).
% 1.29/1.46 tff(1861,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1860, 1858])).
% 1.29/1.46 tff(1862,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1863,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 1.29/1.46 tff(1864,plain,
% 1.29/1.46 (hskp17 | (~c2_1(a163)) | (~c3_1(a163)) | (~c0_1(a163))),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1863, 142, 49, 1533])).
% 1.29/1.46 tff(1865,plain,
% 1.29/1.46 (hskp17),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1864, 98, 1218, 1857])).
% 1.29/1.46 tff(1866,plain,
% 1.29/1.46 (~c1_1(a132)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[750, 1865])).
% 1.29/1.46 tff(1867,plain,
% 1.29/1.46 (~c0_1(a132)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[756, 1865])).
% 1.29/1.46 tff(1868,plain,
% 1.29/1.46 (c3_1(a132)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[765, 1865])).
% 1.29/1.46 tff(1869,plain,
% 1.29/1.46 (~c2_1(a141)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1283, 142, 737, 736, 767, 1868, 1867, 1866, 84])).
% 1.29/1.46 tff(1870,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1290, 142, 737, 736, 767, 49, 1218, 290, 98, 1869])).
% 1.29/1.46 tff(1871,plain,((~c0_1(a163)) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141)) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1872,plain,
% 1.29/1.46 (~c0_1(a163)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1871, 74, 66, 58, 49])).
% 1.29/1.46 tff(1873,plain,
% 1.29/1.46 (hskp10),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1416, 1872])).
% 1.29/1.46 tff(1874,plain,
% 1.29/1.46 (~c3_1(a111)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1235, 1873])).
% 1.29/1.46 tff(1875,plain,
% 1.29/1.46 (~c0_1(a111)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1247, 1873])).
% 1.29/1.46 tff(1876,plain,
% 1.29/1.46 (~c2_1(a111)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1241, 1873])).
% 1.29/1.46 tff(1877,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1878,plain,
% 1.29/1.46 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1879,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1878])).
% 1.29/1.46 tff(1880,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1879, 1877])).
% 1.29/1.46 tff(1881,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1882,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 1.29/1.46 tff(1883,plain,
% 1.29/1.46 ((~c2_1(a141)) | c0_1(a163)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1882, 142, 737, 736, 767, 49, 1857, 84])).
% 1.29/1.46 tff(1884,plain,
% 1.29/1.46 (~c2_1(a141)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1883, 224])).
% 1.29/1.46 tff(1885,assumption,(~c0_1(a135)), introduced(assumption)).
% 1.29/1.46 tff(1886,plain,
% 1.29/1.46 (~hskp19),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[420, 1885])).
% 1.29/1.46 tff(1887,plain,
% 1.29/1.46 (~hskp11),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[974, 1886])).
% 1.29/1.46 tff(1888,plain,
% 1.29/1.46 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1889,plain,
% 1.29/1.46 ((hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a163)) | (~c2_1(a163)) | (~c0_1(a163))) <=> (hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1890,plain,
% 1.29/1.46 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a163)) | (~c2_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1889])).
% 1.29/1.46 tff(1891,plain,
% 1.29/1.46 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a163)) | (~c2_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1890, 1888])).
% 1.29/1.46 tff(1892,plain,
% 1.29/1.46 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a163)) | (~c2_1(a163)) | (~c0_1(a163)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1893,plain,
% 1.29/1.46 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1892, 1891])).
% 1.29/1.46 tff(1894,plain,
% 1.29/1.46 (hskp19 | hskp11 | (~c3_1(a163)) | (~c0_1(a163))),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1893, 142, 1218, 941])).
% 1.29/1.46 tff(1895,plain,
% 1.29/1.46 (~c0_1(a163)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1894, 1887, 1857, 1886])).
% 1.29/1.46 tff(1896,plain,
% 1.29/1.46 (hskp19 | hskp11 | (~c2_1(a141))),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1051, 142, 737, 767, 941])).
% 1.29/1.46 tff(1897,plain,
% 1.29/1.46 (~c2_1(a141)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1896, 1887, 1886])).
% 1.29/1.46 tff(1898,plain,
% 1.29/1.46 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.29/1.46 inference(bind,[status(th)],[])).
% 1.29/1.46 tff(1899,plain,
% 1.29/1.46 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.29/1.46 inference(quant_intro,[status(thm)],[1898])).
% 1.29/1.46 tff(1900,plain,
% 1.29/1.46 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1901,plain,
% 1.29/1.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.29/1.46 inference(bind,[status(th)],[])).
% 1.29/1.46 tff(1902,plain,
% 1.29/1.46 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.29/1.46 inference(quant_intro,[status(thm)],[1901])).
% 1.29/1.46 tff(1903,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.29/1.46 tff(1904,plain,
% 1.29/1.46 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.29/1.46 tff(1905,plain,
% 1.29/1.46 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1904, 1900])).
% 1.29/1.46 tff(1906,plain,(
% 1.29/1.46 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.29/1.46 inference(skolemize,[status(sab)],[1905])).
% 1.29/1.46 tff(1907,plain,
% 1.29/1.46 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1906, 1899])).
% 1.29/1.46 tff(1908,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1909,plain,
% 1.29/1.46 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | (~c3_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1910,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | (~c3_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1909])).
% 1.29/1.46 tff(1911,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | (~c3_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1910, 1908])).
% 1.29/1.46 tff(1912,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | (~c3_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1913,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1912, 1911])).
% 1.29/1.46 tff(1914,plain,
% 1.29/1.46 (c0_1(a135) | (~c3_1(a135)) | c0_1(a163)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1913, 142, 737, 736, 767, 49, 1857, 424, 723])).
% 1.29/1.46 tff(1915,plain,
% 1.29/1.46 (~c3_1(a135)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1914, 1895, 1885])).
% 1.29/1.46 tff(1916,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1917,plain,
% 1.29/1.46 ((hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | c3_1(a135)) <=> (hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1918,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | c3_1(a135))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1917])).
% 1.29/1.46 tff(1919,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | c3_1(a135))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1918, 1916])).
% 1.29/1.46 tff(1920,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | c3_1(a135))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1921,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 1.29/1.46 tff(1922,plain,
% 1.29/1.46 (hskp13 | c0_1(a135) | c3_1(a135)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1921, 142, 737, 736, 767, 424, 1229])).
% 1.29/1.46 tff(1923,plain,
% 1.29/1.46 (hskp13),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1922, 1915, 1885])).
% 1.29/1.46 tff(1924,plain,
% 1.29/1.46 (~c3_1(a114)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[566, 1923])).
% 1.29/1.46 tff(1925,plain,
% 1.29/1.46 (c2_1(a114)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[574, 1923])).
% 1.29/1.46 tff(1926,plain,
% 1.29/1.46 (c1_1(a114)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[582, 1923])).
% 1.29/1.46 tff(1927,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1928,plain,
% 1.29/1.46 ((hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141))) <=> (hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1929,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1928])).
% 1.29/1.46 tff(1930,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1929, 1927])).
% 1.29/1.47 tff(1931,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(1932,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[1931, 1930])).
% 1.29/1.47 tff(1933,plain,
% 1.29/1.47 (hskp12),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1932, 142, 737, 736, 1926, 1925, 1924, 1907, 1897])).
% 1.29/1.47 tff(1934,plain,
% 1.29/1.47 (~c2_1(a113)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1600, 1933])).
% 1.29/1.47 tff(1935,plain,
% 1.29/1.47 (~c0_1(a113)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1631, 1933])).
% 1.29/1.47 tff(1936,plain,
% 1.29/1.47 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1937,plain,
% 1.29/1.47 ((hskp19 | (~ndr1_0) | c3_1(a135) | c2_1(a135) | (~c1_1(a135))) <=> (hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1938,plain,
% 1.29/1.47 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a135) | c2_1(a135) | (~c1_1(a135)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[1937])).
% 1.29/1.47 tff(1939,plain,
% 1.29/1.47 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a135) | c2_1(a135) | (~c1_1(a135)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[1938, 1936])).
% 1.29/1.47 tff(1940,plain,
% 1.29/1.47 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a135) | c2_1(a135) | (~c1_1(a135)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(1941,plain,
% 1.29/1.47 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 1.29/1.47 tff(1942,plain,
% 1.29/1.47 (hskp19 | c3_1(a135) | (~c1_1(a135))),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1941, 142, 424, 11])).
% 1.29/1.47 tff(1943,plain,
% 1.29/1.47 (~c1_1(a135)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1942, 1915, 1886])).
% 1.29/1.47 tff(1944,plain,
% 1.29/1.47 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1945,plain,
% 1.29/1.47 ((hskp5 | (~ndr1_0) | c3_1(a135) | c1_1(a135) | c0_1(a135)) <=> (hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1946,plain,
% 1.29/1.47 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a135) | c1_1(a135) | c0_1(a135))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[1945])).
% 1.29/1.47 tff(1947,plain,
% 1.29/1.47 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a135) | c1_1(a135) | c0_1(a135))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135))),
% 1.29/1.47 inference(transitivity,[status(thm)],[1946, 1944])).
% 1.29/1.47 tff(1948,plain,
% 1.29/1.47 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a135) | c1_1(a135) | c0_1(a135))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(1949,plain,
% 1.29/1.47 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 1.29/1.47 tff(1950,plain,
% 1.29/1.47 (hskp5),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1949, 142, 1885, 1915, 206, 1943])).
% 1.29/1.47 tff(1951,plain,
% 1.29/1.47 (c1_1(a106)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[233, 1950])).
% 1.29/1.47 tff(1952,plain,
% 1.29/1.47 (c0_1(a106)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[304, 1950])).
% 1.29/1.47 tff(1953,plain,
% 1.29/1.47 (c3_1(a113)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1608, 1933])).
% 1.29/1.47 tff(1954,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1955,plain,
% 1.29/1.47 (((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1956,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[1955])).
% 1.29/1.47 tff(1957,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163))),
% 1.29/1.47 inference(transitivity,[status(thm)],[1956, 1954])).
% 1.29/1.47 tff(1958,plain,
% 1.29/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(1959,plain,
% 1.29/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 1.29/1.47 tff(1960,plain,
% 1.29/1.47 (~c3_1(a106)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1959, 142, 1953, 1952, 1951, 49, 1857, 1935, 1934, 723, 1895])).
% 1.29/1.47 tff(1961,plain,
% 1.29/1.47 (~c2_1(a106)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[892, 1950])).
% 1.29/1.47 tff(1962,plain,
% 1.29/1.47 ($false),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[221, 142, 1886, 1951, 1961, 11, 1960])).
% 1.29/1.47 tff(1963,plain,(c0_1(a135) | c1_1(a163) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a135)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.47 tff(1964,plain,
% 1.29/1.47 (c0_1(a135)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1963, 424, 737, 736, 767, 49])).
% 1.29/1.47 tff(1965,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1966,plain,
% 1.29/1.47 (((~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c1_1(a135) | (~c0_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1967,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c1_1(a135) | (~c0_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[1966])).
% 1.29/1.47 tff(1968,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c1_1(a135) | (~c0_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163))),
% 1.29/1.47 inference(transitivity,[status(thm)],[1967, 1965])).
% 1.29/1.47 tff(1969,plain,
% 1.29/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c1_1(a135) | (~c0_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(1970,plain,
% 1.29/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 1.29/1.47 tff(1971,plain,
% 1.29/1.47 (c1_1(a135)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1970, 142, 737, 736, 1964, 49, 1857, 424, 784, 224, 1884])).
% 1.29/1.47 tff(1972,plain,
% 1.29/1.47 (hskp10 | c0_1(a163)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1415, 142, 737, 736, 767, 49, 1218, 1301])).
% 1.29/1.47 tff(1973,plain,
% 1.29/1.47 (hskp10),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1972, 224])).
% 1.29/1.47 tff(1974,plain,
% 1.29/1.47 (~c3_1(a111)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1235, 1973])).
% 1.29/1.47 tff(1975,plain,
% 1.29/1.47 (~c2_1(a111)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1241, 1973])).
% 1.29/1.47 tff(1976,plain,
% 1.29/1.47 (~c0_1(a111)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1247, 1973])).
% 1.29/1.47 tff(1977,plain,
% 1.29/1.47 (hskp13),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1254, 142, 737, 736, 767, 1976, 1975, 1974, 1229])).
% 1.29/1.47 tff(1978,plain,
% 1.29/1.47 (~c3_1(a114)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[566, 1977])).
% 1.29/1.47 tff(1979,plain,
% 1.29/1.47 (c2_1(a114)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[574, 1977])).
% 1.29/1.47 tff(1980,plain,
% 1.29/1.47 (c1_1(a114)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[582, 1977])).
% 1.29/1.47 tff(1981,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1982,plain,
% 1.29/1.47 ((hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135))) <=> (hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1983,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[1982])).
% 1.29/1.47 tff(1984,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[1983, 1981])).
% 1.29/1.47 tff(1985,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(1986,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[1985, 1984])).
% 1.29/1.47 tff(1987,plain,
% 1.29/1.47 (hskp12),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1986, 142, 1964, 1980, 1979, 424, 1978, 1907, 1971])).
% 1.29/1.47 tff(1988,plain,
% 1.29/1.47 (~c2_1(a113)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1600, 1987])).
% 1.29/1.47 tff(1989,plain,
% 1.29/1.47 (~c0_1(a113)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1631, 1987])).
% 1.29/1.47 tff(1990,plain,
% 1.29/1.47 (c3_1(a113)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1608, 1987])).
% 1.29/1.47 tff(1991,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1992,plain,
% 1.29/1.47 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(1993,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[1992])).
% 1.29/1.47 tff(1994,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163))),
% 1.29/1.47 inference(transitivity,[status(thm)],[1993, 1991])).
% 1.29/1.47 tff(1995,plain,
% 1.29/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(1996,plain,
% 1.29/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[1995, 1994])).
% 1.29/1.47 tff(1997,plain,
% 1.29/1.47 ($false),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1996, 142, 737, 736, 767, 1990, 49, 1857, 1989, 1988, 723, 224])).
% 1.29/1.47 tff(1998,plain,(c0_1(a163) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141)) | c1_1(a163) | c2_1(a135)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.47 tff(1999,plain,
% 1.29/1.47 (c2_1(a135)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1998, 1872, 66, 58, 49, 74])).
% 1.29/1.47 tff(2000,plain,
% 1.29/1.47 (~hskp19),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[402, 1999])).
% 1.29/1.47 tff(2001,plain,
% 1.29/1.47 (~c1_1(a111)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1326, 142, 2000, 1876, 1874, 11])).
% 1.29/1.47 tff(2002,plain,
% 1.29/1.47 ((~c2_1(a141)) | c0_1(a163)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1882, 142, 74, 66, 58, 49, 1857, 84])).
% 1.29/1.47 tff(2003,plain,
% 1.29/1.47 (~c2_1(a141)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2002, 1872])).
% 1.29/1.47 tff(2004,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2005,plain,
% 1.29/1.47 ((hskp2 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a111) | c1_1(a111) | c0_1(a111)) <=> (hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2006,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2005])).
% 1.29/1.47 tff(2007,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2006, 2004])).
% 1.29/1.47 tff(2008,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a111) | c1_1(a111) | c0_1(a111))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2009,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 1.29/1.47 tff(2010,plain,
% 1.29/1.47 (hskp2 | c1_1(a111)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2009, 142, 66, 58, 1875, 1876, 246, 2003])).
% 1.29/1.47 tff(2011,plain,
% 1.29/1.47 (hskp2),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2010, 2001])).
% 1.29/1.47 tff(2012,plain,
% 1.29/1.47 (~c3_1(a103)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[383, 2011])).
% 1.29/1.47 tff(2013,plain,
% 1.29/1.47 (hskp5 | c1_1(a111)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1676, 142, 1875, 1874, 206])).
% 1.29/1.47 tff(2014,plain,
% 1.29/1.47 (hskp5),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2013, 2001])).
% 1.29/1.47 tff(2015,plain,
% 1.29/1.47 (~c2_1(a106)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[892, 2014])).
% 1.29/1.47 tff(2016,plain,
% 1.29/1.47 (hskp19 | c2_1(a111) | (~c1_1(a111))),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1326, 142, 1377, 11])).
% 1.29/1.47 tff(2017,plain,
% 1.29/1.47 (~c1_1(a111)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2016, 1, 1757])).
% 1.29/1.47 tff(2018,plain,
% 1.29/1.47 (hskp5 | c0_1(a111) | c1_1(a111)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1676, 142, 1377, 206])).
% 1.29/1.47 tff(2019,plain,
% 1.29/1.47 (hskp5),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2018, 2017, 1378])).
% 1.29/1.47 tff(2020,plain,
% 1.29/1.47 (c1_1(a106)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[233, 2019])).
% 1.29/1.47 tff(2021,plain,
% 1.29/1.47 (c0_1(a106)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[304, 2019])).
% 1.29/1.47 tff(2022,assumption,(~hskp12), introduced(assumption)).
% 1.29/1.47 tff(2023,plain,
% 1.29/1.47 (c3_1(a106)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[235, 2020, 1])).
% 1.29/1.47 tff(2024,plain,
% 1.29/1.47 (hskp2 | c0_1(a111) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1338, 142, 1757, 97, 246])).
% 1.29/1.47 tff(2025,plain,
% 1.29/1.47 (hskp2),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2024, 2023, 1378, 2020, 2017])).
% 1.29/1.47 tff(2026,plain,
% 1.29/1.47 (c1_1(a103)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[261, 2025])).
% 1.29/1.47 tff(2027,plain,
% 1.29/1.47 (c2_1(a103)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[270, 2026, 1])).
% 1.29/1.47 tff(2028,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2029,plain,
% 1.29/1.47 ((hskp12 | (~ndr1_0) | c3_1(a103) | (~c1_1(a103)) | (~c2_1(a103)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106))) <=> (hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2030,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a103) | (~c1_1(a103)) | (~c2_1(a103)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2029])).
% 1.29/1.47 tff(2031,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a103) | (~c1_1(a103)) | (~c2_1(a103)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2030, 2028])).
% 1.29/1.47 tff(2032,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a103) | (~c1_1(a103)) | (~c2_1(a103)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2033,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 1.29/1.47 tff(2034,plain,
% 1.29/1.47 (hskp12 | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106))),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2033, 142, 97, 263, 1907])).
% 1.29/1.47 tff(2035,plain,
% 1.29/1.47 ($false),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2034, 2027, 2026, 2022, 2021, 2020])).
% 1.29/1.47 tff(2036,plain,(hskp19 | hskp12 | c2_1(a106) | c3_1(a103) | c0_1(a111) | c2_1(a111) | c3_1(a111)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.47 tff(2037,plain,
% 1.29/1.47 (hskp12),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2036, 2015, 2000, 2012, 1876, 1875, 1874])).
% 1.29/1.47 tff(2038,plain,
% 1.29/1.47 (~c2_1(a113)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1600, 2037])).
% 1.29/1.47 tff(2039,plain,
% 1.29/1.47 (~c0_1(a113)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1631, 2037])).
% 1.29/1.47 tff(2040,plain,
% 1.29/1.47 (c3_1(a113)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1608, 2037])).
% 1.29/1.47 tff(2041,plain,
% 1.29/1.47 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(2042,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[2041])).
% 1.29/1.47 tff(2043,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2044,plain,
% 1.29/1.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp16) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp16))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(2045,plain,
% 1.29/1.48 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[2044])).
% 1.29/1.48 tff(2046,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.29/1.48 tff(2047,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 1.29/1.48 tff(2048,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2047, 2043])).
% 1.29/1.48 tff(2049,plain,(
% 1.29/1.48 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.29/1.48 inference(skolemize,[status(sab)],[2048])).
% 1.29/1.48 tff(2050,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2049, 2042])).
% 1.29/1.48 tff(2051,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2052,plain,
% 1.29/1.48 ((hskp16 | (~ndr1_0) | c0_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a111) | c1_1(a111) | c3_1(a111)) <=> (hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2053,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~ndr1_0) | c0_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a111) | c1_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163)))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2052])).
% 1.29/1.48 tff(2054,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~ndr1_0) | c0_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a111) | c1_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2053, 2051])).
% 1.29/1.48 tff(2055,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~ndr1_0) | c0_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a111) | c1_1(a111) | c3_1(a111))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2056,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2055, 2054])).
% 1.29/1.48 tff(2057,plain,
% 1.29/1.48 (hskp16 | c1_1(a111)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2056, 142, 1218, 1857, 1876, 1874, 2050, 1872])).
% 1.29/1.48 tff(2058,plain,
% 1.29/1.48 (hskp16),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2057, 2001])).
% 1.29/1.48 tff(2059,plain,
% 1.29/1.48 (c3_1(a126)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[706, 2058])).
% 1.29/1.48 tff(2060,plain,
% 1.29/1.48 (c1_1(a126)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[698, 2058])).
% 1.29/1.48 tff(2061,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2062,plain,
% 1.29/1.48 (((~ndr1_0) | (~c1_1(a126)) | (~c3_1(a126)) | (~c0_1(a126)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2063,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a126)) | (~c3_1(a126)) | (~c0_1(a126)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163)))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2062])).
% 1.29/1.48 tff(2064,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a126)) | (~c3_1(a126)) | (~c0_1(a126)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2063, 2061])).
% 1.29/1.48 tff(2065,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a126)) | (~c3_1(a126)) | (~c0_1(a126)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2066,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2065, 2064])).
% 1.29/1.48 tff(2067,plain,
% 1.29/1.48 (~c0_1(a126)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2066, 142, 2060, 2059, 2040, 49, 1857, 2039, 2038, 723, 1872])).
% 1.29/1.48 tff(2068,plain,
% 1.29/1.48 (~c2_1(a126)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[712, 2058])).
% 1.29/1.48 tff(2069,plain,
% 1.29/1.48 (c1_1(a106)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[233, 2014])).
% 1.29/1.48 tff(2070,plain,
% 1.29/1.48 (c0_1(a106)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[304, 2014])).
% 1.29/1.48 tff(2071,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2072,plain,
% 1.29/1.48 (((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2073,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163)))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2072])).
% 1.29/1.48 tff(2074,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2073, 2071])).
% 1.29/1.48 tff(2075,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2076,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 1.29/1.48 tff(2077,plain,
% 1.29/1.48 (~c3_1(a106)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2076, 142, 2059, 2070, 2069, 49, 1857, 2068, 723, 1872, 2067])).
% 1.29/1.48 tff(2078,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[221, 142, 2000, 2069, 2015, 11, 2077])).
% 1.29/1.48 tff(2079,plain,((~hskp31) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(2080,plain,
% 1.29/1.48 (~hskp31),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2079, 49])).
% 1.29/1.48 tff(2081,assumption,(c1_1(a131)), introduced(assumption)).
% 1.29/1.48 tff(2082,plain,
% 1.29/1.48 (hskp30),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[140, 2080, 1219])).
% 1.29/1.48 tff(2083,plain,
% 1.29/1.48 (c3_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[914, 2082])).
% 1.29/1.48 tff(2084,plain,
% 1.29/1.48 (c2_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[922, 2082])).
% 1.29/1.48 tff(2085,plain,
% 1.29/1.48 (c0_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[930, 2082])).
% 1.29/1.48 tff(2086,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2087,plain,
% 1.29/1.48 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2088,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2087])).
% 1.29/1.48 tff(2089,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2088, 2086])).
% 1.29/1.48 tff(2090,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2091,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2090, 2089])).
% 1.29/1.48 tff(2092,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2091, 142, 2085, 2084, 2083, 49, 1857, 84, 224, 2081])).
% 1.29/1.48 tff(2093,plain,((~c1_1(a131)) | c1_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(2094,plain,
% 1.29/1.48 (~c1_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2093, 224, 49])).
% 1.29/1.48 tff(2095,plain,
% 1.29/1.48 (hskp28 | c1_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1477, 2080, 142, 2085, 2083, 536])).
% 1.29/1.48 tff(2096,plain,
% 1.29/1.48 (hskp28),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2095, 2094])).
% 1.29/1.48 tff(2097,plain,
% 1.29/1.48 (c3_1(a118)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[476, 2096])).
% 1.29/1.48 tff(2098,plain,
% 1.29/1.48 (c2_1(a118)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[484, 2096])).
% 1.29/1.48 tff(2099,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1563, 485, 493, 1069, 1068, 1070, 34, 477])).
% 1.29/1.48 tff(2100,plain,((~hskp28) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~hskp4)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(2101,plain,
% 1.29/1.48 (~hskp4),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2100, 2096, 2083, 2085, 2084])).
% 1.29/1.48 tff(2102,plain,
% 1.29/1.48 (hskp19),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[983, 2082])).
% 1.29/1.48 tff(2103,plain,
% 1.29/1.48 (~c2_1(a135)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[402, 2102])).
% 1.29/1.48 tff(2104,plain,
% 1.29/1.48 (c0_1(a135)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[420, 2102])).
% 1.29/1.48 tff(2105,plain,
% 1.29/1.48 (c1_1(a118)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[492, 2096])).
% 1.29/1.48 tff(2106,plain,
% 1.29/1.48 (~c3_1(a135)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[396, 2102])).
% 1.29/1.48 tff(2107,plain,
% 1.29/1.48 (hskp10 | hskp4 | c1_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1743, 142, 2085, 2083, 1737])).
% 1.29/1.48 tff(2108,plain,
% 1.29/1.48 (hskp10),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2107, 2101, 2094])).
% 1.29/1.48 tff(2109,plain,
% 1.29/1.48 (~c0_1(a111)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1247, 2108])).
% 1.29/1.48 tff(2110,plain,
% 1.29/1.48 (~c3_1(a111)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1235, 2108])).
% 1.29/1.48 tff(2111,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1850, 2110, 2109, 2083, 49, 2106, 224, 2105, 2085, 2104, 2103, 2101, 2098, 2097])).
% 1.29/1.48 tff(2112,plain,(c0_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(2113,plain,
% 1.29/1.48 (c0_1(a163)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2112, 49])).
% 1.29/1.48 tff(2114,plain,
% 1.29/1.48 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2115,plain,
% 1.29/1.48 ((hskp31 | hskp28 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2116,plain,
% 1.29/1.48 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2115])).
% 1.29/1.48 tff(2117,plain,
% 1.29/1.48 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2116, 2114])).
% 1.29/1.48 tff(2118,plain,
% 1.29/1.48 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2119,plain,
% 1.29/1.48 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 1.29/1.48 tff(2120,plain,
% 1.29/1.48 (hskp31 | hskp28 | (~c3_1(a163)) | (~c0_1(a163))),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2119, 142, 49, 536])).
% 1.29/1.48 tff(2121,plain,
% 1.29/1.48 (hskp28),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2120, 2113, 1857, 2080])).
% 1.29/1.48 tff(2122,plain,
% 1.29/1.48 (c3_1(a118)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[476, 2121])).
% 1.29/1.48 tff(2123,plain,
% 1.29/1.48 (c2_1(a118)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[484, 2121])).
% 1.29/1.48 tff(2124,plain,
% 1.29/1.48 (~hskp4),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2100, 2121, 2083, 2085, 2084])).
% 1.29/1.48 tff(2125,plain,
% 1.29/1.48 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2126,plain,
% 1.29/1.48 ((hskp10 | hskp4 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2127,plain,
% 1.29/1.48 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2126])).
% 1.29/1.48 tff(2128,plain,
% 1.29/1.48 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2127, 2125])).
% 1.29/1.48 tff(2129,plain,
% 1.29/1.48 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2130,plain,
% 1.29/1.48 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 1.29/1.48 tff(2131,plain,
% 1.29/1.48 (hskp10 | hskp4 | (~c3_1(a163)) | (~c0_1(a163))),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2130, 142, 49, 1737])).
% 1.29/1.48 tff(2132,plain,
% 1.29/1.48 (hskp10),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2131, 2124, 1857, 2113])).
% 1.29/1.48 tff(2133,plain,
% 1.29/1.48 (~c3_1(a111)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1235, 2132])).
% 1.29/1.48 tff(2134,plain,
% 1.29/1.48 (c1_1(a118)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[492, 2121])).
% 1.29/1.48 tff(2135,plain,
% 1.29/1.48 (~c0_1(a111)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1247, 2132])).
% 1.29/1.48 tff(2136,plain,
% 1.29/1.48 (~c2_1(a111)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1241, 2132])).
% 1.29/1.48 tff(2137,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1845, 2136, 2135, 2106, 2134, 2124, 2104, 2103, 2133, 2123, 2122])).
% 1.29/1.48 tff(2138,plain,(c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(2139,plain,
% 1.29/1.48 (~hskp24),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[998, 2138])).
% 1.29/1.48 tff(2140,plain,
% 1.29/1.48 (hskp30),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[140, 23, 2139])).
% 1.29/1.48 tff(2141,plain,
% 1.29/1.48 (c2_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[922, 2140])).
% 1.29/1.48 tff(2142,plain,
% 1.29/1.48 (c0_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[930, 2140])).
% 1.29/1.48 tff(2143,plain,
% 1.29/1.48 (c3_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[914, 2140])).
% 1.29/1.48 tff(2144,plain,
% 1.29/1.48 (~hskp28),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2100, 34, 2143, 2142, 2141])).
% 1.29/1.48 tff(2145,plain,
% 1.29/1.48 (~hskp15),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[548, 2144, 23])).
% 1.29/1.48 tff(2146,plain,
% 1.29/1.48 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2147,plain,
% 1.29/1.48 ((hskp28 | hskp15 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105))) <=> (hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2148,plain,
% 1.29/1.48 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2147])).
% 1.29/1.48 tff(2149,plain,
% 1.29/1.48 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2148, 2146])).
% 1.29/1.48 tff(2150,plain,
% 1.29/1.48 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2151,plain,
% 1.29/1.48 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 1.29/1.48 tff(2152,plain,
% 1.29/1.48 (~c0_1(a105)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2151, 142, 2144, 2145, 48, 40, 33])).
% 1.29/1.48 tff(2153,plain,
% 1.29/1.48 (hskp28 | c1_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1477, 23, 142, 2142, 2143, 536])).
% 1.29/1.48 tff(2154,plain,
% 1.29/1.48 (c1_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2153, 2144])).
% 1.29/1.48 tff(2155,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2156,plain,
% 1.29/1.48 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105))) <=> (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2157,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105)))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2156])).
% 1.29/1.48 tff(2158,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2157, 2155])).
% 1.29/1.48 tff(2159,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2160,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 1.29/1.48 tff(2161,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2160, 142, 2142, 2141, 2143, 48, 40, 84, 2154, 2152])).
% 1.29/1.48 tff(2162,plain,((~hskp4) | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(2163,plain,
% 1.29/1.48 (~hskp4),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2162, 23])).
% 1.29/1.48 tff(2164,plain,
% 1.29/1.48 (c1_1(a131)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1743, 142, 22, 2163, 2142, 2143, 1737])).
% 1.29/1.48 tff(2165,plain,
% 1.29/1.48 (hskp19),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[983, 2140])).
% 1.29/1.48 tff(2166,plain,
% 1.29/1.48 (~c3_1(a135)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[396, 2165])).
% 1.29/1.48 tff(2167,plain,
% 1.29/1.48 (~c2_1(a135)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[402, 2165])).
% 1.29/1.48 tff(2168,plain,
% 1.29/1.48 (c0_1(a135)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[420, 2165])).
% 1.29/1.48 tff(2169,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2170,plain,
% 1.29/1.48 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135)) <=> (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2171,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2170])).
% 1.29/1.48 tff(2172,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2171, 2169])).
% 1.29/1.48 tff(2173,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2174,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 1.29/1.49 tff(2175,plain,
% 1.29/1.49 (c1_1(a135)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2174, 142, 2141, 2143, 2168, 2167, 2166, 96, 2164])).
% 1.29/1.49 tff(2176,plain,
% 1.29/1.49 (hskp1 | (~c1_1(a135))),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1151, 142, 2139, 2168, 2167, 21])).
% 1.29/1.49 tff(2177,plain,
% 1.29/1.49 (hskp1),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2176, 2175])).
% 1.29/1.49 tff(2178,plain,
% 1.29/1.49 (~c1_1(a102)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1158, 2177])).
% 1.29/1.49 tff(2179,plain,
% 1.29/1.49 (c2_1(a102)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1208, 2177])).
% 1.29/1.49 tff(2180,plain,
% 1.29/1.49 (~c0_1(a102)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1164, 2177])).
% 1.29/1.49 tff(2181,assumption,(~c1_1(a102)), introduced(assumption)).
% 1.29/1.49 tff(2182,assumption,(~c0_1(a102)), introduced(assumption)).
% 1.29/1.49 tff(2183,assumption,(c2_1(a102)), introduced(assumption)).
% 1.29/1.49 tff(2184,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2185,plain,
% 1.29/1.49 ((hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102))) <=> (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2186,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131))))),
% 1.29/1.49 inference(monotonicity,[status(thm)],[2185])).
% 1.29/1.49 tff(2187,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)))),
% 1.29/1.49 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.29/1.49 tff(2188,plain,
% 1.29/1.49 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))),
% 1.29/1.49 inference(quant_inst,[status(thm)],[])).
% 1.29/1.49 tff(2189,plain,
% 1.29/1.49 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.29/1.49 tff(2190,plain,
% 1.29/1.49 ($false),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2189, 142, 22, 1070, 1068, 2183, 2182, 2181, 1301, 1745])).
% 1.29/1.49 tff(2191,plain,(hskp10 | (~c0_1(a131)) | (~c3_1(a131)) | (~c2_1(a102)) | c0_1(a102) | c1_1(a102) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.29/1.49 tff(2192,plain,
% 1.29/1.49 ($false),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2191, 2180, 2179, 22, 2142, 2143, 2178, 2163])).
% 1.29/1.49 tff(2193,plain,(hskp31 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.29/1.49 tff(2194,plain,
% 1.29/1.49 (hskp31),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2193, 22])).
% 1.29/1.49 tff(2195,plain,
% 1.29/1.49 (c1_1(a141)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[65, 2194])).
% 1.29/1.49 tff(2196,plain,
% 1.29/1.49 (c0_1(a141)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[73, 2194])).
% 1.29/1.49 tff(2197,plain,
% 1.29/1.49 (c3_1(a141)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[57, 2194])).
% 1.29/1.49 tff(2198,assumption,(hskp1), introduced(assumption)).
% 1.29/1.49 tff(2199,plain,
% 1.29/1.49 (~c1_1(a102)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1158, 2198])).
% 1.29/1.49 tff(2200,plain,
% 1.29/1.49 (~c0_1(a102)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1164, 2198])).
% 1.29/1.49 tff(2201,plain,
% 1.29/1.49 (c2_1(a102)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1208, 2198])).
% 1.29/1.49 tff(2202,plain,
% 1.29/1.49 ($false),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1317, 142, 22, 737, 736, 767, 2201, 2200, 2199, 1301])).
% 1.29/1.49 tff(2203,plain,((~hskp1) | hskp10 | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141))), inference(lemma,lemma(discharge,[]))).
% 1.29/1.49 tff(2204,plain,
% 1.29/1.49 (~hskp1),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2203, 2195, 22, 2196, 2197])).
% 1.29/1.49 tff(2205,plain,
% 1.29/1.49 (c2_1(a141)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1307, 142, 2139, 2204, 2196, 2195, 21])).
% 1.29/1.49 tff(2206,assumption,(c2_1(a141)), introduced(assumption)).
% 1.29/1.49 tff(2207,plain,
% 1.29/1.49 ($false),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1896, 975, 1, 2206])).
% 1.29/1.49 tff(2208,plain,(hskp19 | (~c2_1(a141)) | (~c0_1(a141)) | (~c3_1(a141))), inference(lemma,lemma(discharge,[]))).
% 1.29/1.49 tff(2209,plain,
% 1.29/1.49 (hskp19),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2208, 2205, 2196, 2197])).
% 1.29/1.49 tff(2210,plain,
% 1.29/1.49 (~c2_1(a135)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[402, 2209])).
% 1.29/1.49 tff(2211,plain,
% 1.29/1.49 (c0_1(a135)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[420, 2209])).
% 1.29/1.49 tff(2212,plain,
% 1.29/1.49 (~c1_1(a135)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1151, 142, 2139, 2204, 2211, 2210, 21])).
% 1.29/1.49 tff(2213,plain,
% 1.29/1.49 (~c3_1(a135)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[396, 2209])).
% 1.29/1.49 tff(2214,plain,
% 1.29/1.49 ($false),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1143, 142, 2195, 2197, 2211, 2210, 2213, 96, 2212, 2205])).
% 1.29/1.49 tff(2215,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 1.29/1.49 tff(2216,plain,
% 1.29/1.49 (~c3_1(a111)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1235, 2215])).
% 1.29/1.49 tff(2217,plain,
% 1.29/1.49 (~c2_1(a111)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1241, 2215])).
% 1.29/1.49 tff(2218,plain,
% 1.29/1.49 (hskp19 | (~c1_1(a111))),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1326, 142, 2217, 2216, 11])).
% 1.29/1.49 tff(2219,plain,
% 1.29/1.49 (~c1_1(a111)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2218, 1])).
% 1.29/1.49 tff(2220,plain,
% 1.29/1.49 (~c0_1(a111)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[1247, 2215])).
% 1.29/1.49 tff(2221,plain,
% 1.29/1.49 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(2222,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[2221])).
% 1.29/1.49 tff(2223,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2224,plain,
% 1.29/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp31) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp31))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(2225,plain,
% 1.29/1.49 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[2224])).
% 1.29/1.49 tff(2226,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.29/1.49 tff(2227,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 1.29/1.49 tff(2228,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2227, 2223])).
% 1.29/1.49 tff(2229,plain,(
% 1.29/1.49 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.29/1.49 inference(skolemize,[status(sab)],[2228])).
% 1.29/1.49 tff(2230,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2229, 2222])).
% 1.29/1.49 tff(2231,plain,
% 1.29/1.49 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(2232,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[2231])).
% 1.29/1.49 tff(2233,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2234,plain,
% 1.29/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp1))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(2235,plain,
% 1.29/1.49 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[2234])).
% 1.29/1.49 tff(2236,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.29/1.49 tff(2237,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 1.29/1.49 tff(2238,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2237, 2233])).
% 1.29/1.49 tff(2239,plain,(
% 1.29/1.49 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.29/1.49 inference(skolemize,[status(sab)],[2238])).
% 1.29/1.49 tff(2240,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2239, 2232])).
% 1.29/1.49 tff(2241,plain,
% 1.29/1.49 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2242,plain,
% 1.29/1.49 ((hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c1_1(a163))) <=> (hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2243,plain,
% 1.29/1.49 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c1_1(a163)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0)))),
% 1.29/1.49 inference(monotonicity,[status(thm)],[2242])).
% 1.29/1.49 tff(2244,plain,
% 1.29/1.49 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c1_1(a163)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0))),
% 1.29/1.49 inference(transitivity,[status(thm)],[2243, 2241])).
% 1.29/1.49 tff(2245,plain,
% 1.29/1.49 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c1_1(a163)))),
% 1.29/1.49 inference(quant_inst,[status(thm)],[])).
% 1.29/1.49 tff(2246,plain,
% 1.29/1.49 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0)),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 1.29/1.49 tff(2247,plain,
% 1.29/1.49 (hskp19 | c2_1(a163) | c3_1(a163)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2246, 142, 2138, 11])).
% 1.29/1.49 tff(2248,plain,
% 1.29/1.49 (hskp19),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2247, 85, 86])).
% 1.29/1.49 tff(2249,plain,
% 1.29/1.49 (c0_1(a135)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[420, 2248])).
% 1.29/1.49 tff(2250,plain,
% 1.29/1.49 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(2251,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[2250])).
% 1.29/1.49 tff(2252,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2253,plain,
% 1.29/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(2254,plain,
% 1.29/1.49 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[2253])).
% 1.29/1.49 tff(2255,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.29/1.49 tff(2256,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2255, 2254])).
% 1.29/1.49 tff(2257,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2256, 2252])).
% 1.29/1.49 tff(2258,plain,(
% 1.29/1.49 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.29/1.49 inference(skolemize,[status(sab)],[2257])).
% 1.29/1.49 tff(2259,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2258, 2251])).
% 1.29/1.49 tff(2260,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2261,plain,
% 1.29/1.49 ((hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a163) | c3_1(a163) | (~c1_1(a163))) <=> (hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2262,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a163) | c3_1(a163) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 1.29/1.49 inference(monotonicity,[status(thm)],[2261])).
% 1.29/1.49 tff(2263,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a163) | c3_1(a163) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.49 inference(transitivity,[status(thm)],[2262, 2260])).
% 1.29/1.49 tff(2264,plain,
% 1.29/1.49 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a163) | c3_1(a163) | (~c1_1(a163)))),
% 1.29/1.49 inference(quant_inst,[status(thm)],[])).
% 1.29/1.49 tff(2265,plain,
% 1.29/1.49 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2264, 2263])).
% 1.29/1.49 tff(2266,plain,
% 1.29/1.49 (hskp8),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2265, 142, 74, 66, 58, 2138, 85, 2259, 224])).
% 1.29/1.49 tff(2267,plain,
% 1.29/1.49 (~c3_1(a109)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[155, 2266])).
% 1.29/1.49 tff(2268,plain,
% 1.29/1.49 (~c0_1(a109)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[186, 2266])).
% 1.29/1.49 tff(2269,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2270,plain,
% 1.29/1.49 ((hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | c3_1(a163)) <=> (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2271,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | c3_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 1.29/1.49 inference(monotonicity,[status(thm)],[2270])).
% 1.29/1.49 tff(2272,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | c3_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 1.29/1.49 inference(transitivity,[status(thm)],[2271, 2269])).
% 1.29/1.49 tff(2273,plain,
% 1.29/1.49 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | c3_1(a163))),
% 1.29/1.49 inference(quant_inst,[status(thm)],[])).
% 1.29/1.49 tff(2274,plain,
% 1.29/1.49 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[2273, 2272])).
% 1.29/1.49 tff(2275,plain,
% 1.29/1.49 (hskp13),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[2274, 142, 74, 66, 58, 86, 85, 1229, 224])).
% 1.29/1.49 tff(2276,plain,
% 1.29/1.49 (~c3_1(a114)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[566, 2275])).
% 1.29/1.49 tff(2277,plain,
% 1.29/1.49 (~c3_1(a135)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[396, 2248])).
% 1.29/1.49 tff(2278,plain,
% 1.29/1.49 (~c2_1(a135)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[402, 2248])).
% 1.29/1.49 tff(2279,plain,
% 1.29/1.49 (c1_1(a109)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[163, 2266])).
% 1.29/1.49 tff(2280,plain,
% 1.29/1.49 (c2_1(a114)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[574, 2275])).
% 1.29/1.49 tff(2281,plain,
% 1.29/1.49 (c1_1(a114)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[582, 2275])).
% 1.29/1.49 tff(2282,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2283,plain,
% 1.29/1.49 (((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109))) <=> (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(2284,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135))))),
% 1.29/1.49 inference(monotonicity,[status(thm)],[2283])).
% 1.32/1.49 tff(2285,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[2284, 2282])).
% 1.32/1.49 tff(2286,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(2287,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 1.32/1.49 tff(2288,plain,
% 1.32/1.49 ($false),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2287, 142, 2249, 2281, 2280, 2279, 2278, 2277, 2276, 2268, 2267, 181])).
% 1.32/1.49 tff(2289,plain,((~hskp31) | c2_1(a163) | c3_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.49 tff(2290,plain,
% 1.32/1.49 (~hskp31),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2289, 224, 85, 86])).
% 1.32/1.49 tff(2291,plain,
% 1.32/1.49 (^[U: $i] : refl((hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.32/1.49 inference(bind,[status(th)],[])).
% 1.32/1.49 tff(2292,plain,
% 1.32/1.49 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.32/1.49 inference(quant_intro,[status(thm)],[2291])).
% 1.32/1.49 tff(2293,plain,
% 1.32/1.49 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2294,plain,
% 1.32/1.49 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | 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)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp10) <=> ((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp10))), rewrite(((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp10) <=> (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp10) <=> (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(2295,plain,
% 1.32/1.50 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp10) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[2294])).
% 1.32/1.50 tff(2296,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.32/1.50 tff(2297,plain,
% 1.32/1.50 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2296, 2295])).
% 1.32/1.50 tff(2298,plain,
% 1.32/1.50 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2297, 2293])).
% 1.32/1.50 tff(2299,plain,(
% 1.32/1.50 ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.32/1.50 inference(skolemize,[status(sab)],[2298])).
% 1.32/1.50 tff(2300,plain,
% 1.32/1.50 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2299, 2292])).
% 1.32/1.50 tff(2301,plain,
% 1.32/1.50 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2302,plain,
% 1.32/1.50 ((hskp15 | hskp10 | (~ndr1_0) | c3_1(a163) | c0_1(a163) | (~c1_1(a163))) <=> (hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2303,plain,
% 1.32/1.50 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163)))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2302])).
% 1.32/1.50 tff(2304,plain,
% 1.32/1.50 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2303, 2301])).
% 1.32/1.50 tff(2305,plain,
% 1.32/1.50 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2306,plain,
% 1.32/1.50 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2305, 2304])).
% 1.32/1.50 tff(2307,plain,
% 1.32/1.50 (hskp15 | hskp10 | c3_1(a163) | c0_1(a163)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2306, 142, 2138, 2300])).
% 1.32/1.50 tff(2308,plain,
% 1.32/1.50 (hskp15),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2307, 22, 85, 224])).
% 1.32/1.50 tff(2309,plain,
% 1.32/1.50 (~c1_1(a117)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[509, 2308])).
% 1.32/1.50 tff(2310,plain,
% 1.32/1.50 (c3_1(a117)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[525, 2308])).
% 1.32/1.50 tff(2311,plain,
% 1.32/1.50 (c0_1(a117)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[517, 2308])).
% 1.32/1.50 tff(2312,plain,
% 1.32/1.50 (hskp28),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[548, 2308, 23])).
% 1.32/1.50 tff(2313,plain,
% 1.32/1.50 (~hskp4),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2100, 2312, 2143, 2142, 2141])).
% 1.32/1.50 tff(2314,plain,
% 1.32/1.50 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2315,plain,
% 1.32/1.50 ((hskp10 | hskp4 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117))) <=> (hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2316,plain,
% 1.32/1.50 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2315])).
% 1.32/1.50 tff(2317,plain,
% 1.32/1.50 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2316, 2314])).
% 1.32/1.50 tff(2318,plain,
% 1.32/1.50 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2319,plain,
% 1.32/1.50 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2318, 2317])).
% 1.32/1.50 tff(2320,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2319, 142, 22, 2313, 2311, 2310, 2309, 1737])).
% 1.32/1.50 tff(2321,plain,(hskp10 | hskp31 | c3_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(2322,plain,
% 1.32/1.50 (hskp10),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2321, 2290, 85, 224])).
% 1.32/1.50 tff(2323,plain,
% 1.32/1.50 (~c0_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1247, 2322])).
% 1.32/1.50 tff(2324,plain,
% 1.32/1.50 (~c3_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1235, 2322])).
% 1.32/1.50 tff(2325,plain,
% 1.32/1.50 (hskp30),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[140, 2290, 2139])).
% 1.32/1.50 tff(2326,plain,
% 1.32/1.50 (c2_1(a131)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[922, 2325])).
% 1.32/1.50 tff(2327,plain,
% 1.32/1.50 (c0_1(a131)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[930, 2325])).
% 1.32/1.50 tff(2328,plain,
% 1.32/1.50 (c3_1(a131)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[914, 2325])).
% 1.32/1.50 tff(2329,plain,
% 1.32/1.50 (hskp28 | c1_1(a131)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1477, 2290, 142, 2327, 2328, 536])).
% 1.32/1.50 tff(2330,plain,
% 1.32/1.50 (c1_1(a131)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2329, 503])).
% 1.32/1.50 tff(2331,plain,
% 1.32/1.50 (~hskp15),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[548, 503, 2290])).
% 1.32/1.50 tff(2332,plain,
% 1.32/1.50 (hskp10),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2307, 2331, 85, 224])).
% 1.32/1.50 tff(2333,plain,
% 1.32/1.50 (~c2_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1241, 2332])).
% 1.32/1.50 tff(2334,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2335,plain,
% 1.32/1.50 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2336,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2335])).
% 1.32/1.50 tff(2337,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2336, 2334])).
% 1.32/1.50 tff(2338,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2339,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 1.32/1.50 tff(2340,plain,
% 1.32/1.50 (c1_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2339, 142, 2326, 2328, 2249, 2278, 2277, 2333, 1377, 96, 2330])).
% 1.32/1.50 tff(2341,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2342,plain,
% 1.32/1.50 ((hskp13 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c2_1(a163) | c0_1(a163) | c3_1(a163)) <=> (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2343,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c2_1(a163) | c0_1(a163) | c3_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2342])).
% 1.32/1.50 tff(2344,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c2_1(a163) | c0_1(a163) | c3_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2343, 2341])).
% 1.32/1.50 tff(2345,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c2_1(a163) | c0_1(a163) | c3_1(a163))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2346,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2345, 2344])).
% 1.32/1.50 tff(2347,plain,
% 1.32/1.50 (hskp13),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2346, 142, 2327, 2328, 86, 85, 1229, 224, 2330])).
% 1.32/1.50 tff(2348,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1390, 2347, 2340, 2278, 2277, 1378, 1377, 2249])).
% 1.32/1.50 tff(2349,plain,(hskp28 | c0_1(a111) | c3_1(a111) | c2_1(a163) | c3_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(2350,plain,
% 1.32/1.50 (hskp28),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2349, 1377, 1378, 86, 85, 224])).
% 1.32/1.50 tff(2351,plain,
% 1.32/1.50 (~hskp4),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2100, 2350, 2328, 2327, 2326])).
% 1.32/1.50 tff(2352,plain,
% 1.32/1.50 (c3_1(a118)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[476, 2350])).
% 1.32/1.50 tff(2353,plain,
% 1.32/1.50 (c2_1(a118)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[484, 2350])).
% 1.32/1.50 tff(2354,plain,
% 1.32/1.50 (c1_1(a118)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[492, 2350])).
% 1.32/1.50 tff(2355,plain,
% 1.32/1.50 (c2_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1845, 2354, 2277, 1378, 2351, 2249, 2278, 1377, 2353, 2352])).
% 1.32/1.50 tff(2356,plain,
% 1.32/1.50 (~hskp10),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1241, 2355])).
% 1.32/1.50 tff(2357,plain,
% 1.32/1.50 (hskp10 | hskp4 | c1_1(a131)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1743, 142, 2327, 2328, 1737])).
% 1.32/1.50 tff(2358,plain,
% 1.32/1.50 (c1_1(a131)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2357, 2356, 2351])).
% 1.32/1.50 tff(2359,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2360,plain,
% 1.32/1.50 (((~ndr1_0) | c3_1(a111) | (~c1_1(a111)) | (~c2_1(a111)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111))) <=> (c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2361,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a111) | (~c1_1(a111)) | (~c2_1(a111)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2360])).
% 1.32/1.50 tff(2362,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a111) | (~c1_1(a111)) | (~c2_1(a111)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2361, 2359])).
% 1.32/1.50 tff(2363,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a111) | (~c1_1(a111)) | (~c2_1(a111)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2364,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2363, 2362])).
% 1.32/1.50 tff(2365,plain,
% 1.32/1.50 ((~c2_1(a111)) | (~c1_1(a111))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2364, 142, 2249, 2278, 2277, 1378, 1377, 181])).
% 1.32/1.50 tff(2366,plain,
% 1.32/1.50 (~c1_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2365, 2355])).
% 1.32/1.50 tff(2367,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2368,plain,
% 1.32/1.50 ((hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a111) | c0_1(a111) | (~c2_1(a111))) <=> (hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2369,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a111) | c0_1(a111) | (~c2_1(a111)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111)))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2368])).
% 1.32/1.50 tff(2370,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a111) | c0_1(a111) | (~c2_1(a111)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2369, 2367])).
% 1.32/1.50 tff(2371,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a111) | c0_1(a111) | (~c2_1(a111)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2372,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111)),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 1.32/1.50 tff(2373,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2372, 142, 2356, 2327, 2328, 1378, 2355, 1301, 2366, 2358])).
% 1.32/1.50 tff(2374,plain,(c3_1(a111) | c0_1(a111) | c2_1(a163) | c3_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(2375,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2374, 2324, 2323, 86, 85, 224])).
% 1.32/1.50 tff(2376,plain,(c0_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(2377,plain,
% 1.32/1.50 (c0_1(a163)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2376, 85, 86])).
% 1.32/1.50 tff(2378,plain,
% 1.32/1.50 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2379,plain,
% 1.32/1.50 ((hskp24 | hskp1 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163))) <=> (hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2380,plain,
% 1.32/1.50 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2379])).
% 1.32/1.50 tff(2381,plain,
% 1.32/1.50 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2380, 2378])).
% 1.32/1.50 tff(2382,plain,
% 1.32/1.50 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2383,plain,
% 1.32/1.50 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2382, 2381])).
% 1.32/1.50 tff(2384,plain,
% 1.32/1.50 (hskp1 | c2_1(a163) | (~c0_1(a163))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2383, 142, 2139, 2138, 21])).
% 1.32/1.50 tff(2385,plain,
% 1.32/1.50 (hskp1),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2384, 2377, 86])).
% 1.32/1.50 tff(2386,plain,
% 1.32/1.50 (~c1_1(a102)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1158, 2385])).
% 1.32/1.50 tff(2387,plain,
% 1.32/1.50 (~c0_1(a102)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1164, 2385])).
% 1.32/1.50 tff(2388,plain,
% 1.32/1.50 (c2_1(a102)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1208, 2385])).
% 1.32/1.50 tff(2389,plain,
% 1.32/1.50 (hskp10),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1317, 142, 74, 66, 58, 2388, 2387, 2386, 1301])).
% 1.32/1.50 tff(2390,plain,
% 1.32/1.50 (~c3_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1235, 2389])).
% 1.32/1.50 tff(2391,plain,
% 1.32/1.50 (~c2_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1241, 2389])).
% 1.32/1.50 tff(2392,plain,
% 1.32/1.50 (~c0_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1247, 2389])).
% 1.32/1.50 tff(2393,plain,
% 1.32/1.50 (hskp13),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1254, 142, 74, 66, 58, 2392, 2391, 2390, 1229])).
% 1.32/1.50 tff(2394,plain,
% 1.32/1.50 (~c3_1(a114)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[566, 2393])).
% 1.32/1.50 tff(2395,plain,
% 1.32/1.50 (c2_1(a114)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[574, 2393])).
% 1.32/1.50 tff(2396,plain,
% 1.32/1.50 (c1_1(a114)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[582, 2393])).
% 1.32/1.50 tff(2397,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2398,plain,
% 1.32/1.50 (((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114))) <=> (c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2399,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2398])).
% 1.32/1.50 tff(2400,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2399, 2397])).
% 1.32/1.50 tff(2401,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2402,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2401, 2400])).
% 1.32/1.50 tff(2403,plain,
% 1.32/1.50 (c0_1(a114)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2402, 142, 2396, 2395, 86, 85, 2394, 181, 2377])).
% 1.32/1.50 tff(2404,plain,
% 1.32/1.50 (~c1_1(a111)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1390, 2393, 2278, 2277, 2392, 2390, 2249])).
% 1.32/1.50 tff(2405,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2406,plain,
% 1.32/1.50 (((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> (c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2407,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2406])).
% 1.32/1.50 tff(2408,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2407, 2405])).
% 1.32/1.50 tff(2409,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2410,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2409, 2408])).
% 1.32/1.50 tff(2411,plain,
% 1.32/1.50 (c3_1(a102)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2410, 142, 2395, 2388, 2394, 2392, 2390, 2387, 331, 2404, 2403])).
% 1.32/1.50 tff(2412,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2413,plain,
% 1.32/1.50 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> (c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2414,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2413])).
% 1.32/1.51 tff(2415,plain,
% 1.32/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[2414, 2412])).
% 1.32/1.51 tff(2416,plain,
% 1.32/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(2417,plain,
% 1.32/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 1.32/1.51 tff(2418,plain,
% 1.32/1.51 ((~c2_1(a141)) | c1_1(a111)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2417, 142, 66, 58, 86, 85, 2391, 2390, 96, 2377])).
% 1.32/1.51 tff(2419,plain,
% 1.32/1.51 (~c2_1(a141)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2418, 2404])).
% 1.32/1.51 tff(2420,plain,
% 1.32/1.51 (hskp12),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1932, 142, 74, 66, 2396, 2395, 2394, 1907, 2419])).
% 1.32/1.51 tff(2421,plain,
% 1.32/1.51 (~c2_1(a113)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1600, 2420])).
% 1.32/1.51 tff(2422,plain,
% 1.32/1.51 (~c0_1(a113)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1631, 2420])).
% 1.32/1.51 tff(2423,plain,
% 1.32/1.51 (c3_1(a113)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1608, 2420])).
% 1.32/1.51 tff(2424,plain,
% 1.32/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2425,plain,
% 1.32/1.51 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102))) <=> (c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2426,plain,
% 1.32/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[2425])).
% 1.32/1.51 tff(2427,plain,
% 1.32/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[2426, 2424])).
% 1.32/1.51 tff(2428,plain,
% 1.32/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(2429,plain,
% 1.32/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 1.32/1.51 tff(2430,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2429, 142, 74, 66, 58, 2423, 2422, 2421, 2387, 2386, 723, 2411])).
% 1.32/1.51 tff(2431,plain,((~hskp31) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(2432,plain,
% 1.32/1.51 (~hskp31),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2431, 85, 86])).
% 1.32/1.51 tff(2433,plain,
% 1.32/1.51 (~hskp4),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2162, 2432])).
% 1.32/1.51 tff(2434,plain,
% 1.32/1.51 (hskp30),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[140, 2432, 2139])).
% 1.32/1.51 tff(2435,plain,
% 1.32/1.51 (c3_1(a131)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[914, 2434])).
% 1.32/1.51 tff(2436,plain,
% 1.32/1.51 (c0_1(a131)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[930, 2434])).
% 1.32/1.51 tff(2437,plain,
% 1.32/1.51 (hskp10),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2191, 2436, 2435, 2388, 2387, 2386, 2433])).
% 1.32/1.51 tff(2438,plain,
% 1.32/1.51 (~c3_1(a111)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1235, 2437])).
% 1.32/1.51 tff(2439,plain,
% 1.32/1.51 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2440,plain,
% 1.32/1.51 ((hskp29 | hskp4 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163))) <=> (hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2441,plain,
% 1.32/1.51 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[2440])).
% 1.32/1.51 tff(2442,plain,
% 1.32/1.51 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[2441, 2439])).
% 1.32/1.51 tff(2443,plain,
% 1.32/1.51 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(2444,plain,
% 1.32/1.51 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2443, 2442])).
% 1.32/1.51 tff(2445,plain,
% 1.32/1.51 (hskp29 | hskp4 | c2_1(a163) | (~c0_1(a163))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2444, 142, 2138, 1777])).
% 1.32/1.51 tff(2446,plain,
% 1.32/1.51 (hskp29),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2445, 2433, 86, 2377])).
% 1.32/1.51 tff(2447,plain,
% 1.32/1.51 (c2_1(a128)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1809, 2446])).
% 1.32/1.51 tff(2448,plain,
% 1.32/1.51 (~c0_1(a111)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1247, 2437])).
% 1.32/1.51 tff(2449,plain,
% 1.32/1.51 (c0_1(a128)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1792, 2446])).
% 1.32/1.51 tff(2450,plain,
% 1.32/1.51 (c1_1(a128)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1801, 2446])).
% 1.32/1.51 tff(2451,plain,
% 1.32/1.51 (~c2_1(a111)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1241, 2437])).
% 1.32/1.51 tff(2452,plain,
% 1.32/1.51 (hskp13),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1840, 2451, 2450, 2433, 2449, 2448, 2447, 2438])).
% 1.32/1.51 tff(2453,plain,
% 1.32/1.51 (~c1_1(a111)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1390, 2438, 2278, 2277, 2448, 2452, 2249])).
% 1.32/1.51 tff(2454,plain,
% 1.32/1.51 (^[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)))),
% 1.32/1.51 inference(bind,[status(th)],[])).
% 1.32/1.51 tff(2455,plain,
% 1.32/1.51 (![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))),
% 1.32/1.51 inference(quant_intro,[status(thm)],[2454])).
% 1.32/1.51 tff(2456,plain,
% 1.32/1.51 (![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))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2457,plain,
% 1.32/1.51 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_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))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_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))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))))),
% 1.32/1.51 inference(bind,[status(th)],[])).
% 1.32/1.51 tff(2458,plain,
% 1.32/1.51 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 1.32/1.51 inference(quant_intro,[status(thm)],[2457])).
% 1.32/1.51 tff(2459,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.32/1.51 tff(2460,plain,
% 1.32/1.51 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2459, 2458])).
% 1.32/1.51 tff(2461,plain,
% 1.32/1.51 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2460, 2456])).
% 1.32/1.51 tff(2462,plain,(
% 1.32/1.51 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 1.32/1.51 inference(skolemize,[status(sab)],[2461])).
% 1.32/1.51 tff(2463,plain,
% 1.32/1.51 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2462, 2455])).
% 1.32/1.51 tff(2464,plain,
% 1.32/1.51 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2465,plain,
% 1.32/1.51 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a111) | c0_1(a111) | c2_1(a111)) <=> (hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2466,plain,
% 1.32/1.51 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a111) | c0_1(a111) | c2_1(a111))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111)))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[2465])).
% 1.32/1.51 tff(2467,plain,
% 1.32/1.51 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a111) | c0_1(a111) | c2_1(a111))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 1.32/1.51 inference(transitivity,[status(thm)],[2466, 2464])).
% 1.32/1.51 tff(2468,plain,
% 1.32/1.51 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a111) | c0_1(a111) | c2_1(a111))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(2469,plain,
% 1.32/1.51 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 1.32/1.51 tff(2470,plain,
% 1.32/1.51 (hskp3),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2469, 142, 2433, 2448, 2451, 2463, 2453])).
% 1.32/1.51 tff(2471,plain,
% 1.32/1.51 (((~hskp3) | (~c1_1(a104))) <=> ((~hskp3) | (~c1_1(a104)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2472,plain,
% 1.32/1.51 (((~c1_1(a104)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a104)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2473,axiom,((~c1_1(a104)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.32/1.51 tff(2474,plain,
% 1.32/1.51 ((~hskp3) | (~c1_1(a104))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 1.32/1.51 tff(2475,plain,
% 1.32/1.51 ((~hskp3) | (~c1_1(a104))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2474, 2471])).
% 1.32/1.51 tff(2476,plain,
% 1.32/1.51 (~c1_1(a104)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2475, 2470])).
% 1.32/1.51 tff(2477,plain,
% 1.32/1.51 (((~hskp3) | c2_1(a104)) <=> ((~hskp3) | c2_1(a104))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2478,axiom,((~hskp3) | c2_1(a104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.32/1.51 tff(2479,plain,
% 1.32/1.51 ((~hskp3) | c2_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 1.32/1.51 tff(2480,plain,
% 1.32/1.51 ((~hskp3) | c2_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2479, 2477])).
% 1.32/1.51 tff(2481,plain,
% 1.32/1.51 ((~hskp3) | c2_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2480, 2477])).
% 1.32/1.51 tff(2482,plain,
% 1.32/1.51 ((~hskp3) | c2_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2481, 2477])).
% 1.32/1.51 tff(2483,plain,
% 1.32/1.51 ((~hskp3) | c2_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2482, 2477])).
% 1.32/1.51 tff(2484,plain,
% 1.32/1.51 (c2_1(a104)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2483, 2470])).
% 1.32/1.51 tff(2485,plain,
% 1.32/1.51 (((~hskp3) | c0_1(a104)) <=> ((~hskp3) | c0_1(a104))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2486,axiom,((~hskp3) | c0_1(a104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.32/1.51 tff(2487,plain,
% 1.32/1.51 ((~hskp3) | c0_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 1.32/1.51 tff(2488,plain,
% 1.32/1.51 ((~hskp3) | c0_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2487, 2485])).
% 1.32/1.51 tff(2489,plain,
% 1.32/1.51 ((~hskp3) | c0_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2488, 2485])).
% 1.32/1.51 tff(2490,plain,
% 1.32/1.51 ((~hskp3) | c0_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2489, 2485])).
% 1.32/1.51 tff(2491,plain,
% 1.32/1.51 ((~hskp3) | c0_1(a104)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2490, 2485])).
% 1.32/1.51 tff(2492,plain,
% 1.32/1.51 (c0_1(a104)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2491, 2470])).
% 1.32/1.51 tff(2493,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2494,plain,
% 1.32/1.51 ((hskp31 | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104))) <=> (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2495,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[2494])).
% 1.32/1.51 tff(2496,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[2495, 2493])).
% 1.32/1.51 tff(2497,plain,
% 1.32/1.51 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(2498,plain,
% 1.32/1.51 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 1.32/1.51 tff(2499,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2498, 2432, 142, 2449, 2450, 2447, 2492, 2484, 2476, 2230])).
% 1.32/1.51 tff(2500,plain,(c3_1(a163) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(2501,plain,
% 1.32/1.51 (c3_1(a163)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2500, 86])).
% 1.32/1.51 tff(2502,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2503,plain,
% 1.32/1.51 ((hskp1 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163))) <=> (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2504,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[2503])).
% 1.32/1.51 tff(2505,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[2504, 2502])).
% 1.32/1.51 tff(2506,plain,
% 1.32/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(2507,plain,
% 1.32/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2506, 2505])).
% 1.32/1.51 tff(2508,plain,
% 1.32/1.51 (hskp1),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2507, 142, 2142, 2141, 2143, 2138, 86, 2501, 2240])).
% 1.32/1.51 tff(2509,plain,
% 1.32/1.51 (~c1_1(a102)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1158, 2508])).
% 1.32/1.51 tff(2510,plain,
% 1.32/1.51 (~c0_1(a102)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1164, 2508])).
% 1.32/1.51 tff(2511,plain,
% 1.32/1.51 (c2_1(a102)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1208, 2508])).
% 1.32/1.51 tff(2512,plain,
% 1.32/1.51 (hskp10),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2191, 2511, 2143, 2142, 2510, 2509, 2163])).
% 1.32/1.51 tff(2513,plain,
% 1.32/1.51 (~c0_1(a111)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1247, 2512])).
% 1.32/1.51 tff(2514,plain,
% 1.32/1.51 (~c3_1(a111)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1235, 2512])).
% 1.32/1.51 tff(2515,plain,
% 1.32/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2516,plain,
% 1.32/1.51 (((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)) | c3_1(a135) | c1_1(a135) | (~c0_1(a135))) <=> ((~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2517,plain,
% 1.32/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)) | c3_1(a135) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[2516])).
% 1.32/1.51 tff(2518,plain,
% 1.32/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)) | c3_1(a135) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[2517, 2515])).
% 1.32/1.51 tff(2519,plain,
% 1.32/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)) | c3_1(a135) | c1_1(a135) | (~c0_1(a135)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(2520,plain,
% 1.32/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 1.32/1.51 tff(2521,plain,
% 1.32/1.51 (c1_1(a135)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2520, 142, 2142, 2141, 2143, 2168, 2138, 86, 2501, 2166, 1577])).
% 1.32/1.51 tff(2522,plain,
% 1.32/1.51 (~c2_1(a111)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1241, 2512])).
% 1.32/1.51 tff(2523,plain,
% 1.32/1.51 (hskp13),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1842, 2522, 2163, 2521, 2514, 2513, 2168, 2167])).
% 1.32/1.51 tff(2524,plain,
% 1.32/1.51 (~c1_1(a111)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1390, 2514, 2166, 2167, 2513, 2523, 2168])).
% 1.32/1.51 tff(2525,plain,
% 1.32/1.51 (hskp3),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2469, 142, 2163, 2513, 2522, 2463, 2524])).
% 1.32/1.51 tff(2526,plain,
% 1.32/1.51 (~c1_1(a104)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2475, 2525])).
% 1.32/1.51 tff(2527,plain,
% 1.32/1.51 (c2_1(a104)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2483, 2525])).
% 1.32/1.51 tff(2528,plain,
% 1.32/1.51 (c0_1(a104)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2491, 2525])).
% 1.32/1.51 tff(2529,plain,
% 1.32/1.51 (hskp29 | (~c1_1(a135))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1783, 142, 2163, 2168, 2167, 1777])).
% 1.32/1.51 tff(2530,plain,
% 1.32/1.51 (hskp29),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2529, 2521])).
% 1.32/1.51 tff(2531,plain,
% 1.32/1.51 (c2_1(a128)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1809, 2530])).
% 1.32/1.51 tff(2532,plain,
% 1.32/1.51 (c1_1(a128)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1801, 2530])).
% 1.32/1.51 tff(2533,plain,
% 1.32/1.51 (c0_1(a128)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1792, 2530])).
% 1.32/1.51 tff(2534,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2498, 23, 142, 2533, 2532, 2531, 2528, 2527, 2526, 2230])).
% 1.32/1.51 tff(2535,plain,(hskp31 | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(2536,plain,
% 1.32/1.51 (hskp31),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2535, 86])).
% 1.32/1.51 tff(2537,plain,
% 1.32/1.51 (c1_1(a141)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[65, 2536])).
% 1.32/1.51 tff(2538,plain,
% 1.32/1.51 (c3_1(a141)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[57, 2536])).
% 1.32/1.51 tff(2539,plain,
% 1.32/1.51 (c0_1(a141)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[73, 2536])).
% 1.32/1.51 tff(2540,assumption,(~hskp1), introduced(assumption)).
% 1.32/1.51 tff(2541,plain,
% 1.32/1.51 (hskp1 | c2_1(a141)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1307, 142, 2139, 737, 736, 21])).
% 1.32/1.51 tff(2542,plain,
% 1.32/1.51 (c2_1(a141)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2541, 2540])).
% 1.32/1.51 tff(2543,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2544,plain,
% 1.32/1.51 ((hskp1 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163))) <=> (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(2545,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[2544])).
% 1.32/1.51 tff(2546,plain,
% 1.32/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[2545, 2543])).
% 1.32/1.51 tff(2547,plain,
% 1.32/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2548,plain,
% 1.32/1.52 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2547, 2546])).
% 1.32/1.52 tff(2549,plain,
% 1.32/1.52 (hskp1 | (~c2_1(a141))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2548, 142, 737, 767, 2138, 86, 2501, 2240])).
% 1.32/1.52 tff(2550,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2549, 2542, 2540])).
% 1.32/1.52 tff(2551,plain,(hskp1 | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a163) | (~c1_1(a141))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(2552,plain,
% 1.32/1.52 (hskp1),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2551, 2539, 2538, 86, 2537])).
% 1.32/1.52 tff(2553,plain,
% 1.32/1.52 (~c1_1(a102)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1158, 2552])).
% 1.32/1.52 tff(2554,plain,
% 1.32/1.52 (~c0_1(a102)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1164, 2552])).
% 1.32/1.52 tff(2555,plain,
% 1.32/1.52 (hskp1),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2551, 74, 58, 86, 66])).
% 1.32/1.52 tff(2556,plain,
% 1.32/1.52 (~c1_1(a102)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1158, 2555])).
% 1.32/1.52 tff(2557,plain,
% 1.32/1.52 (~c0_1(a102)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1164, 2555])).
% 1.32/1.52 tff(2558,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2559,plain,
% 1.32/1.52 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102))) <=> (c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2560,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163)))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[2559])).
% 1.32/1.52 tff(2561,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163))),
% 1.32/1.52 inference(transitivity,[status(thm)],[2560, 2558])).
% 1.32/1.52 tff(2562,plain,
% 1.32/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2563,plain,
% 1.32/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163)),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2562, 2561])).
% 1.32/1.52 tff(2564,plain,
% 1.32/1.52 (~c3_1(a102)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2563, 142, 74, 66, 58, 86, 2501, 2557, 2556, 723, 224])).
% 1.32/1.52 tff(2565,plain,
% 1.32/1.52 (hskp10),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2203, 2555, 74, 66, 58])).
% 1.32/1.52 tff(2566,plain,
% 1.32/1.52 (~c3_1(a111)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1235, 2565])).
% 1.32/1.52 tff(2567,plain,
% 1.32/1.52 (~c2_1(a111)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1241, 2565])).
% 1.32/1.52 tff(2568,plain,
% 1.32/1.52 (~c0_1(a111)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1247, 2565])).
% 1.32/1.52 tff(2569,plain,
% 1.32/1.52 (hskp13),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1254, 142, 74, 66, 58, 2568, 2567, 2566, 1229])).
% 1.32/1.52 tff(2570,plain,
% 1.32/1.52 (~c3_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[566, 2569])).
% 1.32/1.52 tff(2571,plain,
% 1.32/1.52 (c2_1(a102)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1208, 2555])).
% 1.32/1.52 tff(2572,plain,
% 1.32/1.52 (c2_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[574, 2569])).
% 1.32/1.52 tff(2573,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2574,plain,
% 1.32/1.52 (((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102)) <=> (c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2575,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[2574])).
% 1.32/1.52 tff(2576,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 1.32/1.52 inference(transitivity,[status(thm)],[2575, 2573])).
% 1.32/1.52 tff(2577,plain,
% 1.32/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2578,plain,
% 1.32/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 1.32/1.52 tff(2579,plain,
% 1.32/1.52 (~c0_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2578, 142, 2572, 2571, 2570, 2557, 2556, 331, 2564])).
% 1.32/1.52 tff(2580,plain,
% 1.32/1.52 (c1_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[582, 2569])).
% 1.32/1.52 tff(2581,plain,
% 1.32/1.52 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2582,plain,
% 1.32/1.52 ((hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a114) | c3_1(a114) | (~c1_1(a114))) <=> (hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2583,plain,
% 1.32/1.52 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a114) | c3_1(a114) | (~c1_1(a114)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114)))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[2582])).
% 1.32/1.52 tff(2584,plain,
% 1.32/1.52 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a114) | c3_1(a114) | (~c1_1(a114)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114))),
% 1.32/1.52 inference(transitivity,[status(thm)],[2583, 2581])).
% 1.32/1.52 tff(2585,plain,
% 1.32/1.52 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a114) | c3_1(a114) | (~c1_1(a114)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2586,plain,
% 1.32/1.52 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114)),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2585, 2584])).
% 1.32/1.52 tff(2587,plain,
% 1.32/1.52 (hskp8),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2586, 142, 74, 66, 58, 2580, 2570, 2259, 2579])).
% 1.32/1.52 tff(2588,plain,
% 1.32/1.52 (c1_1(a109)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[163, 2587])).
% 1.32/1.52 tff(2589,plain,
% 1.32/1.52 (~c3_1(a109)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[155, 2587])).
% 1.32/1.52 tff(2590,plain,
% 1.32/1.52 (~c0_1(a109)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[186, 2587])).
% 1.32/1.52 tff(2591,assumption,(~c3_1(a109)), introduced(assumption)).
% 1.32/1.52 tff(2592,assumption,(c1_1(a109)), introduced(assumption)).
% 1.32/1.52 tff(2593,plain,
% 1.32/1.52 (hskp19 | c2_1(a109)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[170, 142, 2592, 2591, 11])).
% 1.32/1.52 tff(2594,plain,
% 1.32/1.52 (c2_1(a109)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2593, 1])).
% 1.32/1.52 tff(2595,plain,
% 1.32/1.52 (hskp19 | (~c1_1(a111))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1326, 142, 1757, 1377, 11])).
% 1.32/1.52 tff(2596,plain,
% 1.32/1.52 (~c1_1(a111)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2595, 1])).
% 1.32/1.52 tff(2597,plain,
% 1.32/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2598,plain,
% 1.32/1.52 ((hskp2 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c1_1(a111) | c0_1(a111)) <=> (hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2599,plain,
% 1.32/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111)))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[2598])).
% 1.32/1.52 tff(2600,plain,
% 1.32/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 1.32/1.52 inference(transitivity,[status(thm)],[2599, 2597])).
% 1.32/1.52 tff(2601,plain,
% 1.32/1.52 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c1_1(a111) | c0_1(a111))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2602,plain,
% 1.32/1.52 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111)),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2601, 2600])).
% 1.32/1.52 tff(2603,plain,
% 1.32/1.52 (hskp2 | c1_1(a111)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2602, 142, 2138, 86, 2501, 1378, 1757, 246])).
% 1.32/1.52 tff(2604,plain,
% 1.32/1.52 (hskp2),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2603, 2596])).
% 1.32/1.52 tff(2605,plain,
% 1.32/1.52 (~c3_1(a103)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[383, 2604])).
% 1.32/1.52 tff(2606,assumption,(~c0_1(a109)), introduced(assumption)).
% 1.32/1.52 tff(2607,plain,
% 1.32/1.52 (c0_1(a103)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[278, 2604])).
% 1.32/1.52 tff(2608,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2609,plain,
% 1.32/1.52 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> (c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2610,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111)))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[2609])).
% 1.32/1.52 tff(2611,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 1.32/1.52 inference(transitivity,[status(thm)],[2610, 2608])).
% 1.32/1.52 tff(2612,plain,
% 1.32/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2613,plain,
% 1.32/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111)),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2612, 2611])).
% 1.32/1.52 tff(2614,plain,
% 1.32/1.52 (~c2_1(a103)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2613, 142, 2607, 1378, 1377, 2606, 2591, 2605, 331, 2596, 2594])).
% 1.32/1.52 tff(2615,assumption,(~c3_1(a102)), introduced(assumption)).
% 1.32/1.52 tff(2616,plain,
% 1.32/1.52 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2617,plain,
% 1.32/1.52 ((hskp19 | hskp17 | (~ndr1_0) | c3_1(a102) | c1_1(a102) | (~c2_1(a102))) <=> (hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2618,plain,
% 1.32/1.52 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a102) | c1_1(a102) | (~c2_1(a102)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[2617])).
% 1.32/1.52 tff(2619,plain,
% 1.32/1.52 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a102) | c1_1(a102) | (~c2_1(a102)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)))),
% 1.32/1.52 inference(transitivity,[status(thm)],[2618, 2616])).
% 1.32/1.52 tff(2620,plain,
% 1.32/1.52 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a102) | c1_1(a102) | (~c2_1(a102)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2621,plain,
% 1.32/1.52 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2620, 2619])).
% 1.32/1.52 tff(2622,plain,
% 1.32/1.52 (hskp19 | hskp17 | c3_1(a102)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2621, 142, 2183, 2181, 1266])).
% 1.32/1.52 tff(2623,plain,
% 1.32/1.52 (hskp17),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2622, 1, 2615])).
% 1.32/1.52 tff(2624,plain,
% 1.32/1.52 (~c1_1(a132)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[750, 2623])).
% 1.32/1.52 tff(2625,plain,
% 1.32/1.52 (~c0_1(a132)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[756, 2623])).
% 1.32/1.52 tff(2626,plain,
% 1.32/1.52 (c1_1(a103)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[261, 2604])).
% 1.32/1.52 tff(2627,plain,
% 1.32/1.52 (c3_1(a132)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[765, 2623])).
% 1.32/1.52 tff(2628,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1366, 142, 975, 2627, 2626, 2625, 2624, 2605, 1359, 2614])).
% 1.32/1.52 tff(2629,plain,(hskp19 | c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c2_1(a163) | c2_1(a111) | (~c1_1(a109)) | c3_1(a102) | (~c2_1(a102)) | c1_1(a102)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(2630,plain,
% 1.32/1.52 (hskp19),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2629, 2568, 2566, 2590, 2589, 86, 2567, 2588, 2564, 2571, 2556])).
% 1.32/1.52 tff(2631,plain,
% 1.32/1.52 (~c3_1(a135)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[396, 2630])).
% 1.32/1.52 tff(2632,plain,
% 1.32/1.52 (~c2_1(a135)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[402, 2630])).
% 1.32/1.52 tff(2633,plain,
% 1.32/1.52 (c0_1(a135)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[420, 2630])).
% 1.32/1.52 tff(2634,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[589, 142, 2633, 2580, 2572, 2632, 2631, 2570, 181, 2579])).
% 1.32/1.52 tff(2635,plain,((~hskp31) | c2_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(2636,plain,
% 1.32/1.52 (c0_1(a163)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2635, 2536, 86])).
% 1.32/1.52 tff(2637,plain,
% 1.32/1.52 (hskp10),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2203, 2539, 2552, 2537, 2538])).
% 1.32/1.52 tff(2638,plain,
% 1.32/1.52 (~c3_1(a111)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1235, 2637])).
% 1.32/1.52 tff(2639,plain,
% 1.32/1.52 (~c2_1(a111)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1241, 2637])).
% 1.32/1.52 tff(2640,plain,
% 1.32/1.52 (~c0_1(a111)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1247, 2637])).
% 1.32/1.52 tff(2641,plain,
% 1.32/1.52 (hskp13),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1254, 142, 2539, 2537, 2538, 2640, 2639, 2638, 1229])).
% 1.32/1.52 tff(2642,plain,
% 1.32/1.52 (~c3_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[566, 2641])).
% 1.32/1.52 tff(2643,plain,
% 1.32/1.52 (c2_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[574, 2641])).
% 1.32/1.52 tff(2644,plain,
% 1.32/1.52 (c1_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[582, 2641])).
% 1.32/1.52 tff(2645,plain,
% 1.32/1.52 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2646,plain,
% 1.32/1.52 ((hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163))) <=> (hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2647,plain,
% 1.32/1.52 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[2646])).
% 1.32/1.52 tff(2648,plain,
% 1.32/1.52 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163)))),
% 1.32/1.52 inference(transitivity,[status(thm)],[2647, 2645])).
% 1.32/1.52 tff(2649,plain,
% 1.32/1.52 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2650,plain,
% 1.32/1.52 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2649, 2648])).
% 1.32/1.52 tff(2651,plain,
% 1.32/1.52 (hskp12),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2650, 142, 2644, 2643, 2138, 86, 2642, 1907, 2636])).
% 1.32/1.52 tff(2652,plain,
% 1.32/1.52 (~c2_1(a113)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1600, 2651])).
% 1.32/1.52 tff(2653,plain,
% 1.32/1.52 (~c0_1(a113)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1631, 2651])).
% 1.32/1.52 tff(2654,plain,
% 1.32/1.52 (c3_1(a113)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1608, 2651])).
% 1.32/1.52 tff(2655,plain,
% 1.32/1.52 (~c3_1(a102)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2429, 142, 2539, 2537, 2538, 2654, 2653, 2652, 2554, 2553, 723])).
% 1.32/1.52 tff(2656,plain,
% 1.32/1.52 (c2_1(a102)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1208, 2552])).
% 1.32/1.52 tff(2657,plain,
% 1.32/1.52 (~c0_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2578, 142, 2643, 2656, 2642, 2554, 2553, 331, 2655])).
% 1.32/1.52 tff(2658,plain,
% 1.32/1.52 (hskp8),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2586, 142, 2539, 2537, 2538, 2644, 2642, 2259, 2657])).
% 1.32/1.52 tff(2659,plain,
% 1.32/1.52 (~c3_1(a109)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[155, 2658])).
% 1.32/1.52 tff(2660,plain,
% 1.32/1.52 (~c0_1(a109)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[186, 2658])).
% 1.32/1.52 tff(2661,plain,
% 1.32/1.52 (c1_1(a109)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[163, 2658])).
% 1.32/1.52 tff(2662,plain,
% 1.32/1.52 (hskp19),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2629, 2660, 2638, 2553, 2659, 86, 2639, 2661, 2655, 2656, 2640])).
% 1.32/1.52 tff(2663,plain,
% 1.32/1.52 (~c3_1(a135)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[396, 2662])).
% 1.32/1.52 tff(2664,plain,
% 1.32/1.52 (~c2_1(a135)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[402, 2662])).
% 1.32/1.52 tff(2665,plain,
% 1.32/1.52 (c0_1(a135)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[420, 2662])).
% 1.32/1.52 tff(2666,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2287, 142, 2665, 2644, 2643, 2661, 2664, 2663, 2642, 2660, 2659, 181])).
% 1.32/1.52 tff(2667,plain,(c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(2668,plain,
% 1.32/1.52 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2669,plain,
% 1.32/1.52 ((hskp13 | hskp4 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163))) <=> (hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2670,plain,
% 1.32/1.52 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[2669])).
% 1.32/1.52 tff(2671,plain,
% 1.32/1.52 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 1.32/1.52 inference(transitivity,[status(thm)],[2670, 2668])).
% 1.32/1.52 tff(2672,plain,
% 1.32/1.52 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2673,plain,
% 1.32/1.52 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 1.32/1.52 tff(2674,plain,
% 1.32/1.52 (hskp13 | hskp4 | (~c2_1(a163)) | c3_1(a163)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2673, 142, 2138, 1830])).
% 1.32/1.52 tff(2675,plain,
% 1.32/1.52 (hskp13),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2674, 2163, 2667, 85])).
% 1.32/1.52 tff(2676,plain,
% 1.32/1.52 (~c3_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[566, 2675])).
% 1.32/1.52 tff(2677,plain,
% 1.32/1.52 (c1_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[582, 2675])).
% 1.32/1.52 tff(2678,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2679,plain,
% 1.32/1.52 (((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114))) <=> ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(2680,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[2679])).
% 1.32/1.52 tff(2681,plain,
% 1.32/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 1.32/1.52 inference(transitivity,[status(thm)],[2680, 2678])).
% 1.32/1.52 tff(2682,plain,
% 1.32/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(2683,plain,
% 1.32/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[2682, 2681])).
% 1.32/1.52 tff(2684,plain,
% 1.32/1.52 (c0_1(a114)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[2683, 142, 2168, 2677, 2138, 2667, 85, 2167, 2166, 2676, 181])).
% 1.32/1.53 tff(2685,plain,
% 1.32/1.53 (~c1_1(a111)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1390, 2166, 2216, 2167, 2220, 2675, 2168])).
% 1.32/1.53 tff(2686,plain,
% 1.32/1.53 (hskp4 | hskp3 | c1_1(a111)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2469, 142, 2220, 2217, 2463])).
% 1.32/1.53 tff(2687,plain,
% 1.32/1.53 (hskp3),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2686, 2685, 2163])).
% 1.32/1.53 tff(2688,plain,
% 1.32/1.53 (~c1_1(a104)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2475, 2687])).
% 1.32/1.53 tff(2689,plain,
% 1.32/1.53 (c2_1(a104)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2483, 2687])).
% 1.32/1.53 tff(2690,plain,
% 1.32/1.53 (c0_1(a104)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2491, 2687])).
% 1.32/1.53 tff(2691,plain,
% 1.32/1.53 (c2_1(a114)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[574, 2675])).
% 1.32/1.53 tff(2692,plain,
% 1.32/1.53 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2693,plain,
% 1.32/1.53 ((hskp31 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104))) <=> (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2694,plain,
% 1.32/1.53 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[2693])).
% 1.32/1.53 tff(2695,plain,
% 1.32/1.53 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 1.32/1.53 inference(transitivity,[status(thm)],[2694, 2692])).
% 1.32/1.53 tff(2696,plain,
% 1.32/1.53 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(2697,plain,
% 1.32/1.53 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[2696, 2695])).
% 1.32/1.53 tff(2698,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2697, 23, 142, 2677, 2691, 2690, 2689, 2688, 2230, 2684])).
% 1.32/1.53 tff(2699,plain,(hskp31 | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(2700,plain,
% 1.32/1.53 (hskp31),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2699, 85])).
% 1.32/1.53 tff(2701,plain,
% 1.32/1.53 (c3_1(a141)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[57, 2700])).
% 1.32/1.53 tff(2702,plain,
% 1.32/1.53 (c0_1(a141)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[73, 2700])).
% 1.32/1.53 tff(2703,plain,
% 1.32/1.53 (~c2_1(a141)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2208, 1, 2702, 2701])).
% 1.32/1.53 tff(2704,plain,
% 1.32/1.53 (c1_1(a141)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[65, 2700])).
% 1.32/1.53 tff(2705,plain,
% 1.32/1.53 (hskp2),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2009, 142, 2704, 2701, 2220, 2217, 246, 2703, 2219])).
% 1.32/1.53 tff(2706,plain,
% 1.32/1.53 (~c3_1(a103)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[383, 2705])).
% 1.32/1.53 tff(2707,plain,
% 1.32/1.53 (c1_1(a103)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[261, 2705])).
% 1.32/1.53 tff(2708,plain,
% 1.32/1.53 (c2_1(a103)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[269, 142, 1, 2707, 2706, 11])).
% 1.32/1.53 tff(2709,plain,
% 1.32/1.53 (hskp1 | c2_1(a141)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1307, 142, 2139, 2702, 2704, 21])).
% 1.32/1.53 tff(2710,plain,
% 1.32/1.53 (hskp1),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2709, 2703])).
% 1.32/1.53 tff(2711,plain,
% 1.32/1.53 (~c1_1(a102)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1158, 2710])).
% 1.32/1.53 tff(2712,plain,
% 1.32/1.53 (~c0_1(a102)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1164, 2710])).
% 1.32/1.53 tff(2713,plain,
% 1.32/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2714,plain,
% 1.32/1.53 ((hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141))) <=> (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2715,plain,
% 1.32/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[2714])).
% 1.32/1.53 tff(2716,plain,
% 1.32/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 1.32/1.53 inference(transitivity,[status(thm)],[2715, 2713])).
% 1.32/1.53 tff(2717,plain,
% 1.32/1.53 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(2718,plain,
% 1.32/1.53 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[2717, 2716])).
% 1.32/1.53 tff(2719,plain,
% 1.32/1.53 (hskp12),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2718, 142, 2702, 2704, 2138, 2667, 85, 1907, 2703])).
% 1.32/1.53 tff(2720,plain,
% 1.32/1.53 (~c2_1(a113)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1600, 2719])).
% 1.32/1.53 tff(2721,plain,
% 1.32/1.53 (~c0_1(a113)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1631, 2719])).
% 1.32/1.53 tff(2722,plain,
% 1.32/1.53 (c3_1(a113)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1608, 2719])).
% 1.32/1.53 tff(2723,plain,
% 1.32/1.53 (~c3_1(a102)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2429, 142, 2702, 2704, 2701, 2722, 2721, 2720, 2712, 2711, 723])).
% 1.32/1.53 tff(2724,plain,
% 1.32/1.53 (c2_1(a102)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1208, 2710])).
% 1.32/1.53 tff(2725,plain,
% 1.32/1.53 (c0_1(a103)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[278, 2705])).
% 1.32/1.53 tff(2726,plain,
% 1.32/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2727,plain,
% 1.32/1.53 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> (c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2728,plain,
% 1.32/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111)))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[2727])).
% 1.32/1.53 tff(2729,plain,
% 1.32/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 1.32/1.53 inference(transitivity,[status(thm)],[2728, 2726])).
% 1.32/1.53 tff(2730,plain,
% 1.32/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(2731,plain,
% 1.32/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111)),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[2730, 2729])).
% 1.32/1.53 tff(2732,plain,
% 1.32/1.53 (c3_1(a102) | (~c2_1(a103))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2731, 142, 2725, 2724, 2220, 2216, 2706, 2712, 331, 2219])).
% 1.32/1.53 tff(2733,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2732, 2723, 2708])).
% 1.32/1.53 tff(2734,plain,(hskp19 | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(2735,plain,
% 1.32/1.53 (hskp19),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2734, 85])).
% 1.32/1.53 tff(2736,plain,
% 1.32/1.53 (c0_1(a135)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[420, 2735])).
% 1.32/1.53 tff(2737,plain,
% 1.32/1.53 (hskp13),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1254, 142, 2702, 2704, 2701, 2220, 2217, 2216, 1229])).
% 1.32/1.53 tff(2738,plain,
% 1.32/1.53 (~c2_1(a135)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[402, 2735])).
% 1.32/1.53 tff(2739,plain,
% 1.32/1.53 (~c3_1(a135)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[396, 2735])).
% 1.32/1.53 tff(2740,plain,
% 1.32/1.53 (~c1_1(a111)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1390, 2739, 2216, 2738, 2220, 2737, 2736])).
% 1.32/1.53 tff(2741,plain,
% 1.32/1.53 (hskp5 | c1_1(a111)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1676, 142, 2220, 2216, 206])).
% 1.32/1.53 tff(2742,plain,
% 1.32/1.53 (hskp5),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2741, 2740])).
% 1.32/1.53 tff(2743,plain,
% 1.32/1.53 (~c2_1(a106)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[892, 2742])).
% 1.32/1.53 tff(2744,plain,
% 1.32/1.53 (c1_1(a106)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[233, 2742])).
% 1.32/1.53 tff(2745,plain,
% 1.32/1.53 (c0_1(a106)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[304, 2742])).
% 1.32/1.53 tff(2746,plain,
% 1.32/1.53 (hskp1),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1707, 142, 2139, 2745, 2744, 2743, 21])).
% 1.32/1.53 tff(2747,plain,
% 1.32/1.53 (~c1_1(a102)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1158, 2746])).
% 1.32/1.53 tff(2748,plain,
% 1.32/1.53 (~c0_1(a102)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1164, 2746])).
% 1.32/1.53 tff(2749,plain,
% 1.32/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2750,plain,
% 1.32/1.53 ((hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106))) <=> (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2751,plain,
% 1.32/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[2750])).
% 1.32/1.53 tff(2752,plain,
% 1.32/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 1.32/1.53 inference(transitivity,[status(thm)],[2751, 2749])).
% 1.32/1.53 tff(2753,plain,
% 1.32/1.53 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(2754,plain,
% 1.32/1.53 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 1.32/1.53 tff(2755,plain,
% 1.32/1.53 (hskp12),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2754, 142, 2745, 2744, 2138, 2667, 85, 2743, 1907])).
% 1.32/1.53 tff(2756,plain,
% 1.32/1.53 (~c2_1(a113)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1600, 2755])).
% 1.32/1.53 tff(2757,plain,
% 1.32/1.53 (~c0_1(a113)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1631, 2755])).
% 1.32/1.53 tff(2758,plain,
% 1.32/1.53 (c3_1(a113)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1608, 2755])).
% 1.32/1.53 tff(2759,plain,
% 1.32/1.53 (~c3_1(a102)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2429, 142, 2702, 2704, 2701, 2758, 2757, 2756, 2748, 2747, 723])).
% 1.32/1.53 tff(2760,plain,
% 1.32/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2761,plain,
% 1.32/1.53 (((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c0_1(a163) | (~c1_1(a163))) <=> ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2762,plain,
% 1.32/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163)))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[2761])).
% 1.32/1.53 tff(2763,plain,
% 1.32/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163))),
% 1.32/1.53 inference(transitivity,[status(thm)],[2762, 2760])).
% 1.32/1.53 tff(2764,plain,
% 1.32/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(2765,plain,
% 1.32/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163)),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 1.32/1.53 tff(2766,plain,
% 1.32/1.53 (c0_1(a163)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[2765, 142, 2736, 2138, 2667, 85, 2738, 2739, 181])).
% 1.32/1.53 tff(2767,plain,
% 1.32/1.53 (c2_1(a102)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1208, 2746])).
% 1.32/1.53 tff(2768,plain,
% 1.32/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2769,plain,
% 1.32/1.53 (((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> ((~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(2770,plain,
% 1.32/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[2769])).
% 1.36/1.53 tff(2771,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[2770, 2768])).
% 1.36/1.53 tff(2772,plain,
% 1.36/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(2773,plain,
% 1.36/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[2772, 2771])).
% 1.36/1.53 tff(2774,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[2773, 142, 2767, 2667, 85, 2220, 2216, 2748, 331, 2766, 2740, 2759])).
% 1.36/1.53 tff(2775,plain,(c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(2776,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(2777,plain,
% 1.36/1.53 (((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(2778,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[2777])).
% 1.36/1.53 tff(2779,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[2778, 2776])).
% 1.36/1.53 tff(2780,plain,
% 1.36/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(2781,plain,
% 1.36/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[2780, 2779])).
% 1.36/1.53 tff(2782,plain,
% 1.36/1.53 (c1_1(a111)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[2781, 142, 2168, 2138, 2667, 2775, 2167, 2166, 2217, 2216, 96])).
% 1.36/1.53 tff(2783,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(2784,plain,
% 1.36/1.53 (((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135)) <=> ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(2785,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[2784])).
% 1.36/1.53 tff(2786,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[2785, 2783])).
% 1.36/1.53 tff(2787,plain,
% 1.36/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(2788,plain,
% 1.36/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 1.36/1.53 tff(2789,plain,
% 1.36/1.53 (c1_1(a135)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[2788, 142, 2168, 2138, 2667, 2775, 2167, 2166, 96])).
% 1.36/1.53 tff(2790,plain,
% 1.36/1.53 (hskp13),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1842, 2789, 2217, 2163, 2216, 2220, 2168, 2167])).
% 1.36/1.53 tff(2791,plain,
% 1.36/1.53 ($false),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1390, 2790, 2782, 2216, 2167, 2220, 2166, 2168])).
% 1.36/1.53 tff(2792,plain,(hskp31), inference(lemma,lemma(discharge,[]))).
% 1.36/1.53 tff(2793,plain,
% 1.36/1.53 (c3_1(a141)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[57, 2792])).
% 1.36/1.53 tff(2794,plain,
% 1.36/1.53 (c0_1(a141)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[73, 2792])).
% 1.36/1.53 tff(2795,plain,
% 1.36/1.53 (~c2_1(a141)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[2208, 1, 2794, 2793])).
% 1.36/1.53 tff(2796,plain,
% 1.36/1.53 (c1_1(a141)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[65, 2792])).
% 1.36/1.53 tff(2797,plain,
% 1.36/1.53 (hskp1 | c2_1(a141)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1307, 142, 2139, 2794, 2796, 21])).
% 1.36/1.53 tff(2798,plain,
% 1.36/1.53 (hskp1),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[2797, 2795])).
% 1.36/1.53 tff(2799,plain,
% 1.36/1.53 (~c1_1(a102)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1158, 2798])).
% 1.36/1.53 tff(2800,plain,
% 1.36/1.53 (~c0_1(a102)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1164, 2798])).
% 1.36/1.53 tff(2801,plain,
% 1.36/1.53 (c2_1(a102)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1208, 2798])).
% 1.36/1.53 tff(2802,plain,
% 1.36/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(2803,plain,
% 1.36/1.54 (((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a111) | c0_1(a111) | c2_1(a111)) <=> ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(2804,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a111) | c0_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111)))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[2803])).
% 1.36/1.54 tff(2805,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a111) | c0_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111))),
% 1.36/1.54 inference(transitivity,[status(thm)],[2804, 2802])).
% 1.36/1.54 tff(2806,plain,
% 1.36/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a111) | c0_1(a111) | c2_1(a111))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(2807,plain,
% 1.36/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 1.36/1.54 tff(2808,plain,
% 1.36/1.54 ($false),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[2807, 142, 2801, 2138, 2667, 2775, 2220, 2217, 2800, 2799, 1137, 2219])).
% 1.36/1.54 tff(2809,plain,(hskp19), inference(lemma,lemma(discharge,[]))).
% 1.36/1.54 tff(2810,plain,
% 1.36/1.54 (c0_1(a135)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[420, 2809])).
% 1.36/1.54 tff(2811,plain,
% 1.36/1.54 (~c2_1(a135)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[402, 2809])).
% 1.36/1.54 tff(2812,plain,
% 1.36/1.54 (hskp13),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1254, 142, 2794, 2796, 2793, 2220, 2217, 2216, 1229])).
% 1.36/1.54 tff(2813,plain,
% 1.36/1.54 (~c3_1(a135)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[396, 2809])).
% 1.36/1.54 tff(2814,plain,
% 1.36/1.54 (~c1_1(a111)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1390, 2813, 2216, 2812, 2220, 2811, 2810])).
% 1.36/1.54 tff(2815,plain,
% 1.36/1.54 ($false),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[2781, 142, 2810, 2138, 2667, 2775, 2811, 2813, 2217, 2216, 96, 2814])).
% 1.36/1.54 % SZS output end Proof
% 1.36/1.54 % E exiting
%------------------------------------------------------------------------------