%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN482-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:17 AM UTC 2025
% Result : Unsatisfiable 0.77s 0.99s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN482-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:36:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.77/0.99 % SZS status Unsatisfiable
% 0.77/0.99 % SZS output start Proof
% 0.77/0.99 tff(c1_1_type, type, (
% 0.77/0.99 c1_1: $i > $o)).
% 0.77/0.99 tff(a1758_type, type, (
% 0.77/0.99 a1758: $i)).
% 0.77/0.99 tff(hskp3_type, type, (
% 0.77/0.99 hskp3: $o)).
% 0.77/0.99 tff(c0_1_type, type, (
% 0.77/0.99 c0_1: $i > $o)).
% 0.77/0.99 tff(a1780_type, type, (
% 0.77/0.99 a1780: $i)).
% 0.77/0.99 tff(a1781_type, type, (
% 0.77/0.99 a1781: $i)).
% 0.77/0.99 tff(c2_1_type, type, (
% 0.77/0.99 c2_1: $i > $o)).
% 0.77/0.99 tff(a1783_type, type, (
% 0.77/0.99 a1783: $i)).
% 0.77/0.99 tff(c3_1_type, type, (
% 0.77/0.99 c3_1: $i > $o)).
% 0.77/0.99 tff(ndr1_0_type, type, (
% 0.77/0.99 ndr1_0: $o)).
% 0.77/0.99 tff(hskp19_type, type, (
% 0.77/0.99 hskp19: $o)).
% 0.77/0.99 tff(a1765_type, type, (
% 0.77/0.99 a1765: $i)).
% 0.77/0.99 tff(a1762_type, type, (
% 0.77/0.99 a1762: $i)).
% 0.77/0.99 tff(a1771_type, type, (
% 0.77/0.99 a1771: $i)).
% 0.77/0.99 tff(hskp13_type, type, (
% 0.77/0.99 hskp13: $o)).
% 0.77/0.99 tff(hskp6_type, type, (
% 0.77/0.99 hskp6: $o)).
% 0.77/0.99 tff(a1768_type, type, (
% 0.77/0.99 a1768: $i)).
% 0.77/0.99 tff(hskp11_type, type, (
% 0.77/0.99 hskp11: $o)).
% 0.77/0.99 tff(a1827_type, type, (
% 0.77/0.99 a1827: $i)).
% 0.77/0.99 tff(hskp0_type, type, (
% 0.77/0.99 hskp0: $o)).
% 0.77/0.99 tff(hskp4_type, type, (
% 0.77/0.99 hskp4: $o)).
% 0.77/0.99 tff(a1759_type, type, (
% 0.77/0.99 a1759: $i)).
% 0.77/0.99 tff(a1788_type, type, (
% 0.77/0.99 a1788: $i)).
% 0.77/0.99 tff(a1756_type, type, (
% 0.77/0.99 a1756: $i)).
% 0.77/0.99 tff(hskp27_type, type, (
% 0.77/0.99 hskp27: $o)).
% 0.77/0.99 tff(hskp2_type, type, (
% 0.77/0.99 hskp2: $o)).
% 0.77/0.99 tff(a1757_type, type, (
% 0.77/0.99 a1757: $i)).
% 0.77/0.99 tff(hskp1_type, type, (
% 0.77/0.99 hskp1: $o)).
% 0.77/0.99 tff(hskp28_type, type, (
% 0.77/0.99 hskp28: $o)).
% 0.77/0.99 tff(hskp8_type, type, (
% 0.77/0.99 hskp8: $o)).
% 0.77/0.99 tff(hskp25_type, type, (
% 0.77/0.99 hskp25: $o)).
% 0.77/0.99 tff(a1767_type, type, (
% 0.77/0.99 a1767: $i)).
% 0.77/0.99 tff(hskp10_type, type, (
% 0.77/0.99 hskp10: $o)).
% 0.77/0.99 tff(a1799_type, type, (
% 0.77/0.99 a1799: $i)).
% 0.77/0.99 tff(hskp22_type, type, (
% 0.77/0.99 hskp22: $o)).
% 0.77/0.99 tff(hskp16_type, type, (
% 0.77/0.99 hskp16: $o)).
% 0.77/0.99 tff(hskp21_type, type, (
% 0.77/0.99 hskp21: $o)).
% 0.77/0.99 tff(a1809_type, type, (
% 0.77/0.99 a1809: $i)).
% 0.77/0.99 tff(hskp24_type, type, (
% 0.77/0.99 hskp24: $o)).
% 0.77/0.99 tff(a1763_type, type, (
% 0.77/0.99 a1763: $i)).
% 0.77/0.99 tff(hskp7_type, type, (
% 0.77/0.99 hskp7: $o)).
% 0.77/0.99 tff(a1805_type, type, (
% 0.77/0.99 a1805: $i)).
% 0.77/0.99 tff(hskp29_type, type, (
% 0.77/0.99 hskp29: $o)).
% 0.77/0.99 tff(hskp17_type, type, (
% 0.77/0.99 hskp17: $o)).
% 0.77/0.99 tff(a1823_type, type, (
% 0.77/0.99 a1823: $i)).
% 0.77/0.99 tff(hskp30_type, type, (
% 0.77/0.99 hskp30: $o)).
% 0.77/0.99 tff(a1754_type, type, (
% 0.77/0.99 a1754: $i)).
% 0.77/0.99 tff(a1807_type, type, (
% 0.77/0.99 a1807: $i)).
% 0.77/0.99 tff(a1779_type, type, (
% 0.77/0.99 a1779: $i)).
% 0.77/0.99 tff(hskp15_type, type, (
% 0.77/0.99 hskp15: $o)).
% 0.77/0.99 tff(a1777_type, type, (
% 0.77/0.99 a1777: $i)).
% 0.77/0.99 tff(hskp14_type, type, (
% 0.77/0.99 hskp14: $o)).
% 0.77/0.99 tff(hskp23_type, type, (
% 0.77/0.99 hskp23: $o)).
% 0.77/0.99 tff(a1760_type, type, (
% 0.77/0.99 a1760: $i)).
% 0.77/0.99 tff(a1786_type, type, (
% 0.77/0.99 a1786: $i)).
% 0.77/0.99 tff(hskp20_type, type, (
% 0.77/0.99 hskp20: $o)).
% 0.77/0.99 tff(hskp12_type, type, (
% 0.77/0.99 hskp12: $o)).
% 0.77/0.99 tff(a1770_type, type, (
% 0.77/0.99 a1770: $i)).
% 0.77/0.99 tff(hskp18_type, type, (
% 0.77/0.99 hskp18: $o)).
% 0.77/0.99 tff(a1782_type, type, (
% 0.77/0.99 a1782: $i)).
% 0.77/0.99 tff(a1795_type, type, (
% 0.77/0.99 a1795: $i)).
% 0.77/0.99 tff(hskp5_type, type, (
% 0.77/0.99 hskp5: $o)).
% 0.77/0.99 tff(1,assumption,(~c2_1(a1783)), introduced(assumption)).
% 0.77/0.99 tff(2,plain,
% 0.77/0.99 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(3,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[2])).
% 0.77/0.99 tff(4,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(5,plain,
% 0.77/0.99 (^[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)) | (~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))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_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)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~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)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(6,plain,
% 0.77/0.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[5])).
% 0.77/0.99 tff(7,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.77/0.99 tff(8,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.77/0.99 tff(9,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.77/0.99 tff(10,plain,(
% 0.77/0.99 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.99 inference(skolemize,[status(sab)],[9])).
% 0.77/0.99 tff(11,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.77/0.99 tff(12,assumption,(~hskp19), introduced(assumption)).
% 0.77/0.99 tff(13,plain,
% 0.77/0.99 (^[U: $i] : refl((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(14,plain,
% 0.77/0.99 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[13])).
% 0.77/0.99 tff(15,plain,
% 0.77/0.99 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(16,plain,
% 0.77/0.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(17,plain,
% 0.77/0.99 (![U: $i] : (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[16])).
% 0.77/0.99 tff(18,axiom,(![U: $i] : (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.77/0.99 tff(19,plain,
% 0.77/0.99 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.77/0.99 tff(20,plain,
% 0.77/0.99 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.77/0.99 tff(21,plain,(
% 0.77/0.99 ![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/0.99 inference(skolemize,[status(sab)],[20])).
% 0.77/0.99 tff(22,plain,
% 0.77/0.99 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.77/0.99 tff(23,assumption,(~hskp13), introduced(assumption)).
% 0.77/0.99 tff(24,plain,
% 0.77/0.99 (^[U: $i] : refl((hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(25,plain,
% 0.77/0.99 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[24])).
% 0.77/0.99 tff(26,plain,
% 0.77/0.99 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(27,plain,
% 0.77/0.99 (^[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)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp19) <=> ((hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp19) <=> (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(28,plain,
% 0.77/0.99 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp19) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[27])).
% 0.77/0.99 tff(29,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.77/0.99 tff(30,plain,
% 0.77/0.99 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.77/0.99 tff(31,plain,
% 0.77/0.99 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.77/0.99 tff(32,plain,(
% 0.77/0.99 ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/0.99 inference(skolemize,[status(sab)],[31])).
% 0.77/0.99 tff(33,plain,
% 0.77/0.99 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.77/0.99 tff(34,assumption,(~c3_1(a1759)), introduced(assumption)).
% 0.77/0.99 tff(35,assumption,(~hskp3), introduced(assumption)).
% 0.77/0.99 tff(36,assumption,(~c2_1(a1759)), introduced(assumption)).
% 0.77/0.99 tff(37,plain,
% 0.77/0.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(38,plain,
% 0.77/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[37])).
% 0.77/0.99 tff(39,plain,
% 0.77/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(40,plain,
% 0.77/0.99 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(41,plain,
% 0.77/0.99 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[40])).
% 0.77/0.99 tff(42,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 0.77/0.99 tff(43,plain,
% 0.77/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.77/0.99 tff(44,plain,
% 0.77/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.77/0.99 tff(45,plain,(
% 0.77/0.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/0.99 inference(skolemize,[status(sab)],[44])).
% 0.77/0.99 tff(46,plain,
% 0.77/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.77/0.99 tff(47,assumption,(~c1_1(a1759)), introduced(assumption)).
% 0.77/0.99 tff(48,assumption,(hskp2), introduced(assumption)).
% 0.77/0.99 tff(49,plain,
% 0.77/0.99 (((~hskp2) | (~c2_1(a1757))) <=> ((~hskp2) | (~c2_1(a1757)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(50,plain,
% 0.77/0.99 (((~c2_1(a1757)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1757)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(51,axiom,((~c2_1(a1757)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.77/0.99 tff(52,plain,
% 0.77/0.99 ((~hskp2) | (~c2_1(a1757))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.77/0.99 tff(53,plain,
% 0.77/0.99 ((~hskp2) | (~c2_1(a1757))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.77/0.99 tff(54,plain,
% 0.77/0.99 (~c2_1(a1757)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[53, 48])).
% 0.77/0.99 tff(55,plain,
% 0.77/0.99 (((~hskp2) | c1_1(a1757)) <=> ((~hskp2) | c1_1(a1757))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(56,axiom,((~hskp2) | c1_1(a1757)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.77/0.99 tff(57,plain,
% 0.77/0.99 ((~hskp2) | c1_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.77/0.99 tff(58,plain,
% 0.77/0.99 ((~hskp2) | c1_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[57, 55])).
% 0.77/0.99 tff(59,plain,
% 0.77/0.99 ((~hskp2) | c1_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.77/0.99 tff(60,plain,
% 0.77/0.99 ((~hskp2) | c1_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.77/0.99 tff(61,plain,
% 0.77/0.99 ((~hskp2) | c1_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.77/0.99 tff(62,plain,
% 0.77/0.99 (c1_1(a1757)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[61, 48])).
% 0.77/0.99 tff(63,plain,
% 0.77/0.99 (((~hskp2) | c0_1(a1757)) <=> ((~hskp2) | c0_1(a1757))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(64,axiom,((~hskp2) | c0_1(a1757)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.77/0.99 tff(65,plain,
% 0.77/0.99 ((~hskp2) | c0_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.77/0.99 tff(66,plain,
% 0.77/0.99 ((~hskp2) | c0_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[65, 63])).
% 0.77/0.99 tff(67,plain,
% 0.77/0.99 ((~hskp2) | c0_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[66, 63])).
% 0.77/0.99 tff(68,plain,
% 0.77/0.99 ((~hskp2) | c0_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.77/0.99 tff(69,plain,
% 0.77/0.99 ((~hskp2) | c0_1(a1757)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[68, 63])).
% 0.77/0.99 tff(70,plain,
% 0.77/0.99 (c0_1(a1757)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[69, 48])).
% 0.77/0.99 tff(71,assumption,(~ndr1_0), introduced(assumption)).
% 0.77/0.99 tff(72,plain,
% 0.77/0.99 ((ndr1_0 | (~hskp1)) <=> (ndr1_0 | (~hskp1))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(73,plain,
% 0.77/0.99 (((~hskp1) | ndr1_0) <=> (ndr1_0 | (~hskp1))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(74,axiom,((~hskp1) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 0.77/0.99 tff(75,plain,
% 0.77/0.99 (ndr1_0 | (~hskp1)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.77/0.99 tff(76,plain,
% 0.77/0.99 (ndr1_0 | (~hskp1)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.77/0.99 tff(77,plain,
% 0.77/0.99 (~hskp1),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[76, 71])).
% 0.77/0.99 tff(78,plain,
% 0.77/0.99 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(79,plain,
% 0.77/0.99 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(80,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.77/0.99 tff(81,plain,
% 0.77/0.99 (ndr1_0 | (~hskp28)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.77/0.99 tff(82,plain,
% 0.77/0.99 (ndr1_0 | (~hskp28)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.77/0.99 tff(83,plain,
% 0.77/0.99 (~hskp28),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[82, 71])).
% 0.77/0.99 tff(84,plain,
% 0.77/0.99 ((ndr1_0 | (~hskp4)) <=> (ndr1_0 | (~hskp4))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(85,plain,
% 0.77/0.99 (((~hskp4) | ndr1_0) <=> (ndr1_0 | (~hskp4))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(86,axiom,((~hskp4) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause27')).
% 0.77/0.99 tff(87,plain,
% 0.77/0.99 (ndr1_0 | (~hskp4)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.77/0.99 tff(88,plain,
% 0.77/0.99 (ndr1_0 | (~hskp4)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.77/0.99 tff(89,plain,
% 0.77/0.99 (~hskp4),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[88, 71])).
% 0.77/0.99 tff(90,plain,
% 0.77/0.99 ((hskp28 | hskp4 | hskp1) <=> (hskp28 | hskp4 | hskp1)),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(91,plain,
% 0.77/0.99 (((hskp28 | hskp1) | hskp4) <=> (hskp28 | hskp4 | hskp1)),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(92,plain,
% 0.77/0.99 ((hskp28 | hskp1) <=> (hskp28 | hskp1)),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(93,plain,
% 0.77/0.99 (((hskp28 | hskp1) | hskp4) <=> ((hskp28 | hskp1) | hskp4)),
% 0.77/1.00 inference(monotonicity,[status(thm)],[92])).
% 0.77/1.00 tff(94,plain,
% 0.77/1.00 (((hskp28 | hskp1) | hskp4) <=> (hskp28 | hskp4 | hskp1)),
% 0.77/1.00 inference(transitivity,[status(thm)],[93, 91])).
% 0.77/1.00 tff(95,axiom,((hskp28 | hskp1) | hskp4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 0.77/1.00 tff(96,plain,
% 0.77/1.00 (hskp28 | hskp4 | hskp1),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.77/1.00 tff(97,plain,
% 0.77/1.00 (hskp28 | hskp4 | hskp1),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[96, 90])).
% 0.77/1.00 tff(98,plain,
% 0.77/1.00 (hskp28 | hskp4 | hskp1),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.77/1.00 tff(99,plain,
% 0.77/1.00 (hskp28 | hskp4 | hskp1),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[98, 90])).
% 0.77/1.00 tff(100,plain,
% 0.77/1.00 (hskp28 | hskp4 | hskp1),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[99, 90])).
% 0.77/1.00 tff(101,plain,
% 0.77/1.00 ($false),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[100, 89, 83, 77])).
% 0.77/1.00 tff(102,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.77/1.00 tff(103,plain,
% 0.77/1.00 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(104,plain,
% 0.77/1.00 ((hskp19 | hskp13 | (~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757))) <=> (hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(105,plain,
% 0.77/1.00 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[104])).
% 0.77/1.00 tff(106,plain,
% 0.77/1.00 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[105, 103])).
% 0.77/1.00 tff(107,plain,
% 0.77/1.00 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(108,plain,
% 0.77/1.00 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.77/1.00 tff(109,plain,
% 0.77/1.00 ($false),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[108, 102, 12, 23, 70, 62, 54, 33])).
% 0.77/1.00 tff(110,plain,((~hskp2) | hskp19 | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.77/1.00 tff(111,plain,
% 0.77/1.00 (~hskp2),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[110, 23, 12])).
% 0.77/1.00 tff(112,plain,
% 0.77/1.00 (^[U: $i] : refl((hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(113,plain,
% 0.77/1.00 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[112])).
% 0.77/1.00 tff(114,plain,
% 0.77/1.00 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(115,plain,
% 0.77/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp4) <=> ((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp4))), rewrite(((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp4) <=> (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp4) <=> (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(116,plain,
% 0.77/1.00 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp4) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[115])).
% 0.77/1.00 tff(117,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 0.77/1.00 tff(118,plain,
% 0.77/1.00 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.77/1.00 tff(119,plain,
% 0.77/1.00 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.77/1.00 tff(120,plain,(
% 0.77/1.00 ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.00 inference(skolemize,[status(sab)],[119])).
% 0.77/1.00 tff(121,plain,
% 0.77/1.00 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.77/1.00 tff(122,plain,
% 0.77/1.00 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(123,plain,
% 0.77/1.00 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[122])).
% 0.77/1.00 tff(124,plain,
% 0.77/1.00 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(125,plain,
% 0.77/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(126,plain,
% 0.77/1.00 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[125])).
% 0.77/1.00 tff(127,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.77/1.00 tff(128,plain,
% 0.77/1.00 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.77/1.00 tff(129,plain,
% 0.77/1.00 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.77/1.00 tff(130,plain,(
% 0.77/1.00 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.77/1.00 inference(skolemize,[status(sab)],[129])).
% 0.77/1.00 tff(131,plain,
% 0.77/1.00 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.77/1.00 tff(132,plain,
% 0.77/1.00 (((~hskp4) | c1_1(a1759)) <=> ((~hskp4) | c1_1(a1759))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(133,axiom,((~hskp4) | c1_1(a1759)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.77/1.00 tff(134,plain,
% 0.77/1.00 ((~hskp4) | c1_1(a1759)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.77/1.00 tff(135,plain,
% 0.77/1.00 ((~hskp4) | c1_1(a1759)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[134, 132])).
% 0.77/1.00 tff(136,plain,
% 0.77/1.00 ((~hskp4) | c1_1(a1759)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[135, 132])).
% 0.77/1.00 tff(137,plain,
% 0.77/1.00 ((~hskp4) | c1_1(a1759)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.77/1.00 tff(138,plain,
% 0.77/1.00 ((~hskp4) | c1_1(a1759)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[137, 132])).
% 0.77/1.00 tff(139,plain,
% 0.77/1.00 (~hskp4),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[138, 47])).
% 0.77/1.00 tff(140,plain,
% 0.77/1.00 ((hskp25 | hskp4 | hskp2) <=> (hskp25 | hskp4 | hskp2)),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(141,plain,
% 0.77/1.00 (((hskp2 | hskp4) | hskp25) <=> (hskp25 | hskp4 | hskp2)),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(142,axiom,((hskp2 | hskp4) | hskp25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.77/1.00 tff(143,plain,
% 0.77/1.00 (hskp25 | hskp4 | hskp2),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.77/1.00 tff(144,plain,
% 0.77/1.00 (hskp25 | hskp4 | hskp2),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[143, 140])).
% 0.77/1.00 tff(145,plain,
% 0.77/1.00 (hskp25 | hskp4 | hskp2),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.77/1.00 tff(146,plain,
% 0.77/1.00 (hskp25 | hskp4 | hskp2),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[145, 140])).
% 0.77/1.00 tff(147,plain,
% 0.77/1.00 (hskp25 | hskp4 | hskp2),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[146, 140])).
% 0.77/1.00 tff(148,plain,
% 0.77/1.00 (hskp25),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[147, 111, 139])).
% 0.77/1.00 tff(149,plain,
% 0.77/1.00 (((~hskp25) | (~c1_1(a1827))) <=> ((~hskp25) | (~c1_1(a1827)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(150,plain,
% 0.77/1.00 (((~c1_1(a1827)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a1827)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(151,axiom,((~c1_1(a1827)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.77/1.00 tff(152,plain,
% 0.77/1.00 ((~hskp25) | (~c1_1(a1827))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.77/1.00 tff(153,plain,
% 0.77/1.00 ((~hskp25) | (~c1_1(a1827))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[152, 149])).
% 0.77/1.00 tff(154,plain,
% 0.77/1.00 (~c1_1(a1827)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[153, 148])).
% 0.77/1.00 tff(155,plain,
% 0.77/1.00 (((~hskp25) | (~c0_1(a1827))) <=> ((~hskp25) | (~c0_1(a1827)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(156,plain,
% 0.77/1.00 (((~c0_1(a1827)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1827)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(157,axiom,((~c0_1(a1827)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.77/1.00 tff(158,plain,
% 0.77/1.00 ((~hskp25) | (~c0_1(a1827))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.77/1.00 tff(159,plain,
% 0.77/1.00 ((~hskp25) | (~c0_1(a1827))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[158, 155])).
% 0.77/1.00 tff(160,plain,
% 0.77/1.00 (~c0_1(a1827)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[159, 148])).
% 0.77/1.00 tff(161,plain,
% 0.77/1.00 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(162,plain,
% 0.77/1.00 ((hskp4 | hskp3 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827)) <=> (hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(163,plain,
% 0.77/1.00 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827)))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[162])).
% 0.77/1.00 tff(164,plain,
% 0.77/1.00 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 0.77/1.00 inference(transitivity,[status(thm)],[163, 161])).
% 0.77/1.00 tff(165,plain,
% 0.77/1.00 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(166,plain,
% 0.77/1.00 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.77/1.00 tff(167,plain,
% 0.77/1.00 (c3_1(a1827)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[166, 102, 139, 35, 160, 154, 131])).
% 0.77/1.00 tff(168,plain,
% 0.77/1.00 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(169,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[168])).
% 0.77/1.00 tff(170,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(171,plain,
% 0.77/1.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~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(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(172,plain,
% 0.77/1.00 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[171])).
% 0.77/1.00 tff(173,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 0.77/1.00 tff(174,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.77/1.00 tff(175,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.77/1.00 tff(176,plain,(
% 0.77/1.00 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/1.00 inference(skolemize,[status(sab)],[175])).
% 0.77/1.00 tff(177,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.77/1.00 tff(178,plain,
% 0.77/1.00 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(179,plain,
% 0.77/1.00 ((hskp4 | hskp3 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759)) <=> (hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(180,plain,
% 0.77/1.00 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759)))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[179])).
% 0.77/1.00 tff(181,plain,
% 0.77/1.00 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 0.77/1.00 inference(transitivity,[status(thm)],[180, 178])).
% 0.77/1.00 tff(182,plain,
% 0.77/1.00 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(183,plain,
% 0.77/1.00 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.77/1.00 tff(184,plain,
% 0.77/1.00 (hskp4 | hskp3 | c1_1(a1759) | c0_1(a1759)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[183, 102, 34, 131])).
% 0.77/1.00 tff(185,plain,
% 0.77/1.00 (c0_1(a1759)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[184, 35, 47, 139])).
% 0.77/1.00 tff(186,plain,
% 0.77/1.00 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(187,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[186])).
% 0.77/1.00 tff(188,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(189,plain,
% 0.77/1.00 (^[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))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_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))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(190,plain,
% 0.77/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[189])).
% 0.77/1.00 tff(191,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.77/1.00 tff(192,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.77/1.00 tff(193,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.77/1.00 tff(194,plain,(
% 0.77/1.00 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.77/1.00 inference(skolemize,[status(sab)],[193])).
% 0.77/1.00 tff(195,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.77/1.00 tff(196,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(197,plain,
% 0.77/1.00 ((hskp2 | (~ndr1_0) | c3_1(a1759) | (~c2_1(a1759)) | (~c0_1(a1759)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759))) <=> (hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(198,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1759) | (~c2_1(a1759)) | (~c0_1(a1759)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[197])).
% 0.77/1.00 tff(199,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1759) | (~c2_1(a1759)) | (~c0_1(a1759)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[198, 196])).
% 0.77/1.00 tff(200,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1759) | (~c2_1(a1759)) | (~c0_1(a1759)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(201,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.77/1.00 tff(202,plain,
% 0.77/1.00 (hskp2 | (~c2_1(a1759)) | (~c0_1(a1759))),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[201, 102, 47, 34, 195])).
% 0.77/1.00 tff(203,plain,
% 0.77/1.00 (~c2_1(a1759)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[202, 111, 185])).
% 0.77/1.00 tff(204,plain,
% 0.77/1.00 (((~hskp25) | (~c2_1(a1827))) <=> ((~hskp25) | (~c2_1(a1827)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(205,plain,
% 0.77/1.00 (((~c2_1(a1827)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a1827)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(206,axiom,((~c2_1(a1827)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.77/1.00 tff(207,plain,
% 0.77/1.00 ((~hskp25) | (~c2_1(a1827))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.77/1.00 tff(208,plain,
% 0.77/1.00 ((~hskp25) | (~c2_1(a1827))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[207, 204])).
% 0.77/1.00 tff(209,plain,
% 0.77/1.00 (~c2_1(a1827)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[208, 148])).
% 0.77/1.00 tff(210,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(211,plain,
% 0.77/1.00 ((hskp13 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1759) | c1_1(a1759) | c3_1(a1759)) <=> (hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(212,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1759) | c1_1(a1759) | c3_1(a1759))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[211])).
% 0.77/1.00 tff(213,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1759) | c1_1(a1759) | c3_1(a1759))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[212, 210])).
% 0.77/1.00 tff(214,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1759) | c1_1(a1759) | c3_1(a1759))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(215,plain,
% 0.77/1.00 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.77/1.00 tff(216,plain,
% 0.77/1.00 ($false),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[215, 102, 23, 47, 160, 209, 203, 34, 177, 167])).
% 0.77/1.00 tff(217,plain,(hskp13 | c1_1(a1759) | c3_1(a1759) | hskp3 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.77/1.00 tff(218,plain,
% 0.77/1.00 (hskp13),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[217, 35, 34, 47, 12])).
% 0.77/1.00 tff(219,plain,
% 0.77/1.00 (((~hskp13) | (~c0_1(a1771))) <=> ((~hskp13) | (~c0_1(a1771)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(220,plain,
% 0.77/1.00 (((~c0_1(a1771)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a1771)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(221,axiom,((~c0_1(a1771)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.77/1.00 tff(222,plain,
% 0.77/1.00 ((~hskp13) | (~c0_1(a1771))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.77/1.00 tff(223,plain,
% 0.77/1.00 ((~hskp13) | (~c0_1(a1771))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[222, 219])).
% 0.77/1.00 tff(224,plain,
% 0.77/1.00 (~c0_1(a1771)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[223, 218])).
% 0.77/1.00 tff(225,assumption,(~hskp6), introduced(assumption)).
% 0.77/1.00 tff(226,assumption,(ndr1_0), introduced(assumption)).
% 0.77/1.00 tff(227,assumption,(hskp13), introduced(assumption)).
% 0.77/1.00 tff(228,plain,
% 0.77/1.00 (((~hskp13) | c1_1(a1771)) <=> ((~hskp13) | c1_1(a1771))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(229,axiom,((~hskp13) | c1_1(a1771)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.77/1.00 tff(230,plain,
% 0.77/1.00 ((~hskp13) | c1_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.77/1.00 tff(231,plain,
% 0.77/1.00 ((~hskp13) | c1_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[230, 228])).
% 0.77/1.00 tff(232,plain,
% 0.77/1.00 ((~hskp13) | c1_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[231, 228])).
% 0.77/1.00 tff(233,plain,
% 0.77/1.00 ((~hskp13) | c1_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.77/1.00 tff(234,plain,
% 0.77/1.00 ((~hskp13) | c1_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[233, 228])).
% 0.77/1.00 tff(235,plain,
% 0.77/1.00 (c1_1(a1771)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[234, 227])).
% 0.77/1.00 tff(236,plain,
% 0.77/1.00 (((~hskp13) | c2_1(a1771)) <=> ((~hskp13) | c2_1(a1771))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(237,axiom,((~hskp13) | c2_1(a1771)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.77/1.00 tff(238,plain,
% 0.77/1.00 ((~hskp13) | c2_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.77/1.00 tff(239,plain,
% 0.77/1.00 ((~hskp13) | c2_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[238, 236])).
% 0.77/1.00 tff(240,plain,
% 0.77/1.00 ((~hskp13) | c2_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[239, 236])).
% 0.77/1.00 tff(241,plain,
% 0.77/1.00 ((~hskp13) | c2_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[240, 236])).
% 0.77/1.00 tff(242,plain,
% 0.77/1.00 ((~hskp13) | c2_1(a1771)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[241, 236])).
% 0.77/1.00 tff(243,plain,
% 0.77/1.00 (c2_1(a1771)),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[242, 227])).
% 0.77/1.00 tff(244,plain,
% 0.77/1.00 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(245,plain,
% 0.77/1.01 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[244])).
% 0.77/1.01 tff(246,plain,
% 0.77/1.01 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(247,plain,
% 0.77/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(248,plain,
% 0.77/1.01 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[247])).
% 0.77/1.01 tff(249,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.77/1.01 tff(250,plain,
% 0.77/1.01 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.77/1.01 tff(251,plain,
% 0.77/1.01 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.77/1.01 tff(252,plain,(
% 0.77/1.01 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/1.01 inference(skolemize,[status(sab)],[251])).
% 0.77/1.01 tff(253,plain,
% 0.77/1.01 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[252, 245])).
% 0.77/1.01 tff(254,assumption,(~c0_1(a1771)), introduced(assumption)).
% 0.77/1.01 tff(255,plain,
% 0.77/1.01 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(256,plain,
% 0.77/1.01 ((hskp6 | hskp3 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(257,plain,
% 0.77/1.01 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[256])).
% 0.77/1.01 tff(258,plain,
% 0.77/1.01 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.77/1.01 inference(transitivity,[status(thm)],[257, 255])).
% 0.77/1.01 tff(259,plain,
% 0.77/1.01 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(260,plain,
% 0.77/1.01 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.77/1.01 tff(261,plain,
% 0.77/1.01 (hskp6 | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[260, 35, 254, 253])).
% 0.77/1.01 tff(262,plain,
% 0.77/1.01 ($false),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[261, 243, 235, 226, 225])).
% 0.77/1.01 tff(263,plain,((~hskp13) | (~ndr1_0) | hskp6 | hskp3 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 0.77/1.01 tff(264,plain,
% 0.77/1.01 ((~hskp13) | hskp6 | hskp3 | c0_1(a1771)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[263, 102])).
% 0.77/1.01 tff(265,plain,
% 0.77/1.01 (hskp6),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[264, 224, 35, 218])).
% 0.77/1.01 tff(266,plain,
% 0.77/1.01 (((~hskp6) | (~c0_1(a1762))) <=> ((~hskp6) | (~c0_1(a1762)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(267,plain,
% 0.77/1.01 (((~c0_1(a1762)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a1762)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(268,axiom,((~c0_1(a1762)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.77/1.01 tff(269,plain,
% 0.77/1.01 ((~hskp6) | (~c0_1(a1762))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.77/1.01 tff(270,plain,
% 0.77/1.01 ((~hskp6) | (~c0_1(a1762))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[269, 266])).
% 0.77/1.01 tff(271,plain,
% 0.77/1.01 (~c0_1(a1762)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[270, 265])).
% 0.77/1.01 tff(272,plain,
% 0.77/1.01 (((~hskp6) | c3_1(a1762)) <=> ((~hskp6) | c3_1(a1762))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(273,axiom,((~hskp6) | c3_1(a1762)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.77/1.01 tff(274,plain,
% 0.77/1.01 ((~hskp6) | c3_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.77/1.01 tff(275,plain,
% 0.77/1.01 ((~hskp6) | c3_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[274, 272])).
% 0.77/1.01 tff(276,plain,
% 0.77/1.01 ((~hskp6) | c3_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[275, 272])).
% 0.77/1.01 tff(277,plain,
% 0.77/1.01 ((~hskp6) | c3_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[276, 272])).
% 0.77/1.01 tff(278,plain,
% 0.77/1.01 ((~hskp6) | c3_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[277, 272])).
% 0.77/1.01 tff(279,plain,
% 0.77/1.01 (c3_1(a1762)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[278, 265])).
% 0.77/1.01 tff(280,plain,
% 0.77/1.01 (((~hskp6) | c2_1(a1762)) <=> ((~hskp6) | c2_1(a1762))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(281,axiom,((~hskp6) | c2_1(a1762)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.77/1.01 tff(282,plain,
% 0.77/1.01 ((~hskp6) | c2_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.77/1.01 tff(283,plain,
% 0.77/1.01 ((~hskp6) | c2_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[282, 280])).
% 0.77/1.01 tff(284,plain,
% 0.77/1.01 ((~hskp6) | c2_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[283, 280])).
% 0.77/1.01 tff(285,plain,
% 0.77/1.01 ((~hskp6) | c2_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.77/1.01 tff(286,plain,
% 0.77/1.01 ((~hskp6) | c2_1(a1762)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[285, 280])).
% 0.77/1.01 tff(287,plain,
% 0.77/1.01 (c2_1(a1762)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[286, 265])).
% 0.77/1.01 tff(288,plain,
% 0.77/1.01 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(289,plain,
% 0.77/1.01 ((hskp8 | hskp4 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762))) <=> (hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(290,plain,
% 0.77/1.01 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762))))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[289])).
% 0.77/1.01 tff(291,plain,
% 0.77/1.01 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.77/1.01 inference(transitivity,[status(thm)],[290, 288])).
% 0.77/1.01 tff(292,plain,
% 0.77/1.01 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(293,plain,
% 0.77/1.01 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.77/1.01 tff(294,plain,
% 0.77/1.01 (hskp8),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[293, 102, 139, 287, 279, 271, 121])).
% 0.77/1.01 tff(295,plain,
% 0.77/1.01 (((~hskp8) | (~c1_1(a1765))) <=> ((~hskp8) | (~c1_1(a1765)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(296,plain,
% 0.77/1.01 (((~c1_1(a1765)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1765)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(297,axiom,((~c1_1(a1765)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.77/1.01 tff(298,plain,
% 0.77/1.01 ((~hskp8) | (~c1_1(a1765))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.77/1.01 tff(299,plain,
% 0.77/1.01 ((~hskp8) | (~c1_1(a1765))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[298, 295])).
% 0.77/1.01 tff(300,plain,
% 0.77/1.01 (~c1_1(a1765)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[299, 294])).
% 0.77/1.01 tff(301,plain,
% 0.77/1.01 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(302,plain,
% 0.77/1.01 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[301])).
% 0.77/1.01 tff(303,plain,
% 0.77/1.01 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(304,plain,
% 0.77/1.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(305,plain,
% 0.77/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[304])).
% 0.77/1.01 tff(306,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 0.77/1.01 tff(307,plain,
% 0.77/1.01 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.77/1.01 tff(308,plain,
% 0.77/1.01 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[307, 303])).
% 0.77/1.01 tff(309,plain,(
% 0.77/1.01 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/1.01 inference(skolemize,[status(sab)],[308])).
% 0.77/1.01 tff(310,plain,
% 0.77/1.01 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[309, 302])).
% 0.77/1.01 tff(311,assumption,(hskp6), introduced(assumption)).
% 0.77/1.01 tff(312,plain,
% 0.77/1.01 (~c0_1(a1762)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[270, 311])).
% 0.77/1.01 tff(313,plain,
% 0.77/1.01 (c3_1(a1762)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[278, 311])).
% 0.77/1.01 tff(314,plain,
% 0.77/1.01 (c2_1(a1762)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[286, 311])).
% 0.77/1.01 tff(315,assumption,(~hskp4), introduced(assumption)).
% 0.77/1.01 tff(316,plain,
% 0.77/1.01 (hskp8),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[293, 102, 315, 314, 313, 312, 121])).
% 0.77/1.01 tff(317,plain,
% 0.77/1.01 (~c1_1(a1765)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[299, 316])).
% 0.77/1.01 tff(318,plain,
% 0.77/1.01 (^[U: $i] : refl((hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(319,plain,
% 0.77/1.01 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[318])).
% 0.77/1.01 tff(320,plain,
% 0.77/1.01 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(321,plain,
% 0.77/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp22) <=> ((hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp22))), rewrite(((hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp22) <=> (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(322,plain,
% 0.77/1.01 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp22) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[321])).
% 0.77/1.01 tff(323,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 0.77/1.01 tff(324,plain,
% 0.77/1.01 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.77/1.01 tff(325,plain,
% 0.77/1.01 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.77/1.01 tff(326,plain,(
% 0.77/1.01 ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.01 inference(skolemize,[status(sab)],[325])).
% 0.77/1.01 tff(327,plain,
% 0.77/1.01 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[326, 319])).
% 0.77/1.01 tff(328,assumption,(~hskp22), introduced(assumption)).
% 0.77/1.01 tff(329,plain,
% 0.77/1.01 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(330,plain,
% 0.77/1.01 ((hskp27 | hskp22 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762))) <=> (hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(331,plain,
% 0.77/1.01 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762))))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[330])).
% 0.77/1.01 tff(332,plain,
% 0.77/1.01 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.77/1.01 inference(transitivity,[status(thm)],[331, 329])).
% 0.77/1.01 tff(333,plain,
% 0.77/1.01 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(334,plain,
% 0.77/1.01 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.77/1.01 tff(335,plain,
% 0.77/1.01 (hskp27),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[334, 102, 328, 314, 313, 312, 327])).
% 0.77/1.01 tff(336,plain,
% 0.77/1.01 (((~hskp27) | c3_1(a1756)) <=> ((~hskp27) | c3_1(a1756))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(337,axiom,((~hskp27) | c3_1(a1756)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.77/1.01 tff(338,plain,
% 0.77/1.01 ((~hskp27) | c3_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.77/1.01 tff(339,plain,
% 0.77/1.01 ((~hskp27) | c3_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[338, 336])).
% 0.77/1.01 tff(340,plain,
% 0.77/1.01 ((~hskp27) | c3_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[339, 336])).
% 0.77/1.01 tff(341,plain,
% 0.77/1.01 ((~hskp27) | c3_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[340, 336])).
% 0.77/1.01 tff(342,plain,
% 0.77/1.01 ((~hskp27) | c3_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[341, 336])).
% 0.77/1.01 tff(343,plain,
% 0.77/1.01 (c3_1(a1756)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[342, 335])).
% 0.77/1.01 tff(344,plain,
% 0.77/1.01 (((~hskp27) | c1_1(a1756)) <=> ((~hskp27) | c1_1(a1756))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(345,axiom,((~hskp27) | c1_1(a1756)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.77/1.01 tff(346,plain,
% 0.77/1.01 ((~hskp27) | c1_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.77/1.01 tff(347,plain,
% 0.77/1.01 ((~hskp27) | c1_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[346, 344])).
% 0.77/1.01 tff(348,plain,
% 0.77/1.01 ((~hskp27) | c1_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[347, 344])).
% 0.77/1.01 tff(349,plain,
% 0.77/1.01 ((~hskp27) | c1_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[348, 344])).
% 0.77/1.01 tff(350,plain,
% 0.77/1.01 ((~hskp27) | c1_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[349, 344])).
% 0.77/1.01 tff(351,plain,
% 0.77/1.01 (c1_1(a1756)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[350, 335])).
% 0.77/1.01 tff(352,plain,
% 0.77/1.01 (((~hskp27) | c0_1(a1756)) <=> ((~hskp27) | c0_1(a1756))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(353,axiom,((~hskp27) | c0_1(a1756)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.77/1.01 tff(354,plain,
% 0.77/1.01 ((~hskp27) | c0_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.77/1.01 tff(355,plain,
% 0.77/1.01 ((~hskp27) | c0_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[354, 352])).
% 0.77/1.01 tff(356,plain,
% 0.77/1.01 ((~hskp27) | c0_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[355, 352])).
% 0.77/1.01 tff(357,plain,
% 0.77/1.01 ((~hskp27) | c0_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[356, 352])).
% 0.77/1.01 tff(358,plain,
% 0.77/1.01 ((~hskp27) | c0_1(a1756)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[357, 352])).
% 0.77/1.01 tff(359,plain,
% 0.77/1.01 (c0_1(a1756)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[358, 335])).
% 0.77/1.01 tff(360,assumption,(c1_1(a1756)), introduced(assumption)).
% 0.77/1.01 tff(361,assumption,(c0_1(a1756)), introduced(assumption)).
% 0.77/1.01 tff(362,plain,
% 0.77/1.01 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1756) | (~c1_1(a1756)) | (~c0_1(a1756)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c2_1(a1756) | (~c1_1(a1756)) | (~c0_1(a1756)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(363,plain,
% 0.77/1.01 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1756) | (~c1_1(a1756)) | (~c0_1(a1756)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(364,plain,
% 0.77/1.01 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c2_1(a1756) | (~c1_1(a1756)) | (~c0_1(a1756))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.77/1.01 tff(365,plain,
% 0.77/1.01 (hskp13 | c2_1(a1756)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[364, 102, 12, 361, 360, 33])).
% 0.77/1.01 tff(366,plain,
% 0.77/1.01 (c2_1(a1756)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[365, 23])).
% 0.77/1.01 tff(367,assumption,(~c0_1(a1762)), introduced(assumption)).
% 0.77/1.01 tff(368,assumption,(c2_1(a1762)), introduced(assumption)).
% 0.77/1.01 tff(369,plain,
% 0.77/1.01 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(370,plain,
% 0.77/1.01 ((hskp13 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c1_1(a1762))) <=> (hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(371,plain,
% 0.77/1.01 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762))))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[370])).
% 0.77/1.01 tff(372,plain,
% 0.77/1.01 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.77/1.01 inference(transitivity,[status(thm)],[371, 369])).
% 0.77/1.01 tff(373,plain,
% 0.77/1.01 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(374,plain,
% 0.77/1.01 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.77/1.01 tff(375,plain,
% 0.77/1.01 (hskp13 | (~c1_1(a1762))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[374, 102, 368, 367, 22])).
% 0.77/1.01 tff(376,plain,
% 0.77/1.01 (~c1_1(a1762)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[375, 23])).
% 0.77/1.01 tff(377,plain,
% 0.77/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(378,plain,
% 0.77/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[377])).
% 0.77/1.01 tff(379,plain,
% 0.77/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(380,plain,
% 0.77/1.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_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) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_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) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_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) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_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) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_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) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(381,plain,
% 0.77/1.01 (![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) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[380])).
% 0.77/1.01 tff(382,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','clause198')).
% 0.77/1.01 tff(383,plain,
% 0.77/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.77/1.01 tff(384,plain,
% 0.77/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[383, 379])).
% 0.77/1.01 tff(385,plain,(
% 0.77/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/1.01 inference(skolemize,[status(sab)],[384])).
% 0.77/1.01 tff(386,plain,
% 0.77/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[385, 378])).
% 0.77/1.01 tff(387,assumption,(c3_1(a1762)), introduced(assumption)).
% 0.77/1.01 tff(388,assumption,(c3_1(a1756)), introduced(assumption)).
% 0.77/1.01 tff(389,plain,
% 0.77/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(390,plain,
% 0.77/1.01 (((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762))) <=> (c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(391,plain,
% 0.77/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[390])).
% 0.77/1.01 tff(392,plain,
% 0.77/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.77/1.02 inference(transitivity,[status(thm)],[391, 389])).
% 0.77/1.02 tff(393,plain,
% 0.77/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))),
% 0.77/1.02 inference(quant_inst,[status(thm)],[])).
% 0.77/1.02 tff(394,plain,
% 0.77/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.77/1.02 tff(395,plain,
% 0.77/1.02 ($false),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[394, 102, 361, 360, 388, 387, 367, 386, 376, 366])).
% 0.77/1.02 tff(396,plain,(hskp13 | (~c0_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c3_1(a1762)) | c0_1(a1762) | hskp19 | (~c2_1(a1762))), inference(lemma,lemma(discharge,[]))).
% 0.77/1.02 tff(397,plain,
% 0.77/1.02 (hskp13),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[396, 359, 351, 343, 313, 312, 12, 314])).
% 0.77/1.02 tff(398,plain,
% 0.77/1.02 (~c0_1(a1771)),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[223, 397])).
% 0.77/1.02 tff(399,plain,
% 0.77/1.02 (((~hskp8) | c2_1(a1765)) <=> ((~hskp8) | c2_1(a1765))),
% 0.77/1.02 inference(rewrite,[status(thm)],[])).
% 0.77/1.02 tff(400,axiom,((~hskp8) | c2_1(a1765)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.77/1.02 tff(401,plain,
% 0.77/1.02 ((~hskp8) | c2_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.77/1.02 tff(402,plain,
% 0.77/1.02 ((~hskp8) | c2_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[401, 399])).
% 0.77/1.02 tff(403,plain,
% 0.77/1.02 ((~hskp8) | c2_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[402, 399])).
% 0.77/1.02 tff(404,plain,
% 0.77/1.02 ((~hskp8) | c2_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[403, 399])).
% 0.77/1.02 tff(405,plain,
% 0.77/1.02 ((~hskp8) | c2_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[404, 399])).
% 0.77/1.02 tff(406,plain,
% 0.77/1.02 (c2_1(a1765)),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[405, 316])).
% 0.77/1.02 tff(407,plain,
% 0.77/1.02 (((~hskp8) | c0_1(a1765)) <=> ((~hskp8) | c0_1(a1765))),
% 0.77/1.02 inference(rewrite,[status(thm)],[])).
% 0.77/1.02 tff(408,axiom,((~hskp8) | c0_1(a1765)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.77/1.02 tff(409,plain,
% 0.77/1.02 ((~hskp8) | c0_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.77/1.02 tff(410,plain,
% 0.77/1.02 ((~hskp8) | c0_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[409, 407])).
% 0.77/1.02 tff(411,plain,
% 0.77/1.02 ((~hskp8) | c0_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[410, 407])).
% 0.77/1.02 tff(412,plain,
% 0.77/1.02 ((~hskp8) | c0_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[411, 407])).
% 0.77/1.02 tff(413,plain,
% 0.77/1.02 ((~hskp8) | c0_1(a1765)),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[412, 407])).
% 0.77/1.02 tff(414,plain,
% 0.77/1.02 (c0_1(a1765)),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[413, 316])).
% 0.77/1.02 tff(415,plain,
% 0.77/1.02 (c2_1(a1771)),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[242, 397])).
% 0.77/1.02 tff(416,plain,
% 0.77/1.02 (c1_1(a1771)),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[234, 397])).
% 0.77/1.02 tff(417,plain,
% 0.77/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.77/1.02 inference(rewrite,[status(thm)],[])).
% 0.77/1.02 tff(418,plain,
% 0.77/1.02 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762))) <=> (c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.77/1.02 inference(rewrite,[status(thm)],[])).
% 0.77/1.02 tff(419,plain,
% 0.77/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 0.77/1.02 inference(monotonicity,[status(thm)],[418])).
% 0.77/1.02 tff(420,plain,
% 0.77/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.77/1.02 inference(transitivity,[status(thm)],[419, 417])).
% 0.77/1.02 tff(421,plain,
% 0.77/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))),
% 0.77/1.02 inference(quant_inst,[status(thm)],[])).
% 0.77/1.02 tff(422,plain,
% 0.77/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.77/1.02 tff(423,plain,
% 0.77/1.02 (c1_1(a1762)),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[422, 102, 416, 415, 414, 406, 313, 398, 317, 312, 46])).
% 0.77/1.02 tff(424,plain,
% 0.77/1.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_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)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.77/1.02 inference(bind,[status(th)],[])).
% 0.77/1.02 tff(425,plain,
% 0.77/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.77/1.02 inference(quant_intro,[status(thm)],[424])).
% 0.77/1.02 tff(426,plain,
% 0.77/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.77/1.02 inference(rewrite,[status(thm)],[])).
% 0.77/1.02 tff(427,plain,
% 0.77/1.02 (^[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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.77/1.02 inference(bind,[status(th)],[])).
% 0.77/1.02 tff(428,plain,
% 0.77/1.02 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/1.02 inference(quant_intro,[status(thm)],[427])).
% 0.86/1.02 tff(429,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 0.86/1.02 tff(430,plain,
% 0.86/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.86/1.02 tff(431,plain,
% 0.86/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[430, 426])).
% 0.86/1.02 tff(432,plain,(
% 0.86/1.02 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/1.02 inference(skolemize,[status(sab)],[431])).
% 0.86/1.02 tff(433,plain,
% 0.86/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[432, 425])).
% 0.86/1.02 tff(434,plain,
% 0.86/1.02 (^[U: $i] : refl((hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))),
% 0.86/1.02 inference(bind,[status(th)],[])).
% 0.86/1.02 tff(435,plain,
% 0.86/1.02 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 0.86/1.02 inference(quant_intro,[status(thm)],[434])).
% 0.86/1.02 tff(436,plain,
% 0.86/1.02 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(437,plain,
% 0.86/1.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) | hskp22) <=> ((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | hskp22))), rewrite(((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) | hskp22) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.86/1.02 inference(bind,[status(th)],[])).
% 0.86/1.02 tff(438,plain,
% 0.86/1.02 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) | hskp22) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 0.86/1.02 inference(quant_intro,[status(thm)],[437])).
% 0.86/1.02 tff(439,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.86/1.02 tff(440,plain,
% 0.86/1.02 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.86/1.02 tff(441,plain,
% 0.86/1.02 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[440, 436])).
% 0.86/1.02 tff(442,plain,(
% 0.86/1.02 ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 0.86/1.02 inference(skolemize,[status(sab)],[441])).
% 0.86/1.02 tff(443,plain,
% 0.86/1.02 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[442, 435])).
% 0.86/1.02 tff(444,plain,
% 0.86/1.02 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(445,plain,
% 0.86/1.02 ((hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762))) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(446,plain,
% 0.86/1.02 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[445])).
% 0.86/1.02 tff(447,plain,
% 0.86/1.02 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[446, 444])).
% 0.86/1.02 tff(448,plain,
% 0.86/1.02 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(449,plain,
% 0.86/1.02 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.86/1.02 tff(450,plain,
% 0.86/1.02 (hskp16 | (~c1_1(a1762))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[449, 102, 328, 314, 313, 443])).
% 0.86/1.02 tff(451,plain,
% 0.86/1.02 (hskp16),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[450, 423])).
% 0.86/1.02 tff(452,plain,
% 0.86/1.02 (((~hskp16) | (~c2_1(a1780))) <=> ((~hskp16) | (~c2_1(a1780)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(453,plain,
% 0.86/1.02 (((~c2_1(a1780)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a1780)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(454,axiom,((~c2_1(a1780)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.86/1.02 tff(455,plain,
% 0.86/1.02 ((~hskp16) | (~c2_1(a1780))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.86/1.02 tff(456,plain,
% 0.86/1.02 ((~hskp16) | (~c2_1(a1780))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[455, 452])).
% 0.86/1.02 tff(457,plain,
% 0.86/1.02 (~c2_1(a1780)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[456, 451])).
% 0.86/1.02 tff(458,plain,
% 0.86/1.02 (((~hskp16) | c1_1(a1780)) <=> ((~hskp16) | c1_1(a1780))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(459,axiom,((~hskp16) | c1_1(a1780)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.86/1.02 tff(460,plain,
% 0.86/1.02 ((~hskp16) | c1_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.86/1.02 tff(461,plain,
% 0.86/1.02 ((~hskp16) | c1_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[460, 458])).
% 0.86/1.02 tff(462,plain,
% 0.86/1.02 ((~hskp16) | c1_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[461, 458])).
% 0.86/1.02 tff(463,plain,
% 0.86/1.02 ((~hskp16) | c1_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[462, 458])).
% 0.86/1.02 tff(464,plain,
% 0.86/1.02 ((~hskp16) | c1_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[463, 458])).
% 0.86/1.02 tff(465,plain,
% 0.86/1.02 (c1_1(a1780)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[464, 451])).
% 0.86/1.02 tff(466,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(467,plain,
% 0.86/1.02 (((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762))) <=> (c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(468,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[467])).
% 0.86/1.02 tff(469,plain,
% 0.86/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[468, 466])).
% 0.86/1.02 tff(470,plain,
% 0.86/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(471,plain,
% 0.86/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.86/1.02 tff(472,plain,
% 0.86/1.02 (~c0_1(a1780)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[471, 102, 465, 414, 406, 313, 457, 317, 312, 433, 423])).
% 0.86/1.02 tff(473,plain,
% 0.86/1.02 (((~hskp16) | c3_1(a1780)) <=> ((~hskp16) | c3_1(a1780))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(474,axiom,((~hskp16) | c3_1(a1780)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.86/1.02 tff(475,plain,
% 0.86/1.02 ((~hskp16) | c3_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.86/1.02 tff(476,plain,
% 0.86/1.02 ((~hskp16) | c3_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[475, 473])).
% 0.86/1.02 tff(477,plain,
% 0.86/1.02 ((~hskp16) | c3_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[476, 473])).
% 0.86/1.02 tff(478,plain,
% 0.86/1.02 ((~hskp16) | c3_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[477, 473])).
% 0.86/1.02 tff(479,plain,
% 0.86/1.02 ((~hskp16) | c3_1(a1780)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[478, 473])).
% 0.86/1.02 tff(480,plain,
% 0.86/1.02 (c3_1(a1780)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[479, 451])).
% 0.86/1.02 tff(481,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(482,plain,
% 0.86/1.02 ((hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1780) | c0_1(a1780) | (~c3_1(a1780))) <=> (hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(483,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1780) | c0_1(a1780) | (~c3_1(a1780)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[482])).
% 0.86/1.02 tff(484,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1780) | c0_1(a1780) | (~c3_1(a1780)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[483, 481])).
% 0.86/1.02 tff(485,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1780) | c0_1(a1780) | (~c3_1(a1780)))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(486,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.86/1.02 tff(487,plain,
% 0.86/1.02 ($false),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[486, 102, 35, 359, 351, 343, 480, 457, 11, 472])).
% 0.86/1.02 tff(488,plain,((~hskp6) | hskp3 | hskp22 | hskp19 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.86/1.02 tff(489,plain,
% 0.86/1.02 (hskp22),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[488, 265, 35, 12, 139])).
% 0.86/1.02 tff(490,plain,
% 0.86/1.02 (((~hskp22) | (~c2_1(a1799))) <=> ((~hskp22) | (~c2_1(a1799)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(491,plain,
% 0.86/1.02 (((~c2_1(a1799)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a1799)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(492,axiom,((~c2_1(a1799)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.86/1.02 tff(493,plain,
% 0.86/1.02 ((~hskp22) | (~c2_1(a1799))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[492, 491])).
% 0.86/1.02 tff(494,plain,
% 0.86/1.02 ((~hskp22) | (~c2_1(a1799))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[493, 490])).
% 0.86/1.02 tff(495,plain,
% 0.86/1.02 (~c2_1(a1799)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[494, 489])).
% 0.86/1.02 tff(496,plain,
% 0.86/1.02 (((~hskp22) | (~c0_1(a1799))) <=> ((~hskp22) | (~c0_1(a1799)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(497,plain,
% 0.86/1.02 (((~c0_1(a1799)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a1799)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(498,axiom,((~c0_1(a1799)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.86/1.02 tff(499,plain,
% 0.86/1.02 ((~hskp22) | (~c0_1(a1799))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.86/1.02 tff(500,plain,
% 0.86/1.02 ((~hskp22) | (~c0_1(a1799))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[499, 496])).
% 0.86/1.02 tff(501,plain,
% 0.86/1.02 (~c0_1(a1799)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[500, 489])).
% 0.86/1.02 tff(502,plain,
% 0.86/1.02 (((~hskp22) | c3_1(a1799)) <=> ((~hskp22) | c3_1(a1799))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(503,axiom,((~hskp22) | c3_1(a1799)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.86/1.02 tff(504,plain,
% 0.86/1.02 ((~hskp22) | c3_1(a1799)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.86/1.02 tff(505,plain,
% 0.86/1.02 ((~hskp22) | c3_1(a1799)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[504, 502])).
% 0.86/1.02 tff(506,plain,
% 0.86/1.02 ((~hskp22) | c3_1(a1799)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[505, 502])).
% 0.86/1.02 tff(507,plain,
% 0.86/1.02 ((~hskp22) | c3_1(a1799)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[506, 502])).
% 0.86/1.02 tff(508,plain,
% 0.86/1.02 ((~hskp22) | c3_1(a1799)),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[507, 502])).
% 0.86/1.02 tff(509,plain,
% 0.86/1.02 (c3_1(a1799)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[508, 489])).
% 0.86/1.02 tff(510,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(511,plain,
% 0.86/1.02 ((hskp10 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | (~c0_1(a1759)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799))) <=> (hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(512,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | (~c0_1(a1759)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[511])).
% 0.86/1.02 tff(513,plain,
% 0.86/1.02 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | (~c0_1(a1759)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799)))),
% 0.86/1.02 inference(transitivity,[status(thm)],[512, 510])).
% 0.86/1.02 tff(514,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | (~c0_1(a1759)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(515,plain,
% 0.86/1.02 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.86/1.02 tff(516,plain,
% 0.86/1.02 (hskp10),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[515, 102, 509, 47, 501, 495, 34, 310, 185])).
% 0.86/1.02 tff(517,plain,
% 0.86/1.02 (((~hskp10) | (~c1_1(a1767))) <=> ((~hskp10) | (~c1_1(a1767)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(518,plain,
% 0.86/1.02 (((~c1_1(a1767)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1767)))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(519,axiom,((~c1_1(a1767)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.86/1.02 tff(520,plain,
% 0.86/1.02 ((~hskp10) | (~c1_1(a1767))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.86/1.02 tff(521,plain,
% 0.86/1.02 ((~hskp10) | (~c1_1(a1767))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[520, 517])).
% 0.86/1.02 tff(522,plain,
% 0.86/1.02 (~c1_1(a1767)),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[521, 516])).
% 0.86/1.02 tff(523,plain,
% 0.86/1.02 (((~hskp10) | (~c0_1(a1767))) <=> ((~hskp10) | (~c0_1(a1767)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(524,plain,
% 0.86/1.03 (((~c0_1(a1767)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a1767)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(525,axiom,((~c0_1(a1767)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.86/1.03 tff(526,plain,
% 0.86/1.03 ((~hskp10) | (~c0_1(a1767))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.86/1.03 tff(527,plain,
% 0.86/1.03 ((~hskp10) | (~c0_1(a1767))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[526, 523])).
% 0.86/1.03 tff(528,plain,
% 0.86/1.03 (~c0_1(a1767)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[527, 516])).
% 0.86/1.03 tff(529,plain,
% 0.86/1.03 (c2_1(a1765)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[405, 294])).
% 0.86/1.03 tff(530,plain,
% 0.86/1.03 (c0_1(a1765)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[413, 294])).
% 0.86/1.03 tff(531,plain,
% 0.86/1.03 (((~hskp10) | c3_1(a1767)) <=> ((~hskp10) | c3_1(a1767))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(532,axiom,((~hskp10) | c3_1(a1767)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.86/1.03 tff(533,plain,
% 0.86/1.03 ((~hskp10) | c3_1(a1767)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.86/1.03 tff(534,plain,
% 0.86/1.03 ((~hskp10) | c3_1(a1767)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[533, 531])).
% 0.86/1.03 tff(535,plain,
% 0.86/1.03 ((~hskp10) | c3_1(a1767)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[534, 531])).
% 0.86/1.03 tff(536,plain,
% 0.86/1.03 ((~hskp10) | c3_1(a1767)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[535, 531])).
% 0.86/1.03 tff(537,plain,
% 0.86/1.03 ((~hskp10) | c3_1(a1767)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[536, 531])).
% 0.86/1.03 tff(538,plain,
% 0.86/1.03 (c3_1(a1767)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[537, 516])).
% 0.86/1.03 tff(539,plain,
% 0.86/1.03 (c2_1(a1771)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[242, 218])).
% 0.86/1.03 tff(540,plain,
% 0.86/1.03 (c1_1(a1771)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[234, 218])).
% 0.86/1.03 tff(541,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(542,plain,
% 0.86/1.03 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767))) <=> (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(543,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[542])).
% 0.86/1.03 tff(544,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[543, 541])).
% 0.86/1.03 tff(545,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(546,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.86/1.03 tff(547,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[546, 102, 540, 539, 538, 530, 529, 224, 528, 522, 300, 46])).
% 0.86/1.03 tff(548,plain,(hskp3 | c1_1(a1759) | c3_1(a1759) | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(549,plain,
% 0.86/1.03 (hskp3),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[548, 47, 34, 12])).
% 0.86/1.03 tff(550,plain,
% 0.86/1.03 (((~hskp3) | c2_1(a1758)) <=> ((~hskp3) | c2_1(a1758))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(551,axiom,((~hskp3) | c2_1(a1758)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.86/1.03 tff(552,plain,
% 0.86/1.03 ((~hskp3) | c2_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.86/1.03 tff(553,plain,
% 0.86/1.03 ((~hskp3) | c2_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[552, 550])).
% 0.86/1.03 tff(554,plain,
% 0.86/1.03 ((~hskp3) | c2_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[553, 550])).
% 0.86/1.03 tff(555,plain,
% 0.86/1.03 ((~hskp3) | c2_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[554, 550])).
% 0.86/1.03 tff(556,plain,
% 0.86/1.03 ((~hskp3) | c2_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[555, 550])).
% 0.86/1.03 tff(557,plain,
% 0.86/1.03 (c2_1(a1758)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[556, 549])).
% 0.86/1.03 tff(558,plain,
% 0.86/1.03 (((~hskp3) | c1_1(a1758)) <=> ((~hskp3) | c1_1(a1758))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(559,axiom,((~hskp3) | c1_1(a1758)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.86/1.03 tff(560,plain,
% 0.86/1.03 ((~hskp3) | c1_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.86/1.03 tff(561,plain,
% 0.86/1.03 ((~hskp3) | c1_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[560, 558])).
% 0.86/1.03 tff(562,plain,
% 0.86/1.03 ((~hskp3) | c1_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[561, 558])).
% 0.86/1.03 tff(563,plain,
% 0.86/1.03 ((~hskp3) | c1_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[562, 558])).
% 0.86/1.03 tff(564,plain,
% 0.86/1.03 ((~hskp3) | c1_1(a1758)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[563, 558])).
% 0.86/1.03 tff(565,plain,
% 0.86/1.03 (c1_1(a1758)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[564, 549])).
% 0.86/1.03 tff(566,plain,
% 0.86/1.03 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(567,plain,
% 0.86/1.03 ((hskp13 | (~ndr1_0) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758))) <=> (hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(568,plain,
% 0.86/1.03 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[567])).
% 0.86/1.03 tff(569,plain,
% 0.86/1.03 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[568, 566])).
% 0.86/1.03 tff(570,plain,
% 0.86/1.03 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(571,plain,
% 0.86/1.03 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.86/1.03 tff(572,plain,
% 0.86/1.03 (hskp13 | c0_1(a1758)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[571, 102, 565, 557, 22])).
% 0.86/1.03 tff(573,plain,
% 0.86/1.03 (c0_1(a1758)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[572, 23])).
% 0.86/1.03 tff(574,plain,
% 0.86/1.03 (((~hskp3) | (~c3_1(a1758))) <=> ((~hskp3) | (~c3_1(a1758)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(575,plain,
% 0.86/1.03 (((~c3_1(a1758)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1758)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(576,axiom,((~c3_1(a1758)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.86/1.03 tff(577,plain,
% 0.86/1.03 ((~hskp3) | (~c3_1(a1758))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.86/1.03 tff(578,plain,
% 0.86/1.03 ((~hskp3) | (~c3_1(a1758))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[577, 574])).
% 0.86/1.03 tff(579,plain,
% 0.86/1.03 (~c3_1(a1758)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[578, 549])).
% 0.86/1.03 tff(580,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(581,plain,
% 0.86/1.03 ((hskp2 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759))) <=> (hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(582,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[581])).
% 0.86/1.03 tff(583,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[582, 580])).
% 0.86/1.03 tff(584,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(585,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.86/1.03 tff(586,plain,
% 0.86/1.03 (hskp2 | (~c0_1(a1758)) | (~c0_1(a1759))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[585, 102, 47, 557, 34, 579, 195])).
% 0.86/1.03 tff(587,plain,
% 0.86/1.03 (~c0_1(a1759)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[586, 111, 573])).
% 0.86/1.03 tff(588,plain,
% 0.86/1.03 (^[U: $i] : refl((hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(589,plain,
% 0.86/1.03 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[588])).
% 0.86/1.03 tff(590,plain,
% 0.86/1.03 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(591,plain,
% 0.86/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | 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)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(592,plain,
% 0.86/1.03 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[591])).
% 0.86/1.03 tff(593,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.86/1.03 tff(594,plain,
% 0.86/1.03 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.86/1.03 tff(595,plain,
% 0.86/1.03 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[594, 590])).
% 0.86/1.03 tff(596,plain,(
% 0.86/1.03 ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.03 inference(skolemize,[status(sab)],[595])).
% 0.86/1.03 tff(597,plain,
% 0.86/1.03 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[596, 589])).
% 0.86/1.03 tff(598,plain,
% 0.86/1.03 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(599,plain,
% 0.86/1.03 ((hskp27 | hskp2 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759)) <=> (hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(600,plain,
% 0.86/1.03 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759)))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[599])).
% 0.86/1.03 tff(601,plain,
% 0.86/1.03 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 0.86/1.03 inference(transitivity,[status(thm)],[600, 598])).
% 0.86/1.03 tff(602,plain,
% 0.86/1.03 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(603,plain,
% 0.86/1.03 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.86/1.03 tff(604,plain,
% 0.86/1.03 (hskp27 | hskp2 | c1_1(a1759) | c0_1(a1759)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[603, 102, 34, 597])).
% 0.86/1.03 tff(605,plain,
% 0.86/1.03 (hskp27),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[604, 587, 47, 111])).
% 0.86/1.03 tff(606,plain,
% 0.86/1.03 (c1_1(a1756)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[350, 605])).
% 0.86/1.03 tff(607,plain,
% 0.86/1.03 (c0_1(a1756)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[358, 605])).
% 0.86/1.03 tff(608,plain,
% 0.86/1.03 (c2_1(a1756)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[364, 102, 12, 23, 607, 606, 33])).
% 0.86/1.03 tff(609,plain,
% 0.86/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(610,plain,
% 0.86/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[609])).
% 0.86/1.03 tff(611,plain,
% 0.86/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(612,plain,
% 0.86/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(613,plain,
% 0.86/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[612])).
% 0.86/1.03 tff(614,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 0.86/1.03 tff(615,plain,
% 0.86/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.86/1.03 tff(616,plain,
% 0.86/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[615, 611])).
% 0.86/1.03 tff(617,plain,(
% 0.86/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 0.86/1.03 inference(skolemize,[status(sab)],[616])).
% 0.86/1.03 tff(618,plain,
% 0.86/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[617, 610])).
% 0.86/1.03 tff(619,plain,
% 0.86/1.03 (c3_1(a1756)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[342, 605])).
% 0.86/1.03 tff(620,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(621,plain,
% 0.86/1.03 (((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c0_1(a1756)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758))) <=> (c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(622,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c0_1(a1756)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[621])).
% 0.86/1.03 tff(623,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c0_1(a1756)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[622, 620])).
% 0.86/1.03 tff(624,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c0_1(a1756)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(625,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.86/1.03 tff(626,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[625, 102, 607, 606, 619, 565, 579, 618, 573, 608])).
% 0.86/1.03 tff(627,plain,(hskp13 | hskp19 | c1_1(a1759) | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(628,plain,
% 0.86/1.03 (hskp13),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[627, 47, 12, 34])).
% 0.86/1.03 tff(629,plain,
% 0.86/1.03 (~c0_1(a1771)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[223, 628])).
% 0.86/1.03 tff(630,plain,
% 0.86/1.03 (c2_1(a1771)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[242, 628])).
% 0.86/1.03 tff(631,plain,
% 0.86/1.03 (c1_1(a1771)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[234, 628])).
% 0.86/1.03 tff(632,plain,
% 0.86/1.03 (^[U: $i] : refl((hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(633,plain,
% 0.86/1.03 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[632])).
% 0.86/1.03 tff(634,plain,
% 0.86/1.03 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(635,plain,
% 0.86/1.03 (^[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)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp6) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp6))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp6) <=> (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp6) <=> (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.86/1.03 inference(bind,[status(th)],[])).
% 0.86/1.03 tff(636,plain,
% 0.86/1.03 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp6) <=> ![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/1.03 inference(quant_intro,[status(thm)],[635])).
% 0.86/1.03 tff(637,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.86/1.03 tff(638,plain,
% 0.86/1.03 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.86/1.03 tff(639,plain,
% 0.86/1.03 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[638, 634])).
% 0.86/1.03 tff(640,plain,(
% 0.86/1.03 ![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/1.03 inference(skolemize,[status(sab)],[639])).
% 0.86/1.03 tff(641,plain,
% 0.86/1.03 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[640, 633])).
% 0.86/1.03 tff(642,assumption,(~c3_1(a1758)), introduced(assumption)).
% 0.86/1.03 tff(643,assumption,(c1_1(a1758)), introduced(assumption)).
% 0.86/1.03 tff(644,plain,
% 0.86/1.03 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(645,plain,
% 0.86/1.03 ((hskp19 | hskp6 | (~ndr1_0) | c3_1(a1758) | c0_1(a1758) | (~c1_1(a1758))) <=> (hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(646,plain,
% 0.86/1.03 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1758) | c0_1(a1758) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[645])).
% 0.86/1.03 tff(647,plain,
% 0.86/1.04 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1758) | c0_1(a1758) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[646, 644])).
% 0.86/1.04 tff(648,plain,
% 0.86/1.04 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1758) | c0_1(a1758) | (~c1_1(a1758)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(649,plain,
% 0.86/1.04 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.86/1.04 tff(650,plain,
% 0.86/1.04 (hskp6 | c0_1(a1758)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[649, 102, 12, 643, 642, 641])).
% 0.86/1.04 tff(651,plain,
% 0.86/1.04 (c0_1(a1758)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[650, 225])).
% 0.86/1.04 tff(652,assumption,(c1_1(a1771)), introduced(assumption)).
% 0.86/1.04 tff(653,plain,
% 0.86/1.04 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(654,plain,
% 0.86/1.04 ((hskp19 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c1_1(a1771))) <=> (hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(655,plain,
% 0.86/1.04 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[654])).
% 0.86/1.04 tff(656,plain,
% 0.86/1.04 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[655, 653])).
% 0.86/1.04 tff(657,plain,
% 0.86/1.04 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(658,plain,
% 0.86/1.04 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[657, 656])).
% 0.86/1.04 tff(659,plain,
% 0.86/1.04 (hskp6 | c3_1(a1771)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[658, 102, 12, 652, 254, 641])).
% 0.86/1.04 tff(660,plain,
% 0.86/1.04 (c3_1(a1771)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[659, 225])).
% 0.86/1.04 tff(661,assumption,(c2_1(a1758)), introduced(assumption)).
% 0.86/1.04 tff(662,assumption,(c2_1(a1771)), introduced(assumption)).
% 0.86/1.04 tff(663,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(664,plain,
% 0.86/1.04 (((~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758))) <=> (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(665,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[664])).
% 0.86/1.04 tff(666,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[665, 663])).
% 0.86/1.04 tff(667,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(668,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[667, 666])).
% 0.86/1.04 tff(669,plain,
% 0.86/1.04 ((~c0_1(a1758)) | (~c3_1(a1771))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[668, 102, 652, 662, 643, 661, 642, 618])).
% 0.86/1.04 tff(670,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[669, 660, 651])).
% 0.86/1.04 tff(671,plain,(hskp6 | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c1_1(a1758)) | (~c2_1(a1758)) | c3_1(a1758) | hskp19 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(672,plain,
% 0.86/1.04 (hskp6),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[671, 631, 630, 565, 557, 579, 12, 629])).
% 0.86/1.04 tff(673,plain,
% 0.86/1.04 (~c0_1(a1762)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[270, 672])).
% 0.86/1.04 tff(674,plain,
% 0.86/1.04 (c3_1(a1762)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[278, 672])).
% 0.86/1.04 tff(675,plain,
% 0.86/1.04 (c2_1(a1762)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[286, 672])).
% 0.86/1.04 tff(676,plain,
% 0.86/1.04 (hskp8),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[293, 102, 139, 675, 674, 673, 121])).
% 0.86/1.04 tff(677,plain,
% 0.86/1.04 (~c1_1(a1765)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[299, 676])).
% 0.86/1.04 tff(678,plain,
% 0.86/1.04 (c2_1(a1765)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[405, 676])).
% 0.86/1.04 tff(679,plain,
% 0.86/1.04 (c0_1(a1765)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[413, 676])).
% 0.86/1.04 tff(680,plain,
% 0.86/1.04 (c1_1(a1762)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[422, 102, 631, 630, 679, 678, 674, 629, 677, 673, 46])).
% 0.86/1.04 tff(681,plain,
% 0.86/1.04 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(682,plain,
% 0.86/1.04 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[681])).
% 0.86/1.04 tff(683,plain,
% 0.86/1.04 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(684,plain,
% 0.86/1.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(685,plain,
% 0.86/1.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[684])).
% 0.86/1.04 tff(686,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.86/1.04 tff(687,plain,
% 0.86/1.04 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.86/1.04 tff(688,plain,
% 0.86/1.04 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[687, 683])).
% 0.86/1.04 tff(689,plain,(
% 0.86/1.04 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.86/1.04 inference(skolemize,[status(sab)],[688])).
% 0.86/1.04 tff(690,plain,
% 0.86/1.04 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[689, 682])).
% 0.86/1.04 tff(691,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(692,plain,
% 0.86/1.04 ((hskp21 | (~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(693,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[692])).
% 0.86/1.04 tff(694,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[693, 691])).
% 0.86/1.04 tff(695,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(696,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.86/1.04 tff(697,plain,
% 0.86/1.04 (hskp21),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[696, 102, 631, 630, 679, 678, 629, 677, 690])).
% 0.86/1.04 tff(698,plain,
% 0.86/1.04 (((~hskp21) | (~c3_1(a1788))) <=> ((~hskp21) | (~c3_1(a1788)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(699,plain,
% 0.86/1.04 (((~c3_1(a1788)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a1788)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(700,axiom,((~c3_1(a1788)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.86/1.04 tff(701,plain,
% 0.86/1.04 ((~hskp21) | (~c3_1(a1788))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.86/1.04 tff(702,plain,
% 0.86/1.04 ((~hskp21) | (~c3_1(a1788))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[701, 698])).
% 0.86/1.04 tff(703,plain,
% 0.86/1.04 (~c3_1(a1788)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[702, 697])).
% 0.86/1.04 tff(704,plain,
% 0.86/1.04 (((~hskp21) | c2_1(a1788)) <=> ((~hskp21) | c2_1(a1788))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(705,axiom,((~hskp21) | c2_1(a1788)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.86/1.04 tff(706,plain,
% 0.86/1.04 ((~hskp21) | c2_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.86/1.04 tff(707,plain,
% 0.86/1.04 ((~hskp21) | c2_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[706, 704])).
% 0.86/1.04 tff(708,plain,
% 0.86/1.04 ((~hskp21) | c2_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[707, 704])).
% 0.86/1.04 tff(709,plain,
% 0.86/1.04 ((~hskp21) | c2_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[708, 704])).
% 0.86/1.04 tff(710,plain,
% 0.86/1.04 ((~hskp21) | c2_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[709, 704])).
% 0.86/1.04 tff(711,plain,
% 0.86/1.04 (c2_1(a1788)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[710, 697])).
% 0.86/1.04 tff(712,plain,
% 0.86/1.04 (((~hskp21) | c0_1(a1788)) <=> ((~hskp21) | c0_1(a1788))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(713,axiom,((~hskp21) | c0_1(a1788)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.86/1.04 tff(714,plain,
% 0.86/1.04 ((~hskp21) | c0_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.86/1.04 tff(715,plain,
% 0.86/1.04 ((~hskp21) | c0_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[714, 712])).
% 0.86/1.04 tff(716,plain,
% 0.86/1.04 ((~hskp21) | c0_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[715, 712])).
% 0.86/1.04 tff(717,plain,
% 0.86/1.04 ((~hskp21) | c0_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[716, 712])).
% 0.86/1.04 tff(718,plain,
% 0.86/1.04 ((~hskp21) | c0_1(a1788)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[717, 712])).
% 0.86/1.04 tff(719,plain,
% 0.86/1.04 (c0_1(a1788)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[718, 697])).
% 0.86/1.04 tff(720,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(721,plain,
% 0.86/1.04 (((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)) | c3_1(a1788) | (~c1_1(a1788)) | (~c0_1(a1788))) <=> (c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(722,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)) | c3_1(a1788) | (~c1_1(a1788)) | (~c0_1(a1788)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[721])).
% 0.86/1.04 tff(723,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)) | c3_1(a1788) | (~c1_1(a1788)) | (~c0_1(a1788)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[722, 720])).
% 0.86/1.04 tff(724,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)) | c3_1(a1788) | (~c1_1(a1788)) | (~c0_1(a1788)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(725,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.86/1.04 tff(726,plain,
% 0.86/1.04 (~c1_1(a1788)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[725, 102, 719, 711, 675, 674, 703, 618, 680])).
% 0.86/1.04 tff(727,plain,
% 0.86/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(728,plain,
% 0.86/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[727])).
% 0.86/1.04 tff(729,plain,
% 0.86/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(730,plain,
% 0.86/1.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(731,plain,
% 0.86/1.04 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[730])).
% 0.86/1.04 tff(732,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 0.86/1.04 tff(733,plain,
% 0.86/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[732, 731])).
% 0.86/1.04 tff(734,plain,
% 0.86/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[733, 729])).
% 0.86/1.04 tff(735,plain,(
% 0.86/1.04 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.86/1.04 inference(skolemize,[status(sab)],[734])).
% 0.86/1.04 tff(736,plain,
% 0.86/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[735, 728])).
% 0.86/1.04 tff(737,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(738,plain,
% 0.86/1.04 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765))) <=> (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(739,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[738])).
% 0.86/1.04 tff(740,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[739, 737])).
% 0.86/1.04 tff(741,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(742,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.86/1.04 tff(743,plain,
% 0.86/1.04 (~c0_1(a1758)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[742, 102, 679, 678, 565, 557, 677, 579, 736])).
% 0.86/1.04 tff(744,plain,
% 0.86/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(745,plain,
% 0.86/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[744])).
% 0.86/1.04 tff(746,plain,
% 0.86/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(747,plain,
% 0.86/1.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(748,plain,
% 0.86/1.04 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[747])).
% 0.86/1.04 tff(749,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 0.86/1.05 tff(750,plain,
% 0.86/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.86/1.05 tff(751,plain,
% 0.86/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[750, 746])).
% 0.86/1.05 tff(752,plain,(
% 0.86/1.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.86/1.05 inference(skolemize,[status(sab)],[751])).
% 0.86/1.05 tff(753,plain,
% 0.86/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[752, 745])).
% 0.86/1.05 tff(754,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(755,plain,
% 0.86/1.05 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c3_1(a1765)) | c1_1(a1765) | (~c3_1(a1765)) | (~c0_1(a1765)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758))) <=> (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(756,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c3_1(a1765)) | c1_1(a1765) | (~c3_1(a1765)) | (~c0_1(a1765)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[755])).
% 0.86/1.05 tff(757,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c3_1(a1765)) | c1_1(a1765) | (~c3_1(a1765)) | (~c0_1(a1765)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[756, 754])).
% 0.86/1.05 tff(758,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c3_1(a1765)) | c1_1(a1765) | (~c3_1(a1765)) | (~c0_1(a1765)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(759,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.86/1.05 tff(760,plain,
% 0.86/1.05 (~c3_1(a1765)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[759, 102, 679, 678, 557, 677, 579, 753, 743])).
% 0.86/1.05 tff(761,plain,
% 0.86/1.05 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(762,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[761])).
% 0.86/1.05 tff(763,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(764,plain,
% 0.86/1.05 (^[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) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(765,plain,
% 0.86/1.05 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[764])).
% 0.86/1.05 tff(766,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.86/1.05 tff(767,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.86/1.05 tff(768,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[767, 763])).
% 0.86/1.05 tff(769,plain,(
% 0.86/1.05 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.05 inference(skolemize,[status(sab)],[768])).
% 0.86/1.05 tff(770,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[769, 762])).
% 0.86/1.05 tff(771,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(772,plain,
% 0.86/1.05 ((hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1765) | c3_1(a1765) | (~c2_1(a1765))) <=> (hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(773,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1765) | c3_1(a1765) | (~c2_1(a1765)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[772])).
% 0.86/1.05 tff(774,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1765) | c3_1(a1765) | (~c2_1(a1765)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765))),
% 0.86/1.05 inference(transitivity,[status(thm)],[773, 771])).
% 0.86/1.05 tff(775,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1765) | c3_1(a1765) | (~c2_1(a1765)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(776,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.86/1.05 tff(777,plain,
% 0.86/1.05 (hskp22),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[776, 102, 678, 565, 557, 677, 579, 770, 760])).
% 0.86/1.05 tff(778,plain,
% 0.86/1.05 (~c0_1(a1799)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[500, 777])).
% 0.86/1.05 tff(779,plain,
% 0.86/1.05 (c3_1(a1799)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[508, 777])).
% 0.86/1.05 tff(780,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(781,plain,
% 0.86/1.05 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c0_1(a1799) | c1_1(a1799) | (~c3_1(a1799))) <=> (c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(782,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c0_1(a1799) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[781])).
% 0.86/1.05 tff(783,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c0_1(a1799) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[782, 780])).
% 0.86/1.05 tff(784,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c0_1(a1799) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(785,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[784, 783])).
% 0.86/1.05 tff(786,plain,
% 0.86/1.05 (c1_1(a1799)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[785, 102, 779, 679, 678, 565, 557, 778, 677, 46, 743])).
% 0.86/1.05 tff(787,plain,
% 0.86/1.05 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(788,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[787])).
% 0.86/1.05 tff(789,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(790,plain,
% 0.86/1.05 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp24) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(791,plain,
% 0.86/1.05 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[790])).
% 0.86/1.05 tff(792,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 0.86/1.05 tff(793,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[792, 791])).
% 0.86/1.05 tff(794,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[793, 789])).
% 0.86/1.05 tff(795,plain,(
% 0.86/1.05 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.86/1.05 inference(skolemize,[status(sab)],[794])).
% 0.86/1.05 tff(796,plain,
% 0.86/1.05 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[795, 788])).
% 0.86/1.05 tff(797,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(798,plain,
% 0.86/1.05 ((hskp24 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1765) | c3_1(a1765) | (~c0_1(a1765))) <=> (hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(799,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1765) | c3_1(a1765) | (~c0_1(a1765)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[798])).
% 0.86/1.05 tff(800,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1765) | c3_1(a1765) | (~c0_1(a1765)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765))),
% 0.86/1.05 inference(transitivity,[status(thm)],[799, 797])).
% 0.86/1.05 tff(801,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1765) | c3_1(a1765) | (~c0_1(a1765)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(802,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.86/1.05 tff(803,plain,
% 0.86/1.05 (hskp24),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[802, 102, 679, 675, 674, 677, 796, 680, 760])).
% 0.86/1.05 tff(804,plain,
% 0.86/1.05 (((~hskp24) | (~c3_1(a1809))) <=> ((~hskp24) | (~c3_1(a1809)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(805,plain,
% 0.86/1.05 (((~c3_1(a1809)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a1809)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(806,axiom,((~c3_1(a1809)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.86/1.05 tff(807,plain,
% 0.86/1.05 ((~hskp24) | (~c3_1(a1809))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[806, 805])).
% 0.86/1.05 tff(808,plain,
% 0.86/1.05 ((~hskp24) | (~c3_1(a1809))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[807, 804])).
% 0.86/1.05 tff(809,plain,
% 0.86/1.05 (~c3_1(a1809)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[808, 803])).
% 0.86/1.05 tff(810,plain,
% 0.86/1.05 (((~hskp24) | (~c1_1(a1809))) <=> ((~hskp24) | (~c1_1(a1809)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(811,plain,
% 0.86/1.05 (((~c1_1(a1809)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a1809)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(812,axiom,((~c1_1(a1809)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.86/1.05 tff(813,plain,
% 0.86/1.05 ((~hskp24) | (~c1_1(a1809))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[812, 811])).
% 0.86/1.05 tff(814,plain,
% 0.86/1.05 ((~hskp24) | (~c1_1(a1809))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[813, 810])).
% 0.86/1.05 tff(815,plain,
% 0.86/1.05 (~c1_1(a1809)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[814, 803])).
% 0.86/1.05 tff(816,plain,
% 0.86/1.05 (((~hskp24) | c0_1(a1809)) <=> ((~hskp24) | c0_1(a1809))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(817,axiom,((~hskp24) | c0_1(a1809)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.86/1.05 tff(818,plain,
% 0.86/1.05 ((~hskp24) | c0_1(a1809)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[817, 816])).
% 0.86/1.05 tff(819,plain,
% 0.86/1.05 ((~hskp24) | c0_1(a1809)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[818, 816])).
% 0.86/1.05 tff(820,plain,
% 0.86/1.05 ((~hskp24) | c0_1(a1809)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[819, 816])).
% 0.86/1.05 tff(821,plain,
% 0.86/1.05 ((~hskp24) | c0_1(a1809)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[820, 816])).
% 0.86/1.05 tff(822,plain,
% 0.86/1.05 ((~hskp24) | c0_1(a1809)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[821, 816])).
% 0.86/1.05 tff(823,plain,
% 0.86/1.05 (c0_1(a1809)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[822, 803])).
% 0.86/1.05 tff(824,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(825,plain,
% 0.86/1.05 ((hskp2 | (~ndr1_0) | c3_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1809) | c3_1(a1809) | (~c0_1(a1809))) <=> (hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(826,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1809) | c3_1(a1809) | (~c0_1(a1809)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[825])).
% 0.86/1.05 tff(827,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1809) | c3_1(a1809) | (~c0_1(a1809)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[826, 824])).
% 0.86/1.05 tff(828,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1809) | c3_1(a1809) | (~c0_1(a1809)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(829,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[828, 827])).
% 0.86/1.05 tff(830,plain,
% 0.86/1.05 (hskp2),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[829, 102, 823, 679, 678, 815, 809, 195, 760])).
% 0.86/1.05 tff(831,plain,
% 0.86/1.05 (~c2_1(a1757)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[53, 830])).
% 0.86/1.05 tff(832,plain,
% 0.86/1.05 (c1_1(a1757)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[61, 830])).
% 0.86/1.05 tff(833,plain,
% 0.86/1.05 (c0_1(a1757)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[69, 830])).
% 0.86/1.05 tff(834,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(835,plain,
% 0.86/1.05 (((~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799))) <=> (c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(836,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[835])).
% 0.86/1.06 tff(837,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[836, 834])).
% 0.86/1.06 tff(838,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(839,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[838, 837])).
% 0.86/1.06 tff(840,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[839, 102, 779, 719, 711, 833, 832, 778, 831, 433, 786, 726])).
% 0.86/1.06 tff(841,plain,(c1_1(a1759) | hskp19 | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(842,plain,
% 0.86/1.06 (c1_1(a1759)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[841, 34, 12])).
% 0.86/1.06 tff(843,plain,
% 0.86/1.06 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(844,plain,
% 0.86/1.06 ((hskp19 | hskp13 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759))) <=> (hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(845,plain,
% 0.86/1.06 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[844])).
% 0.86/1.06 tff(846,plain,
% 0.86/1.06 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[845, 843])).
% 0.86/1.06 tff(847,plain,
% 0.86/1.06 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(848,plain,
% 0.86/1.06 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.86/1.06 tff(849,plain,
% 0.86/1.06 (hskp13 | c2_1(a1759) | (~c0_1(a1759))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[848, 102, 12, 842, 33])).
% 0.86/1.06 tff(850,plain,
% 0.86/1.06 (~c0_1(a1759)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[849, 36, 23])).
% 0.86/1.06 tff(851,plain,
% 0.86/1.06 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(852,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[851])).
% 0.86/1.06 tff(853,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(854,plain,
% 0.86/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(855,plain,
% 0.86/1.06 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[854])).
% 0.86/1.06 tff(856,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.86/1.06 tff(857,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.86/1.06 tff(858,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[857, 853])).
% 0.86/1.06 tff(859,plain,(
% 0.86/1.06 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.86/1.06 inference(skolemize,[status(sab)],[858])).
% 0.86/1.06 tff(860,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[859, 852])).
% 0.86/1.06 tff(861,plain,
% 0.86/1.06 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(862,plain,
% 0.86/1.06 ((hskp19 | hskp6 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759))) <=> (hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(863,plain,
% 0.86/1.06 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[862])).
% 0.86/1.06 tff(864,plain,
% 0.86/1.06 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 0.86/1.06 inference(transitivity,[status(thm)],[863, 861])).
% 0.86/1.06 tff(865,plain,
% 0.86/1.06 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(866,plain,
% 0.86/1.06 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.86/1.06 tff(867,plain,
% 0.86/1.06 (hskp6 | (~c1_1(a1759)) | c0_1(a1759)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[866, 102, 12, 34, 641])).
% 0.86/1.06 tff(868,plain,
% 0.86/1.06 (c0_1(a1759)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[867, 225, 842])).
% 0.86/1.06 tff(869,assumption,(c1_1(a1759)), introduced(assumption)).
% 0.86/1.06 tff(870,plain,
% 0.86/1.06 (hskp19 | hskp6 | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[866, 34, 641])).
% 0.86/1.06 tff(871,plain,
% 0.86/1.06 (c0_1(a1759)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[870, 12, 226, 869, 225])).
% 0.86/1.06 tff(872,plain,
% 0.86/1.06 (hskp19 | hskp13 | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[848, 36, 33])).
% 0.86/1.06 tff(873,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[872, 871, 12, 226, 869, 23])).
% 0.86/1.06 tff(874,plain,(hskp19 | (~ndr1_0) | (~c1_1(a1759)) | hskp13 | c2_1(a1759) | hskp6 | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(875,plain,
% 0.86/1.06 (hskp19 | (~c1_1(a1759)) | hskp13 | c2_1(a1759) | hskp6 | c3_1(a1759)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[874, 102])).
% 0.86/1.06 tff(876,plain,
% 0.86/1.06 (c2_1(a1759)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[875, 225, 842, 23, 12, 34])).
% 0.86/1.06 tff(877,plain,
% 0.86/1.06 (((~hskp4) | (~c2_1(a1759))) <=> ((~hskp4) | (~c2_1(a1759)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(878,plain,
% 0.86/1.06 (((~c2_1(a1759)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a1759)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(879,axiom,((~c2_1(a1759)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.86/1.06 tff(880,plain,
% 0.86/1.06 ((~hskp4) | (~c2_1(a1759))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[879, 878])).
% 0.86/1.06 tff(881,plain,
% 0.86/1.06 ((~hskp4) | (~c2_1(a1759))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[880, 877])).
% 0.86/1.06 tff(882,plain,
% 0.86/1.06 (~hskp4),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[881, 876])).
% 0.86/1.06 tff(883,plain,
% 0.86/1.06 (^[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))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(884,plain,
% 0.86/1.06 (![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)))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[883])).
% 0.86/1.06 tff(885,plain,
% 0.86/1.06 (![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)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(886,plain,
% 0.86/1.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | 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))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | 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))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) | hskp4) <=> (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(887,plain,
% 0.86/1.06 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) | hskp4) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[886])).
% 0.86/1.06 tff(888,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 0.86/1.06 tff(889,plain,
% 0.86/1.06 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.86/1.06 tff(890,plain,
% 0.86/1.06 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[889, 885])).
% 0.86/1.06 tff(891,plain,(
% 0.86/1.06 ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.86/1.06 inference(skolemize,[status(sab)],[890])).
% 0.86/1.06 tff(892,plain,
% 0.86/1.06 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[891, 884])).
% 0.86/1.06 tff(893,plain,
% 0.86/1.06 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(894,plain,
% 0.86/1.06 ((hskp29 | hskp4 | (~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759))) <=> (hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(895,plain,
% 0.86/1.06 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[894])).
% 0.86/1.06 tff(896,plain,
% 0.86/1.06 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[895, 893])).
% 0.86/1.06 tff(897,plain,
% 0.86/1.06 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(898,plain,
% 0.86/1.06 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.86/1.06 tff(899,plain,
% 0.86/1.06 (hskp29 | hskp4 | (~c2_1(a1759)) | (~c0_1(a1759))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[898, 102, 842, 892])).
% 0.86/1.06 tff(900,plain,
% 0.86/1.06 (hskp29),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[899, 882, 876, 868])).
% 0.86/1.06 tff(901,plain,
% 0.86/1.06 (((~hskp29) | c3_1(a1805)) <=> ((~hskp29) | c3_1(a1805))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(902,axiom,((~hskp29) | c3_1(a1805)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.86/1.06 tff(903,plain,
% 0.86/1.06 ((~hskp29) | c3_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.86/1.06 tff(904,plain,
% 0.86/1.06 ((~hskp29) | c3_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[903, 901])).
% 0.86/1.06 tff(905,plain,
% 0.86/1.06 ((~hskp29) | c3_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[904, 901])).
% 0.86/1.06 tff(906,plain,
% 0.86/1.06 ((~hskp29) | c3_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[905, 901])).
% 0.86/1.06 tff(907,plain,
% 0.86/1.06 ((~hskp29) | c3_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[906, 901])).
% 0.86/1.06 tff(908,plain,
% 0.86/1.06 (c3_1(a1805)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[907, 900])).
% 0.86/1.06 tff(909,plain,
% 0.86/1.06 (hskp25),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[147, 882, 111])).
% 0.86/1.06 tff(910,plain,
% 0.86/1.06 (((~hskp29) | c0_1(a1805)) <=> ((~hskp29) | c0_1(a1805))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(911,axiom,((~hskp29) | c0_1(a1805)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.86/1.06 tff(912,plain,
% 0.86/1.06 ((~hskp29) | c0_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[911, 910])).
% 0.86/1.06 tff(913,plain,
% 0.86/1.06 ((~hskp29) | c0_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[912, 910])).
% 0.86/1.06 tff(914,plain,
% 0.86/1.06 ((~hskp29) | c0_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[913, 910])).
% 0.86/1.06 tff(915,plain,
% 0.86/1.06 ((~hskp29) | c0_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[914, 910])).
% 0.86/1.06 tff(916,plain,
% 0.86/1.06 ((~hskp29) | c0_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[915, 910])).
% 0.86/1.06 tff(917,plain,
% 0.86/1.06 (c0_1(a1805)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[916, 900])).
% 0.86/1.06 tff(918,plain,
% 0.86/1.06 (((~hskp29) | c2_1(a1805)) <=> ((~hskp29) | c2_1(a1805))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(919,axiom,((~hskp29) | c2_1(a1805)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.86/1.06 tff(920,plain,
% 0.86/1.06 ((~hskp29) | c2_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.86/1.06 tff(921,plain,
% 0.86/1.06 ((~hskp29) | c2_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[920, 918])).
% 0.86/1.06 tff(922,plain,
% 0.86/1.06 ((~hskp29) | c2_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[921, 918])).
% 0.86/1.06 tff(923,plain,
% 0.86/1.06 ((~hskp29) | c2_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[922, 918])).
% 0.86/1.06 tff(924,plain,
% 0.86/1.06 ((~hskp29) | c2_1(a1805)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[923, 918])).
% 0.86/1.06 tff(925,plain,
% 0.86/1.06 (c2_1(a1805)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[924, 900])).
% 0.86/1.06 tff(926,plain,
% 0.86/1.06 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(927,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[926])).
% 0.86/1.06 tff(928,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(929,plain,
% 0.86/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(930,plain,
% 0.86/1.06 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[929])).
% 0.86/1.06 tff(931,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.86/1.06 tff(932,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.86/1.06 tff(933,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[932, 928])).
% 0.86/1.06 tff(934,plain,(
% 0.86/1.06 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.06 inference(skolemize,[status(sab)],[933])).
% 0.86/1.06 tff(935,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[934, 927])).
% 0.86/1.06 tff(936,assumption,(hskp25), introduced(assumption)).
% 0.86/1.06 tff(937,plain,
% 0.86/1.06 (~c1_1(a1827)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[153, 936])).
% 0.86/1.06 tff(938,plain,
% 0.86/1.06 (~c0_1(a1827)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[159, 936])).
% 0.86/1.06 tff(939,assumption,(c3_1(a1805)), introduced(assumption)).
% 0.86/1.06 tff(940,assumption,(c2_1(a1805)), introduced(assumption)).
% 0.86/1.06 tff(941,assumption,(c0_1(a1805)), introduced(assumption)).
% 0.86/1.06 tff(942,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(943,plain,
% 0.86/1.06 ((hskp6 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c1_1(a1827) | c0_1(a1827) | (~c3_1(a1827))) <=> (hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(944,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c1_1(a1827) | c0_1(a1827) | (~c3_1(a1827)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[943])).
% 0.86/1.06 tff(945,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c1_1(a1827) | c0_1(a1827) | (~c3_1(a1827)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[944, 942])).
% 0.86/1.06 tff(946,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c1_1(a1827) | c0_1(a1827) | (~c3_1(a1827)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(947,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.86/1.06 tff(948,plain,
% 0.86/1.06 (~c3_1(a1827)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[947, 102, 225, 941, 940, 939, 938, 937, 935])).
% 0.86/1.06 tff(949,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[166, 102, 315, 35, 938, 937, 131, 948])).
% 0.86/1.06 tff(950,plain,((~hskp25) | hskp4 | hskp3 | hskp6 | (~c0_1(a1805)) | (~c2_1(a1805)) | (~c3_1(a1805))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(951,plain,
% 0.86/1.06 (hskp3),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[950, 925, 917, 225, 882, 909, 908])).
% 0.86/1.06 tff(952,plain,
% 0.86/1.06 (c2_1(a1758)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[556, 951])).
% 0.86/1.06 tff(953,plain,
% 0.86/1.06 (c1_1(a1758)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[564, 951])).
% 0.86/1.06 tff(954,plain,
% 0.86/1.06 (c0_1(a1758)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[571, 102, 23, 953, 952, 22])).
% 0.86/1.06 tff(955,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(956,plain,
% 0.86/1.06 (((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759))) <=> ((~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(957,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[956])).
% 0.86/1.06 tff(958,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[957, 955])).
% 0.86/1.06 tff(959,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(960,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[959, 958])).
% 0.86/1.06 tff(961,plain,
% 0.86/1.06 (~c1_1(a1805)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[960, 102, 925, 908, 842, 876, 34, 618, 868])).
% 0.86/1.06 tff(962,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(963,plain,
% 0.86/1.06 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805))) <=> (c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(964,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[963])).
% 0.86/1.06 tff(965,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[964, 962])).
% 0.86/1.06 tff(966,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(967,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.86/1.06 tff(968,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[967, 102, 917, 925, 842, 953, 952, 34, 736, 868, 961, 954])).
% 0.86/1.06 tff(969,plain,(hskp6 | c3_1(a1759) | hskp13 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(970,plain,
% 0.86/1.06 (hskp6),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[969, 23, 34, 12])).
% 0.86/1.06 tff(971,plain,
% 0.86/1.06 (~c0_1(a1762)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[270, 970])).
% 0.86/1.06 tff(972,plain,
% 0.86/1.06 (c2_1(a1762)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[286, 970])).
% 0.86/1.06 tff(973,plain,
% 0.86/1.06 (~c1_1(a1762)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[374, 102, 23, 972, 971, 22])).
% 0.86/1.06 tff(974,plain,
% 0.86/1.06 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(975,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[974])).
% 0.86/1.06 tff(976,plain,
% 0.86/1.06 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(977,plain,
% 0.86/1.07 (^[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))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(978,plain,
% 0.86/1.07 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[977])).
% 0.86/1.07 tff(979,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.86/1.07 tff(980,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.86/1.07 tff(981,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[980, 976])).
% 0.86/1.07 tff(982,plain,(
% 0.86/1.07 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.07 inference(skolemize,[status(sab)],[981])).
% 0.86/1.07 tff(983,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[982, 975])).
% 0.86/1.07 tff(984,plain,
% 0.86/1.07 (c3_1(a1762)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[278, 970])).
% 0.86/1.07 tff(985,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(986,plain,
% 0.86/1.07 ((hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762))) <=> (hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(987,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762)))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[986])).
% 0.86/1.07 tff(988,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762))),
% 0.86/1.07 inference(transitivity,[status(thm)],[987, 985])).
% 0.86/1.07 tff(989,plain,
% 0.86/1.07 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(990,plain,
% 0.86/1.07 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[989, 988])).
% 0.86/1.07 tff(991,plain,
% 0.86/1.07 (hskp7),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[990, 102, 984, 842, 971, 36, 983, 850, 973])).
% 0.86/1.07 tff(992,plain,
% 0.86/1.07 (((~hskp7) | (~c1_1(a1763))) <=> ((~hskp7) | (~c1_1(a1763)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(993,plain,
% 0.86/1.07 (((~c1_1(a1763)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1763)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(994,axiom,((~c1_1(a1763)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.86/1.07 tff(995,plain,
% 0.86/1.07 ((~hskp7) | (~c1_1(a1763))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.86/1.07 tff(996,plain,
% 0.86/1.07 ((~hskp7) | (~c1_1(a1763))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[995, 992])).
% 0.86/1.07 tff(997,plain,
% 0.86/1.07 (~c1_1(a1763)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[996, 991])).
% 0.86/1.07 tff(998,plain,
% 0.86/1.07 (((~hskp7) | c3_1(a1763)) <=> ((~hskp7) | c3_1(a1763))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(999,axiom,((~hskp7) | c3_1(a1763)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.86/1.07 tff(1000,plain,
% 0.86/1.07 ((~hskp7) | c3_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[999, 998])).
% 0.86/1.07 tff(1001,plain,
% 0.86/1.07 ((~hskp7) | c3_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1000, 998])).
% 0.86/1.07 tff(1002,plain,
% 0.86/1.07 ((~hskp7) | c3_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1001, 998])).
% 0.86/1.07 tff(1003,plain,
% 0.86/1.07 ((~hskp7) | c3_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1002, 998])).
% 0.86/1.07 tff(1004,plain,
% 0.86/1.07 ((~hskp7) | c3_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1003, 998])).
% 0.86/1.07 tff(1005,plain,
% 0.86/1.07 (c3_1(a1763)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1004, 991])).
% 0.86/1.07 tff(1006,plain,
% 0.86/1.07 (((~hskp7) | c0_1(a1763)) <=> ((~hskp7) | c0_1(a1763))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1007,axiom,((~hskp7) | c0_1(a1763)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.86/1.07 tff(1008,plain,
% 0.86/1.07 ((~hskp7) | c0_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.86/1.07 tff(1009,plain,
% 0.86/1.07 ((~hskp7) | c0_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1008, 1006])).
% 0.86/1.07 tff(1010,plain,
% 0.86/1.07 ((~hskp7) | c0_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1009, 1006])).
% 0.86/1.07 tff(1011,plain,
% 0.86/1.07 ((~hskp7) | c0_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1010, 1006])).
% 0.86/1.07 tff(1012,plain,
% 0.86/1.07 ((~hskp7) | c0_1(a1763)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1011, 1006])).
% 0.86/1.07 tff(1013,plain,
% 0.86/1.07 (c0_1(a1763)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1012, 991])).
% 0.86/1.07 tff(1014,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1015,plain,
% 0.86/1.07 ((hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759))) <=> (hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1016,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[1015])).
% 0.86/1.07 tff(1017,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[1016, 1014])).
% 0.86/1.07 tff(1018,plain,
% 0.86/1.07 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(1019,plain,
% 0.86/1.07 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.86/1.07 tff(1020,plain,
% 0.86/1.07 (hskp11),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1019, 102, 1013, 1005, 842, 997, 36, 860, 850])).
% 0.86/1.07 tff(1021,plain,
% 0.86/1.07 (((~hskp11) | (~c2_1(a1768))) <=> ((~hskp11) | (~c2_1(a1768)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1022,plain,
% 0.86/1.07 (((~c2_1(a1768)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1768)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1023,axiom,((~c2_1(a1768)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.86/1.07 tff(1024,plain,
% 0.86/1.07 ((~hskp11) | (~c2_1(a1768))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.86/1.07 tff(1025,plain,
% 0.86/1.07 ((~hskp11) | (~c2_1(a1768))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1024, 1021])).
% 0.86/1.07 tff(1026,plain,
% 0.86/1.07 (~c2_1(a1768)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1025, 1020])).
% 0.86/1.07 tff(1027,plain,
% 0.86/1.07 (((~hskp11) | c0_1(a1768)) <=> ((~hskp11) | c0_1(a1768))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1028,axiom,((~hskp11) | c0_1(a1768)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.86/1.07 tff(1029,plain,
% 0.86/1.07 ((~hskp11) | c0_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 0.86/1.07 tff(1030,plain,
% 0.86/1.07 ((~hskp11) | c0_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1029, 1027])).
% 0.86/1.07 tff(1031,plain,
% 0.86/1.07 ((~hskp11) | c0_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1030, 1027])).
% 0.86/1.07 tff(1032,plain,
% 0.86/1.07 ((~hskp11) | c0_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1031, 1027])).
% 0.86/1.07 tff(1033,plain,
% 0.86/1.07 ((~hskp11) | c0_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1032, 1027])).
% 0.86/1.07 tff(1034,plain,
% 0.86/1.07 (c0_1(a1768)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1033, 1020])).
% 0.86/1.07 tff(1035,plain,
% 0.86/1.07 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1036,plain,
% 0.86/1.07 ((hskp19 | hskp13 | (~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768))) <=> (hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1037,plain,
% 0.86/1.07 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[1036])).
% 0.86/1.07 tff(1038,plain,
% 0.86/1.07 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[1037, 1035])).
% 0.86/1.07 tff(1039,plain,
% 0.86/1.07 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(1040,plain,
% 0.86/1.07 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 0.86/1.07 tff(1041,plain,
% 0.86/1.07 (~c1_1(a1768)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1040, 102, 12, 23, 1034, 1026, 33])).
% 0.86/1.07 tff(1042,plain,
% 0.86/1.07 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(1043,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[1042])).
% 0.86/1.07 tff(1044,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1045,plain,
% 0.86/1.07 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_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) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(1046,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[1045])).
% 0.86/1.07 tff(1047,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 0.86/1.07 tff(1048,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.86/1.07 tff(1049,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1048, 1044])).
% 0.86/1.07 tff(1050,plain,(
% 0.86/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.86/1.07 inference(skolemize,[status(sab)],[1049])).
% 0.86/1.07 tff(1051,plain,
% 0.86/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1050, 1043])).
% 0.86/1.07 tff(1052,plain,
% 0.86/1.07 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(1053,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[1052])).
% 0.86/1.07 tff(1054,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1055,plain,
% 0.86/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(1056,plain,
% 0.86/1.07 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[1055])).
% 0.86/1.07 tff(1057,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.86/1.07 tff(1058,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.86/1.07 tff(1059,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1058, 1054])).
% 0.86/1.07 tff(1060,plain,(
% 0.86/1.07 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.86/1.07 inference(skolemize,[status(sab)],[1059])).
% 0.86/1.07 tff(1061,plain,
% 0.86/1.07 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1060, 1053])).
% 0.86/1.07 tff(1062,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1063,plain,
% 0.86/1.07 ((hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1759) | c3_1(a1759) | (~c1_1(a1759))) <=> (hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1064,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1759) | c3_1(a1759) | (~c1_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762)))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[1063])).
% 0.86/1.07 tff(1065,plain,
% 0.86/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1759) | c3_1(a1759) | (~c1_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 0.86/1.07 inference(transitivity,[status(thm)],[1064, 1062])).
% 0.86/1.07 tff(1066,plain,
% 0.86/1.07 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1759) | c3_1(a1759) | (~c1_1(a1759)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(1067,plain,
% 0.86/1.07 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.86/1.07 tff(1068,plain,
% 0.86/1.07 (hskp17),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1067, 102, 972, 984, 842, 34, 1061, 850, 973])).
% 0.86/1.07 tff(1069,plain,
% 0.86/1.07 (((~hskp17) | (~c1_1(a1781))) <=> ((~hskp17) | (~c1_1(a1781)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1070,plain,
% 0.86/1.07 (((~c1_1(a1781)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1781)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1071,axiom,((~c1_1(a1781)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.86/1.07 tff(1072,plain,
% 0.86/1.07 ((~hskp17) | (~c1_1(a1781))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 0.86/1.07 tff(1073,plain,
% 0.86/1.07 ((~hskp17) | (~c1_1(a1781))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1072, 1069])).
% 0.86/1.07 tff(1074,plain,
% 0.86/1.07 (~c1_1(a1781)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1073, 1068])).
% 0.86/1.07 tff(1075,plain,
% 0.86/1.07 (((~hskp11) | c3_1(a1768)) <=> ((~hskp11) | c3_1(a1768))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1076,axiom,((~hskp11) | c3_1(a1768)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.86/1.07 tff(1077,plain,
% 0.86/1.07 ((~hskp11) | c3_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 0.86/1.07 tff(1078,plain,
% 0.86/1.07 ((~hskp11) | c3_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1077, 1075])).
% 0.86/1.07 tff(1079,plain,
% 0.86/1.07 ((~hskp11) | c3_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1078, 1075])).
% 0.86/1.07 tff(1080,plain,
% 0.86/1.07 ((~hskp11) | c3_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1079, 1075])).
% 0.86/1.07 tff(1081,plain,
% 0.86/1.07 ((~hskp11) | c3_1(a1768)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1080, 1075])).
% 0.86/1.07 tff(1082,plain,
% 0.86/1.07 (c3_1(a1768)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1081, 1020])).
% 0.86/1.07 tff(1083,plain,
% 0.86/1.07 (((~hskp17) | c3_1(a1781)) <=> ((~hskp17) | c3_1(a1781))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1084,axiom,((~hskp17) | c3_1(a1781)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.86/1.07 tff(1085,plain,
% 0.86/1.07 ((~hskp17) | c3_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 0.86/1.07 tff(1086,plain,
% 0.86/1.07 ((~hskp17) | c3_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1085, 1083])).
% 0.86/1.07 tff(1087,plain,
% 0.86/1.07 ((~hskp17) | c3_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1086, 1083])).
% 0.86/1.07 tff(1088,plain,
% 0.86/1.07 ((~hskp17) | c3_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1087, 1083])).
% 0.86/1.07 tff(1089,plain,
% 0.86/1.07 ((~hskp17) | c3_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1088, 1083])).
% 0.86/1.07 tff(1090,plain,
% 0.86/1.07 (c3_1(a1781)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1089, 1068])).
% 0.86/1.07 tff(1091,plain,
% 0.86/1.07 (((~hskp17) | c2_1(a1781)) <=> ((~hskp17) | c2_1(a1781))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1092,axiom,((~hskp17) | c2_1(a1781)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.86/1.07 tff(1093,plain,
% 0.86/1.07 ((~hskp17) | c2_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.86/1.07 tff(1094,plain,
% 0.86/1.07 ((~hskp17) | c2_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1093, 1091])).
% 0.86/1.07 tff(1095,plain,
% 0.86/1.07 ((~hskp17) | c2_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1094, 1091])).
% 0.86/1.07 tff(1096,plain,
% 0.86/1.07 ((~hskp17) | c2_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1095, 1091])).
% 0.86/1.07 tff(1097,plain,
% 0.86/1.07 ((~hskp17) | c2_1(a1781)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1096, 1091])).
% 0.86/1.07 tff(1098,plain,
% 0.86/1.07 (c2_1(a1781)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1097, 1068])).
% 0.86/1.07 tff(1099,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1100,plain,
% 0.86/1.08 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1101,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1100])).
% 0.86/1.08 tff(1102,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1101, 1099])).
% 0.86/1.08 tff(1103,plain,
% 0.86/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1104,plain,
% 0.86/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 0.86/1.08 tff(1105,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1104, 102, 1098, 1090, 1082, 972, 984, 1074, 1026, 971, 1051, 1041])).
% 0.86/1.08 tff(1106,plain,(c2_1(a1759) | hskp19 | hskp13 | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1107,plain,
% 0.86/1.08 (c2_1(a1759)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1106, 23, 12, 34])).
% 0.86/1.08 tff(1108,plain,
% 0.86/1.08 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1109,plain,
% 0.86/1.08 ((hskp13 | (~ndr1_0) | c0_1(a1759) | (~c2_1(a1759)) | (~c1_1(a1759))) <=> (hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1110,plain,
% 0.86/1.08 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1759) | (~c2_1(a1759)) | (~c1_1(a1759)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1109])).
% 0.86/1.08 tff(1111,plain,
% 0.86/1.08 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1759) | (~c2_1(a1759)) | (~c1_1(a1759)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1110, 1108])).
% 0.86/1.08 tff(1112,plain,
% 0.86/1.08 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1759) | (~c2_1(a1759)) | (~c1_1(a1759)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1113,plain,
% 0.86/1.08 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 0.86/1.08 tff(1114,plain,
% 0.86/1.08 (hskp13 | (~c2_1(a1759)) | c0_1(a1759)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1113, 102, 842, 22])).
% 0.86/1.08 tff(1115,plain,
% 0.86/1.08 (c0_1(a1759)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1114, 1107, 23])).
% 0.86/1.08 tff(1116,plain,
% 0.86/1.08 (~hskp4),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[881, 1107])).
% 0.86/1.08 tff(1117,plain,
% 0.86/1.08 (hskp8 | hskp4),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[293, 102, 972, 984, 971, 121])).
% 0.86/1.08 tff(1118,plain,
% 0.86/1.08 (hskp8),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1117, 1116])).
% 0.86/1.08 tff(1119,plain,
% 0.86/1.08 (~c1_1(a1765)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[299, 1118])).
% 0.86/1.08 tff(1120,plain,
% 0.86/1.08 (c2_1(a1765)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[405, 1118])).
% 0.86/1.08 tff(1121,plain,
% 0.86/1.08 (c0_1(a1765)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[413, 1118])).
% 0.86/1.08 tff(1122,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1123,plain,
% 0.86/1.08 (((~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765))) <=> (c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1124,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1123])).
% 0.86/1.08 tff(1125,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1124, 1122])).
% 0.86/1.08 tff(1126,plain,
% 0.86/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1127,plain,
% 0.86/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 0.86/1.08 tff(1128,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1127, 102, 1121, 1120, 842, 1119, 1107, 34, 736, 1115])).
% 0.86/1.08 tff(1129,plain,(hskp13 | c3_1(a1759) | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1130,plain,
% 0.86/1.08 (hskp13),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1129, 34, 12])).
% 0.86/1.08 tff(1131,plain,
% 0.86/1.08 (c1_1(a1771)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[234, 1130])).
% 0.86/1.08 tff(1132,plain,
% 0.86/1.08 (~c0_1(a1771)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[223, 227])).
% 0.86/1.08 tff(1133,plain,
% 0.86/1.08 (hskp3),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[264, 225, 1132, 227])).
% 0.86/1.08 tff(1134,plain,
% 0.86/1.08 (~c3_1(a1758)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[578, 1133])).
% 0.86/1.08 tff(1135,plain,
% 0.86/1.08 (c1_1(a1758)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[564, 1133])).
% 0.86/1.08 tff(1136,plain,
% 0.86/1.08 (c2_1(a1758)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[556, 1133])).
% 0.86/1.08 tff(1137,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[671, 1136, 1135, 235, 243, 225, 1134, 12, 1132])).
% 0.86/1.08 tff(1138,plain,(hskp6 | hskp19 | (~hskp13)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1139,plain,
% 0.86/1.08 (hskp6),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1138, 1130, 12])).
% 0.86/1.08 tff(1140,plain,
% 0.86/1.08 (~c0_1(a1762)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[270, 1139])).
% 0.86/1.08 tff(1141,plain,
% 0.86/1.08 (c3_1(a1762)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[278, 1139])).
% 0.86/1.08 tff(1142,plain,
% 0.86/1.08 (c2_1(a1762)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[286, 1139])).
% 0.86/1.08 tff(1143,plain,
% 0.86/1.08 (~c0_1(a1771)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[223, 1130])).
% 0.86/1.08 tff(1144,plain,
% 0.86/1.08 (c2_1(a1771)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[242, 1130])).
% 0.86/1.08 tff(1145,assumption,(hskp22), introduced(assumption)).
% 0.86/1.08 tff(1146,plain,
% 0.86/1.08 (~c2_1(a1799)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[494, 1145])).
% 0.86/1.08 tff(1147,plain,
% 0.86/1.08 (c3_1(a1799)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[508, 1145])).
% 0.86/1.08 tff(1148,plain,
% 0.86/1.08 (~c0_1(a1799)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[500, 1145])).
% 0.86/1.08 tff(1149,assumption,(~c1_1(a1762)), introduced(assumption)).
% 0.86/1.08 tff(1150,assumption,(~c2_1(a1799)), introduced(assumption)).
% 0.86/1.08 tff(1151,assumption,(c3_1(a1799)), introduced(assumption)).
% 0.86/1.08 tff(1152,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1153,plain,
% 0.86/1.08 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1154,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1153])).
% 0.86/1.08 tff(1155,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1154, 1152])).
% 0.86/1.08 tff(1156,plain,
% 0.86/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1157,plain,
% 0.86/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.86/1.08 tff(1158,plain,
% 0.86/1.08 (c1_1(a1799)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1157, 102, 1151, 368, 387, 1150, 367, 1051, 1149])).
% 0.86/1.08 tff(1159,assumption,(~c0_1(a1799)), introduced(assumption)).
% 0.86/1.08 tff(1160,plain,
% 0.86/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1161,plain,
% 0.86/1.08 ((hskp7 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762))) <=> (hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1162,plain,
% 0.86/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1161])).
% 0.86/1.08 tff(1163,plain,
% 0.86/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1162, 1160])).
% 0.86/1.08 tff(1164,plain,
% 0.86/1.08 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1165,plain,
% 0.86/1.08 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 0.86/1.08 tff(1166,plain,
% 0.86/1.08 (hskp7),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1165, 102, 387, 1159, 1150, 367, 983, 1149, 1158])).
% 0.86/1.08 tff(1167,plain,
% 0.86/1.08 (~c1_1(a1763)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[996, 1166])).
% 0.86/1.08 tff(1168,assumption,(hskp7), introduced(assumption)).
% 0.86/1.08 tff(1169,plain,
% 0.86/1.08 (c0_1(a1763)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1012, 1168])).
% 0.86/1.08 tff(1170,plain,
% 0.86/1.08 (c3_1(a1763)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1004, 1168])).
% 0.86/1.08 tff(1171,assumption,(~c3_1(a1771)), introduced(assumption)).
% 0.86/1.08 tff(1172,assumption,(~c1_1(a1763)), introduced(assumption)).
% 0.86/1.08 tff(1173,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1174,plain,
% 0.86/1.08 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771))) <=> (c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1175,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1174])).
% 0.86/1.08 tff(1176,plain,
% 0.86/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1175, 1173])).
% 0.86/1.08 tff(1177,plain,
% 0.86/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1178,plain,
% 0.86/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 0.86/1.08 tff(1179,plain,
% 0.86/1.08 ((~c0_1(a1763)) | (~c3_1(a1763))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1178, 226, 662, 368, 387, 254, 1172, 753, 1149, 1171])).
% 0.86/1.08 tff(1180,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1179, 1170, 1169])).
% 0.86/1.08 tff(1181,plain,((~hskp7) | (~ndr1_0) | (~c2_1(a1771)) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c1_1(a1763) | c1_1(a1762) | c3_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1182,plain,
% 0.86/1.08 ((~hskp7) | (~c2_1(a1771)) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c1_1(a1763) | c1_1(a1762) | c3_1(a1771)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1181, 102])).
% 0.86/1.08 tff(1183,plain,
% 0.86/1.08 (c3_1(a1771)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1182, 1167, 662, 368, 387, 254, 1149, 1166])).
% 0.86/1.08 tff(1184,plain,
% 0.86/1.08 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.86/1.08 inference(bind,[status(th)],[])).
% 0.86/1.08 tff(1185,plain,
% 0.86/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.08 inference(quant_intro,[status(thm)],[1184])).
% 0.86/1.08 tff(1186,plain,
% 0.86/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1187,plain,
% 0.86/1.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.86/1.08 inference(bind,[status(th)],[])).
% 0.86/1.08 tff(1188,plain,
% 0.86/1.08 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.08 inference(quant_intro,[status(thm)],[1187])).
% 0.86/1.08 tff(1189,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.86/1.08 tff(1190,plain,
% 0.86/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.86/1.08 tff(1191,plain,
% 0.86/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1190, 1186])).
% 0.86/1.08 tff(1192,plain,(
% 0.86/1.08 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.08 inference(skolemize,[status(sab)],[1191])).
% 0.86/1.08 tff(1193,plain,
% 0.86/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1192, 1185])).
% 0.86/1.08 tff(1194,plain,
% 0.86/1.08 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1195,plain,
% 0.86/1.08 ((hskp8 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762))) <=> (hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1196,plain,
% 0.86/1.08 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1195])).
% 0.86/1.08 tff(1197,plain,
% 0.86/1.08 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1196, 1194])).
% 0.86/1.08 tff(1198,plain,
% 0.86/1.08 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1199,plain,
% 0.86/1.08 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.86/1.08 tff(1200,plain,
% 0.86/1.08 (hskp8 | (~c3_1(a1771))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1199, 102, 652, 662, 387, 367, 1193, 1149])).
% 0.86/1.08 tff(1201,plain,
% 0.86/1.08 (hskp8),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1200, 1183])).
% 0.86/1.08 tff(1202,plain,
% 0.86/1.08 (~c1_1(a1765)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[299, 1201])).
% 0.86/1.08 tff(1203,plain,
% 0.86/1.08 (c2_1(a1765)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[405, 1201])).
% 0.86/1.08 tff(1204,plain,
% 0.86/1.08 (c0_1(a1765)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[413, 1201])).
% 0.86/1.08 tff(1205,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[422, 102, 652, 662, 1204, 1203, 387, 254, 1202, 367, 46, 1149])).
% 0.86/1.08 tff(1206,plain,(c1_1(a1762) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1762)) | c0_1(a1771) | c0_1(a1762) | (~c2_1(a1762)) | c0_1(a1799) | c2_1(a1799) | (~c3_1(a1799))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1207,plain,
% 0.86/1.08 (c1_1(a1762)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1206, 1148, 662, 387, 254, 367, 368, 652, 1146, 1147])).
% 0.86/1.08 tff(1208,plain,
% 0.86/1.08 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.86/1.08 inference(bind,[status(th)],[])).
% 0.86/1.08 tff(1209,plain,
% 0.86/1.08 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.86/1.08 inference(quant_intro,[status(thm)],[1208])).
% 0.86/1.08 tff(1210,plain,
% 0.86/1.08 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1211,plain,
% 0.86/1.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp17) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.86/1.09 inference(bind,[status(th)],[])).
% 0.86/1.09 tff(1212,plain,
% 0.86/1.09 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.86/1.09 inference(quant_intro,[status(thm)],[1211])).
% 0.86/1.09 tff(1213,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 0.86/1.09 tff(1214,plain,
% 0.86/1.09 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 0.86/1.09 tff(1215,plain,
% 0.86/1.09 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1214, 1210])).
% 0.86/1.09 tff(1216,plain,(
% 0.86/1.09 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.86/1.09 inference(skolemize,[status(sab)],[1215])).
% 0.86/1.09 tff(1217,plain,
% 0.86/1.09 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1216, 1209])).
% 0.86/1.09 tff(1218,plain,
% 0.86/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1219,plain,
% 0.86/1.09 ((hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762))) <=> (hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1220,plain,
% 0.86/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[1219])).
% 0.86/1.09 tff(1221,plain,
% 0.86/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.86/1.09 inference(transitivity,[status(thm)],[1220, 1218])).
% 0.86/1.09 tff(1222,plain,
% 0.86/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(1223,plain,
% 0.86/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 0.86/1.09 tff(1224,plain,
% 0.86/1.09 (hskp17 | (~c1_1(a1762))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1223, 102, 368, 387, 367, 1217])).
% 0.86/1.09 tff(1225,plain,
% 0.86/1.09 (hskp17),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1224, 1207])).
% 0.86/1.09 tff(1226,plain,
% 0.86/1.09 (c3_1(a1781)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1089, 1225])).
% 0.86/1.09 tff(1227,plain,
% 0.86/1.09 (~c1_1(a1781)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1073, 1225])).
% 0.86/1.09 tff(1228,plain,
% 0.86/1.09 (c2_1(a1781)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1097, 1225])).
% 0.86/1.09 tff(1229,assumption,(c0_1(a1781)), introduced(assumption)).
% 0.86/1.09 tff(1230,plain,
% 0.86/1.09 (^[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)) | c0_1(W) | (~c3_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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.86/1.09 inference(bind,[status(th)],[])).
% 0.86/1.09 tff(1231,plain,
% 0.86/1.09 (![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)) | c0_1(W) | (~c3_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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.86/1.09 inference(quant_intro,[status(thm)],[1230])).
% 0.86/1.09 tff(1232,plain,
% 0.86/1.09 (![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)) | c0_1(W) | (~c3_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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1233,plain,
% 0.86/1.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_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)) | (~c3_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)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_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) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_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) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.93/1.09 inference(bind,[status(th)],[])).
% 0.93/1.09 tff(1234,plain,
% 0.93/1.09 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/1.09 inference(quant_intro,[status(thm)],[1233])).
% 0.93/1.09 tff(1235,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 0.93/1.09 tff(1236,plain,
% 0.93/1.09 (![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 0.93/1.09 tff(1237,plain,
% 0.93/1.09 (![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[1236, 1232])).
% 0.93/1.09 tff(1238,plain,(
% 0.93/1.09 ![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/1.09 inference(skolemize,[status(sab)],[1237])).
% 0.93/1.09 tff(1239,plain,
% 0.93/1.09 (![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[1238, 1231])).
% 0.93/1.09 tff(1240,assumption,(~c1_1(a1781)), introduced(assumption)).
% 0.93/1.09 tff(1241,assumption,(c3_1(a1781)), introduced(assumption)).
% 0.93/1.09 tff(1242,assumption,(c2_1(a1781)), introduced(assumption)).
% 0.93/1.09 tff(1243,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1244,plain,
% 0.93/1.09 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1245,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[1244])).
% 0.93/1.09 tff(1246,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[1245, 1243])).
% 0.93/1.09 tff(1247,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(1248,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.93/1.09 tff(1249,plain,
% 0.93/1.09 (c1_1(a1799)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1248, 102, 1151, 1242, 1241, 368, 387, 1150, 1240, 367, 1051])).
% 0.93/1.09 tff(1250,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1251,plain,
% 0.93/1.09 ((hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799))) <=> (hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1252,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[1251])).
% 0.93/1.09 tff(1253,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[1252, 1250])).
% 0.93/1.09 tff(1254,plain,
% 0.93/1.09 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(1255,plain,
% 0.93/1.09 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 0.93/1.09 tff(1256,plain,
% 0.93/1.09 (hskp11 | (~c0_1(a1781))),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1255, 102, 1241, 1159, 1150, 1240, 860, 1249])).
% 0.93/1.09 tff(1257,plain,
% 0.93/1.09 (hskp11),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1256, 1229])).
% 0.93/1.09 tff(1258,plain,
% 0.93/1.09 (~c2_1(a1768)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1025, 1257])).
% 0.93/1.09 tff(1259,plain,
% 0.93/1.09 (c0_1(a1768)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1033, 1257])).
% 0.93/1.09 tff(1260,plain,
% 0.93/1.09 (((~![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))) <=> ((~![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1261,plain,
% 0.93/1.09 (((~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1262,plain,
% 0.93/1.09 (((~![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[1261])).
% 0.93/1.09 tff(1263,plain,
% 0.93/1.09 (((~![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[1262, 1260])).
% 0.93/1.09 tff(1264,plain,
% 0.93/1.09 ((~![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(1265,plain,
% 0.93/1.09 ((~![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)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 0.93/1.09 tff(1266,plain,
% 0.93/1.09 (c1_1(a1768)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1265, 102, 1242, 1241, 1259, 368, 387, 1258, 367, 1239, 1229])).
% 0.93/1.09 tff(1267,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1268,plain,
% 0.93/1.09 (((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799))) <=> (c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1269,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[1268])).
% 0.93/1.09 tff(1270,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[1269, 1267])).
% 0.93/1.09 tff(1271,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(1272,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 0.93/1.09 tff(1273,plain,
% 0.93/1.09 ($false),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1272, 102, 1151, 1242, 1259, 1159, 1240, 1258, 433, 1249, 1229, 1266])).
% 0.93/1.09 tff(1274,plain,((~c0_1(a1781)) | (~c3_1(a1799)) | (~c2_1(a1781)) | c0_1(a1799) | c1_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | c2_1(a1799)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.09 tff(1275,plain,
% 0.93/1.09 (~c0_1(a1781)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1274, 1147, 1228, 1148, 1227, 1226, 368, 387, 367, 1146])).
% 0.93/1.09 tff(1276,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1277,plain,
% 0.93/1.09 ((hskp8 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1278,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[1277])).
% 0.93/1.09 tff(1279,plain,
% 0.93/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[1278, 1276])).
% 0.93/1.09 tff(1280,plain,
% 0.93/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(1281,plain,
% 0.93/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 0.93/1.09 tff(1282,plain,
% 0.93/1.09 (hskp8 | c0_1(a1781)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1281, 102, 1226, 368, 387, 1227, 1193, 1207])).
% 0.93/1.09 tff(1283,plain,
% 0.93/1.09 (hskp8),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1282, 1275])).
% 0.93/1.09 tff(1284,plain,
% 0.93/1.09 (~c1_1(a1765)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[299, 1283])).
% 0.93/1.09 tff(1285,plain,
% 0.93/1.09 (c2_1(a1765)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[405, 1283])).
% 0.93/1.09 tff(1286,plain,
% 0.93/1.09 (c0_1(a1765)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[413, 1283])).
% 0.93/1.09 tff(1287,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1288,plain,
% 0.93/1.09 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781))) <=> (c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.09 inference(rewrite,[status(thm)],[])).
% 0.93/1.09 tff(1289,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781))))),
% 0.93/1.09 inference(monotonicity,[status(thm)],[1288])).
% 0.93/1.09 tff(1290,plain,
% 0.93/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.09 inference(transitivity,[status(thm)],[1289, 1287])).
% 0.93/1.09 tff(1291,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.09 inference(quant_inst,[status(thm)],[])).
% 0.93/1.09 tff(1292,plain,
% 0.93/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781))),
% 0.93/1.09 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.93/1.09 tff(1293,plain,
% 0.93/1.09 ($false),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1292, 102, 1226, 652, 662, 1286, 1285, 1227, 254, 1284, 46, 1275])).
% 0.93/1.09 tff(1294,plain,((~hskp22) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.09 tff(1295,plain,
% 0.93/1.09 (~hskp22),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1294, 1131, 1144, 1143, 1142, 1141, 1140])).
% 0.93/1.09 tff(1296,plain,
% 0.93/1.09 (hskp8 | hskp4),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[293, 102, 314, 313, 312, 121])).
% 0.93/1.09 tff(1297,plain,
% 0.93/1.09 (hskp8),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[1296, 315])).
% 0.93/1.09 tff(1298,plain,
% 0.93/1.09 (~c1_1(a1765)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[299, 1297])).
% 0.93/1.09 tff(1299,plain,
% 0.93/1.09 (c2_1(a1765)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[405, 1297])).
% 0.93/1.09 tff(1300,plain,
% 0.93/1.09 (c0_1(a1765)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[413, 1297])).
% 0.93/1.09 tff(1301,plain,
% 0.93/1.09 (c1_1(a1762)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[422, 102, 652, 662, 1300, 1299, 313, 254, 1298, 312, 46])).
% 0.93/1.09 tff(1302,plain,
% 0.93/1.09 (hskp21),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[696, 102, 652, 662, 1300, 1299, 254, 1298, 690])).
% 0.93/1.09 tff(1303,plain,
% 0.93/1.09 (~c3_1(a1788)),
% 0.93/1.09 inference(unit_resolution,[status(thm)],[702, 1302])).
% 0.93/1.09 tff(1304,plain,
% 0.93/1.09 (c2_1(a1788)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[710, 1302])).
% 0.93/1.10 tff(1305,plain,
% 0.93/1.10 (c0_1(a1788)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[718, 1302])).
% 0.93/1.10 tff(1306,plain,
% 0.93/1.10 (~c1_1(a1788)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[725, 102, 1305, 1304, 314, 313, 1303, 618, 1301])).
% 0.93/1.10 tff(1307,plain,
% 0.93/1.10 (hskp22),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[488, 315, 311, 12, 35])).
% 0.93/1.10 tff(1308,plain,
% 0.93/1.10 (~c2_1(a1799)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[494, 1307])).
% 0.93/1.10 tff(1309,plain,
% 0.93/1.10 (~c0_1(a1799)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[500, 1307])).
% 0.93/1.10 tff(1310,plain,
% 0.93/1.10 (c3_1(a1799)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[508, 1307])).
% 0.93/1.10 tff(1311,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1312,plain,
% 0.93/1.10 ((hskp10 | (~ndr1_0) | c3_1(a1788) | c1_1(a1788) | (~c0_1(a1788)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799))) <=> (hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1313,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1788) | c1_1(a1788) | (~c0_1(a1788)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[1312])).
% 0.93/1.10 tff(1314,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1788) | c1_1(a1788) | (~c0_1(a1788)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[1313, 1311])).
% 0.93/1.10 tff(1315,plain,
% 0.93/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1788) | c1_1(a1788) | (~c0_1(a1788)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(1316,plain,
% 0.93/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 0.93/1.10 tff(1317,plain,
% 0.93/1.10 (hskp10),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1316, 102, 1310, 1305, 1309, 1308, 1303, 310, 1306])).
% 0.93/1.10 tff(1318,plain,
% 0.93/1.10 (~c1_1(a1767)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[521, 1317])).
% 0.93/1.10 tff(1319,plain,
% 0.93/1.10 (~c0_1(a1767)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[527, 1317])).
% 0.93/1.10 tff(1320,plain,
% 0.93/1.10 (c3_1(a1767)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[537, 1317])).
% 0.93/1.10 tff(1321,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1322,plain,
% 0.93/1.10 (((~ndr1_0) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767))) <=> (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1323,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[1322])).
% 0.93/1.10 tff(1324,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[1323, 1321])).
% 0.93/1.10 tff(1325,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(1326,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 0.93/1.10 tff(1327,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1326, 102, 1305, 1304, 652, 662, 1320, 254, 1319, 1318, 46, 1306])).
% 0.93/1.10 tff(1328,plain,(hskp4 | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~hskp6) | hskp19 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(1329,plain,
% 0.93/1.10 (hskp4),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1328, 35, 1144, 1143, 1139, 12, 1131])).
% 0.93/1.10 tff(1330,plain,
% 0.93/1.10 (~c2_1(a1759)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[881, 1329])).
% 0.93/1.10 tff(1331,assumption,(~c0_1(a1759)), introduced(assumption)).
% 0.93/1.10 tff(1332,plain,
% 0.93/1.10 (hskp7),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[990, 102, 387, 869, 367, 36, 983, 1331, 1149])).
% 0.93/1.10 tff(1333,plain,
% 0.93/1.10 (~c1_1(a1763)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[996, 1332])).
% 0.93/1.10 tff(1334,plain,
% 0.93/1.10 (c3_1(a1771)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1182, 1333, 662, 368, 387, 254, 1149, 1332])).
% 0.93/1.10 tff(1335,plain,
% 0.93/1.10 (hskp8),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1200, 1334])).
% 0.93/1.10 tff(1336,plain,
% 0.93/1.10 (~c1_1(a1765)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[299, 1335])).
% 0.93/1.10 tff(1337,plain,
% 0.93/1.10 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1338,plain,
% 0.93/1.10 ((hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771))) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1339,plain,
% 0.93/1.10 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[1338])).
% 0.93/1.10 tff(1340,plain,
% 0.93/1.10 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[1339, 1337])).
% 0.93/1.10 tff(1341,plain,
% 0.93/1.10 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(1342,plain,
% 0.93/1.10 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.93/1.10 tff(1343,plain,
% 0.93/1.10 (hskp22 | hskp16 | (~c3_1(a1771))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1342, 102, 652, 662, 443])).
% 0.93/1.10 tff(1344,plain,
% 0.93/1.10 (hskp16),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1343, 1334, 328])).
% 0.93/1.10 tff(1345,plain,
% 0.93/1.10 (~c2_1(a1780)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[456, 1344])).
% 0.93/1.10 tff(1346,plain,
% 0.93/1.10 (c2_1(a1765)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[405, 1335])).
% 0.93/1.10 tff(1347,plain,
% 0.93/1.10 (c0_1(a1765)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[413, 1335])).
% 0.93/1.10 tff(1348,plain,
% 0.93/1.10 (c1_1(a1780)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[464, 1344])).
% 0.93/1.10 tff(1349,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1350,plain,
% 0.93/1.10 (((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771))) <=> (c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1351,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[1350])).
% 0.93/1.10 tff(1352,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[1351, 1349])).
% 0.93/1.10 tff(1353,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(1354,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 0.93/1.10 tff(1355,plain,
% 0.93/1.10 (~c0_1(a1780)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1354, 102, 1348, 652, 1347, 1346, 1345, 254, 1336, 433, 1334])).
% 0.93/1.10 tff(1356,plain,
% 0.93/1.10 (c3_1(a1780)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[479, 1344])).
% 0.93/1.10 tff(1357,plain,
% 0.93/1.10 (hskp27 | hskp22),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[334, 102, 368, 387, 367, 327])).
% 0.93/1.10 tff(1358,plain,
% 0.93/1.10 (hskp27),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1357, 328])).
% 0.93/1.10 tff(1359,plain,
% 0.93/1.10 (c3_1(a1756)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[342, 1358])).
% 0.93/1.10 tff(1360,plain,
% 0.93/1.10 (c1_1(a1756)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[350, 1358])).
% 0.93/1.10 tff(1361,plain,
% 0.93/1.10 (c0_1(a1756)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[358, 1358])).
% 0.93/1.10 tff(1362,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[486, 102, 35, 1361, 1360, 1359, 1356, 1345, 11, 1355])).
% 0.93/1.10 tff(1363,plain,(c1_1(a1762) | hskp3 | (~c1_1(a1771)) | c0_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1762)) | c0_1(a1762) | hskp22 | (~c2_1(a1762)) | (~c1_1(a1759)) | c2_1(a1759) | c0_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(1364,plain,
% 0.93/1.10 (c1_1(a1762)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1363, 328, 652, 254, 662, 387, 367, 35, 368, 869, 36, 1331])).
% 0.93/1.10 tff(1365,plain,
% 0.93/1.10 (hskp22 | hskp16 | (~c1_1(a1762))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[449, 102, 368, 387, 443])).
% 0.93/1.10 tff(1366,plain,
% 0.93/1.10 (hskp16),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1365, 1364, 328])).
% 0.93/1.10 tff(1367,plain,
% 0.93/1.10 (~c2_1(a1780)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[456, 1366])).
% 0.93/1.10 tff(1368,plain,
% 0.93/1.10 (c3_1(a1780)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[479, 1366])).
% 0.93/1.10 tff(1369,plain,
% 0.93/1.10 (c0_1(a1780)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[486, 102, 35, 1361, 1360, 1359, 1368, 1367, 11])).
% 0.93/1.10 tff(1370,plain,
% 0.93/1.10 (hskp17),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1224, 1364])).
% 0.93/1.10 tff(1371,plain,
% 0.93/1.10 (~c1_1(a1781)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1073, 1370])).
% 0.93/1.10 tff(1372,plain,
% 0.93/1.10 (c1_1(a1780)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[464, 1366])).
% 0.93/1.10 tff(1373,plain,
% 0.93/1.10 (c2_1(a1781)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1097, 1370])).
% 0.93/1.10 tff(1374,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1375,plain,
% 0.93/1.10 (((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762))) <=> (c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1376,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[1375])).
% 0.93/1.10 tff(1377,plain,
% 0.93/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[1376, 1374])).
% 0.93/1.10 tff(1378,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(1379,plain,
% 0.93/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.93/1.10 tff(1380,plain,
% 0.93/1.10 ((~c0_1(a1780)) | (~c0_1(a1781))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1379, 102, 1373, 1372, 387, 1371, 1367, 367, 433, 1364])).
% 0.93/1.10 tff(1381,plain,
% 0.93/1.10 (~c0_1(a1781)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1380, 1369])).
% 0.93/1.10 tff(1382,plain,
% 0.93/1.10 (c3_1(a1781)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1089, 1370])).
% 0.93/1.10 tff(1383,plain,
% 0.93/1.10 (hskp8 | c0_1(a1781)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1281, 102, 1382, 368, 387, 1371, 1193, 1364])).
% 0.93/1.10 tff(1384,plain,
% 0.93/1.10 (hskp8),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1383, 1381])).
% 0.93/1.10 tff(1385,plain,
% 0.93/1.10 (~c1_1(a1765)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[299, 1384])).
% 0.93/1.10 tff(1386,plain,
% 0.93/1.10 (c2_1(a1765)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[405, 1384])).
% 0.93/1.10 tff(1387,plain,
% 0.93/1.10 (c0_1(a1765)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[413, 1384])).
% 0.93/1.10 tff(1388,plain,
% 0.93/1.10 ($false),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1292, 102, 1382, 652, 662, 1387, 1386, 1371, 254, 1385, 46, 1381])).
% 0.93/1.10 tff(1389,plain,(hskp22 | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | hskp3 | (~c1_1(a1759)) | c2_1(a1759) | c0_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.10 tff(1390,plain,
% 0.93/1.10 (c0_1(a1759)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1389, 1330, 1144, 1143, 1142, 1141, 1140, 1295, 842, 35, 1131])).
% 0.93/1.10 tff(1391,plain,
% 0.93/1.10 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.93/1.10 inference(bind,[status(th)],[])).
% 0.93/1.10 tff(1392,plain,
% 0.93/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[1391])).
% 0.93/1.10 tff(1393,plain,
% 0.93/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1394,plain,
% 0.93/1.10 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.93/1.10 inference(bind,[status(th)],[])).
% 0.93/1.10 tff(1395,plain,
% 0.93/1.10 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.93/1.10 inference(quant_intro,[status(thm)],[1394])).
% 0.93/1.10 tff(1396,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.93/1.10 tff(1397,plain,
% 0.93/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 0.93/1.10 tff(1398,plain,
% 0.93/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[1397, 1393])).
% 0.93/1.10 tff(1399,plain,(
% 0.93/1.10 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.93/1.10 inference(skolemize,[status(sab)],[1398])).
% 0.93/1.10 tff(1400,plain,
% 0.93/1.10 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[1399, 1392])).
% 0.93/1.10 tff(1401,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1402,plain,
% 0.93/1.10 ((hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762))) <=> (hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1403,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762))))),
% 0.93/1.10 inference(monotonicity,[status(thm)],[1402])).
% 0.93/1.10 tff(1404,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 0.93/1.10 inference(transitivity,[status(thm)],[1403, 1401])).
% 0.93/1.10 tff(1405,plain,
% 0.93/1.10 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 0.93/1.10 inference(quant_inst,[status(thm)],[])).
% 0.93/1.10 tff(1406,plain,
% 0.93/1.10 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762))),
% 0.93/1.10 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 0.93/1.10 tff(1407,plain,
% 0.93/1.10 (hskp3 | (~c0_1(a1759)) | (~c1_1(a1762))),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1406, 102, 1141, 842, 1140, 34, 1400])).
% 0.93/1.10 tff(1408,plain,
% 0.93/1.10 (~c1_1(a1762)),
% 0.93/1.10 inference(unit_resolution,[status(thm)],[1407, 1390, 35])).
% 0.93/1.10 tff(1409,plain,
% 0.93/1.10 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.10 tff(1410,plain,
% 0.93/1.10 ((hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771))) <=> (hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 0.93/1.10 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1411,plain,
% 0.93/1.11 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[1410])).
% 0.93/1.11 tff(1412,plain,
% 0.93/1.11 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[1411, 1409])).
% 0.93/1.11 tff(1413,plain,
% 0.93/1.11 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(1414,plain,
% 0.93/1.11 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 0.93/1.11 tff(1415,plain,
% 0.93/1.11 (hskp3 | (~c0_1(a1759)) | (~c3_1(a1771))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1414, 102, 1131, 842, 1143, 34, 1400])).
% 0.93/1.11 tff(1416,plain,
% 0.93/1.11 (~c3_1(a1771)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1415, 1390, 35])).
% 0.93/1.11 tff(1417,plain,
% 0.93/1.11 (^[U: $i] : refl((hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(1418,plain,
% 0.93/1.11 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[1417])).
% 0.93/1.11 tff(1419,plain,
% 0.93/1.11 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1420,plain,
% 0.93/1.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp25) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp25))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp25) <=> (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp25) <=> (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(1421,plain,
% 0.93/1.11 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp25) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[1420])).
% 0.93/1.11 tff(1422,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 0.93/1.11 tff(1423,plain,
% 0.93/1.11 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 0.93/1.11 tff(1424,plain,
% 0.93/1.11 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1423, 1419])).
% 0.93/1.11 tff(1425,plain,(
% 0.93/1.11 ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(skolemize,[status(sab)],[1424])).
% 0.93/1.11 tff(1426,plain,
% 0.93/1.11 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1425, 1418])).
% 0.93/1.11 tff(1427,plain,
% 0.93/1.11 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1428,plain,
% 0.93/1.11 ((hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1429,plain,
% 0.93/1.11 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[1428])).
% 0.93/1.11 tff(1430,plain,
% 0.93/1.11 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[1429, 1427])).
% 0.93/1.11 tff(1431,plain,
% 0.93/1.11 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(1432,plain,
% 0.93/1.11 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 0.93/1.11 tff(1433,plain,
% 0.93/1.11 (hskp25 | hskp3 | c3_1(a1771)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1432, 102, 1131, 1144, 1426])).
% 0.93/1.11 tff(1434,plain,
% 0.93/1.11 (hskp25),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1433, 1416, 35])).
% 0.93/1.11 tff(1435,plain,
% 0.93/1.11 (~c2_1(a1827)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[208, 1434])).
% 0.93/1.11 tff(1436,plain,
% 0.93/1.11 (~c1_1(a1827)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[153, 1434])).
% 0.93/1.11 tff(1437,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1438,plain,
% 0.93/1.11 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1827) | c1_1(a1827) | (~c3_1(a1827)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1439,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1827) | c1_1(a1827) | (~c3_1(a1827)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[1438])).
% 0.93/1.11 tff(1440,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1827) | c1_1(a1827) | (~c3_1(a1827)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[1439, 1437])).
% 0.93/1.11 tff(1441,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1827) | c1_1(a1827) | (~c3_1(a1827)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(1442,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 0.93/1.11 tff(1443,plain,
% 0.93/1.11 (~c3_1(a1827)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1442, 102, 1142, 1141, 1436, 1435, 1140, 1051, 1408])).
% 0.93/1.11 tff(1444,plain,
% 0.93/1.11 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(1445,plain,
% 0.93/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[1444])).
% 0.93/1.11 tff(1446,plain,
% 0.93/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1447,plain,
% 0.93/1.11 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(1448,plain,
% 0.93/1.11 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[1447])).
% 0.93/1.11 tff(1449,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 0.93/1.11 tff(1450,plain,
% 0.93/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 0.93/1.11 tff(1451,plain,
% 0.93/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1450, 1446])).
% 0.93/1.11 tff(1452,plain,(
% 0.93/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.93/1.11 inference(skolemize,[status(sab)],[1451])).
% 0.93/1.11 tff(1453,plain,
% 0.93/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1452, 1445])).
% 0.93/1.11 tff(1454,plain,
% 0.93/1.11 (~c0_1(a1827)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[159, 1434])).
% 0.93/1.11 tff(1455,plain,
% 0.93/1.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1456,plain,
% 0.93/1.11 ((hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1771))) <=> (hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1457,plain,
% 0.93/1.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[1456])).
% 0.93/1.11 tff(1458,plain,
% 0.93/1.11 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[1457, 1455])).
% 0.93/1.11 tff(1459,plain,
% 0.93/1.11 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1771)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(1460,plain,
% 0.93/1.11 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 0.93/1.11 tff(1461,plain,
% 0.93/1.11 (hskp17),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1460, 102, 1131, 1142, 1141, 1143, 1061, 1408, 1416])).
% 0.93/1.11 tff(1462,plain,
% 0.93/1.11 (c3_1(a1781)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1089, 1461])).
% 0.93/1.11 tff(1463,plain,
% 0.93/1.11 (~c1_1(a1781)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1073, 1461])).
% 0.93/1.11 tff(1464,plain,
% 0.93/1.11 (c2_1(a1781)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1097, 1461])).
% 0.93/1.11 tff(1465,assumption,(c0_1(a1759)), introduced(assumption)).
% 0.93/1.11 tff(1466,assumption,(hskp29), introduced(assumption)).
% 0.93/1.11 tff(1467,plain,
% 0.93/1.11 (c3_1(a1805)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[907, 1466])).
% 0.93/1.11 tff(1468,plain,
% 0.93/1.11 (c2_1(a1805)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[924, 1466])).
% 0.93/1.11 tff(1469,plain,
% 0.93/1.11 (c0_1(a1805)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[916, 1466])).
% 0.93/1.11 tff(1470,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1471,plain,
% 0.93/1.11 (((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759))) <=> (c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1472,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[1471])).
% 0.93/1.11 tff(1473,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[1472, 1470])).
% 0.93/1.11 tff(1474,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(1475,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 0.93/1.11 tff(1476,plain,
% 0.93/1.11 (~c1_1(a1805)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1475, 226, 1469, 1468, 1467, 869, 34, 618, 1465])).
% 0.93/1.11 tff(1477,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1478,plain,
% 0.93/1.11 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771))) <=> (c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1479,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[1478])).
% 0.93/1.11 tff(1480,plain,
% 0.93/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[1479, 1477])).
% 0.93/1.11 tff(1481,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(1482,plain,
% 0.93/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 0.93/1.11 tff(1483,plain,
% 0.93/1.11 ($false),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1482, 226, 1469, 1467, 1242, 1241, 662, 1240, 254, 753, 1171, 1476])).
% 0.93/1.11 tff(1484,plain,((~hskp29) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1771)) | c1_1(a1781) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1759)) | c3_1(a1759) | (~c0_1(a1759))), inference(lemma,lemma(discharge,[]))).
% 0.93/1.11 tff(1485,plain,
% 0.93/1.11 ((~hskp29) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1771)) | c1_1(a1781) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1759)) | c3_1(a1759) | (~c0_1(a1759))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1484, 102])).
% 0.93/1.11 tff(1486,plain,
% 0.93/1.11 (~hskp29),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1485, 1464, 1390, 1416, 1144, 1463, 1143, 1462, 842, 34])).
% 0.93/1.11 tff(1487,plain,
% 0.93/1.11 (^[U: $i] : refl((hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(1488,plain,
% 0.93/1.11 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[1487])).
% 0.93/1.11 tff(1489,plain,
% 0.93/1.11 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1490,plain,
% 0.93/1.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp30) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp30))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp30) <=> (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp30) <=> (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(1491,plain,
% 0.93/1.11 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp30) <=> ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[1490])).
% 0.93/1.11 tff(1492,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.93/1.11 tff(1493,plain,
% 0.93/1.11 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.93/1.11 tff(1494,plain,
% 0.93/1.11 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1493, 1489])).
% 0.93/1.11 tff(1495,plain,(
% 0.93/1.11 ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(skolemize,[status(sab)],[1494])).
% 0.93/1.11 tff(1496,plain,
% 0.93/1.11 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1495, 1488])).
% 0.93/1.11 tff(1497,plain,
% 0.93/1.11 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1498,plain,
% 0.93/1.11 ((hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(1499,plain,
% 0.93/1.11 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[1498])).
% 0.93/1.11 tff(1500,plain,
% 0.93/1.11 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[1499, 1497])).
% 0.93/1.11 tff(1501,plain,
% 0.93/1.11 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(1502,plain,
% 0.93/1.11 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 0.93/1.11 tff(1503,plain,
% 0.93/1.11 (hskp30 | hskp29 | c3_1(a1771)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1502, 102, 1131, 1144, 1496])).
% 0.93/1.11 tff(1504,plain,
% 0.93/1.11 (hskp30),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[1503, 1486, 1416])).
% 0.93/1.11 tff(1505,plain,
% 0.93/1.11 (((~hskp30) | c3_1(a1823)) <=> ((~hskp30) | c3_1(a1823))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1506,axiom,((~hskp30) | c3_1(a1823)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.93/1.12 tff(1507,plain,
% 0.93/1.12 ((~hskp30) | c3_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 0.93/1.12 tff(1508,plain,
% 0.93/1.12 ((~hskp30) | c3_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1507, 1505])).
% 0.93/1.12 tff(1509,plain,
% 0.93/1.12 ((~hskp30) | c3_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1508, 1505])).
% 0.93/1.12 tff(1510,plain,
% 0.93/1.12 ((~hskp30) | c3_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1509, 1505])).
% 0.93/1.12 tff(1511,plain,
% 0.93/1.12 ((~hskp30) | c3_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1510, 1505])).
% 0.93/1.12 tff(1512,plain,
% 0.93/1.12 (c3_1(a1823)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1511, 1504])).
% 0.93/1.12 tff(1513,plain,
% 0.93/1.12 (((~hskp30) | c2_1(a1823)) <=> ((~hskp30) | c2_1(a1823))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1514,axiom,((~hskp30) | c2_1(a1823)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.93/1.12 tff(1515,plain,
% 0.93/1.12 ((~hskp30) | c2_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 0.93/1.12 tff(1516,plain,
% 0.93/1.12 ((~hskp30) | c2_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1515, 1513])).
% 0.93/1.12 tff(1517,plain,
% 0.93/1.12 ((~hskp30) | c2_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1516, 1513])).
% 0.93/1.12 tff(1518,plain,
% 0.93/1.12 ((~hskp30) | c2_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1517, 1513])).
% 0.93/1.12 tff(1519,plain,
% 0.93/1.12 ((~hskp30) | c2_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1518, 1513])).
% 0.93/1.12 tff(1520,plain,
% 0.93/1.12 (c2_1(a1823)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1519, 1504])).
% 0.93/1.12 tff(1521,plain,
% 0.93/1.12 (((~hskp30) | c1_1(a1823)) <=> ((~hskp30) | c1_1(a1823))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1522,axiom,((~hskp30) | c1_1(a1823)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.93/1.12 tff(1523,plain,
% 0.93/1.12 ((~hskp30) | c1_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 0.93/1.12 tff(1524,plain,
% 0.93/1.12 ((~hskp30) | c1_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1523, 1521])).
% 0.93/1.12 tff(1525,plain,
% 0.93/1.12 ((~hskp30) | c1_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1524, 1521])).
% 0.93/1.12 tff(1526,plain,
% 0.93/1.12 ((~hskp30) | c1_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1525, 1521])).
% 0.93/1.12 tff(1527,plain,
% 0.93/1.12 ((~hskp30) | c1_1(a1823)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1526, 1521])).
% 0.93/1.12 tff(1528,plain,
% 0.93/1.12 (c1_1(a1823)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1527, 1504])).
% 0.93/1.12 tff(1529,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1530,plain,
% 0.93/1.12 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1827) | c1_1(a1827) | c3_1(a1827) | c3_1(a1827) | c2_1(a1827) | c0_1(a1827)) <=> (c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1531,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1827) | c1_1(a1827) | c3_1(a1827) | c3_1(a1827) | c2_1(a1827) | c0_1(a1827))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[1530])).
% 0.93/1.12 tff(1532,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1827) | c1_1(a1827) | c3_1(a1827) | c3_1(a1827) | c2_1(a1827) | c0_1(a1827))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 0.93/1.12 inference(transitivity,[status(thm)],[1531, 1529])).
% 0.93/1.12 tff(1533,plain,
% 0.93/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1827) | c1_1(a1827) | c3_1(a1827) | c3_1(a1827) | c2_1(a1827) | c0_1(a1827))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(1534,plain,
% 0.93/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 0.93/1.12 tff(1535,plain,
% 0.93/1.12 ($false),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1534, 102, 1528, 1520, 1512, 1454, 1436, 1435, 1453, 1443])).
% 0.93/1.12 tff(1536,plain,(hskp3 | c3_1(a1759) | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.93/1.12 tff(1537,plain,
% 0.93/1.12 (hskp3),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1536, 34, 12])).
% 0.93/1.12 tff(1538,plain,
% 0.93/1.12 (c1_1(a1758)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[564, 1537])).
% 0.93/1.12 tff(1539,plain,
% 0.93/1.12 (~c3_1(a1758)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[578, 1537])).
% 0.93/1.12 tff(1540,plain,
% 0.93/1.12 (c2_1(a1758)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[556, 1537])).
% 0.93/1.12 tff(1541,plain,
% 0.93/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(1542,plain,
% 0.93/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[1541])).
% 0.93/1.12 tff(1543,plain,
% 0.93/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1544,plain,
% 0.93/1.12 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~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))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~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))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_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)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 0.93/1.12 inference(bind,[status(th)],[])).
% 0.93/1.12 tff(1545,plain,
% 0.93/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_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)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.93/1.12 inference(quant_intro,[status(thm)],[1544])).
% 0.93/1.12 tff(1546,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 0.93/1.12 tff(1547,plain,
% 0.93/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1546, 1545])).
% 0.93/1.12 tff(1548,plain,
% 0.93/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1547, 1543])).
% 0.93/1.12 tff(1549,plain,(
% 0.93/1.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.93/1.12 inference(skolemize,[status(sab)],[1548])).
% 0.93/1.12 tff(1550,plain,
% 0.93/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1549, 1542])).
% 0.93/1.12 tff(1551,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1552,plain,
% 0.93/1.12 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762))) <=> (c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1553,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762)))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[1552])).
% 0.93/1.12 tff(1554,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762))),
% 0.93/1.12 inference(transitivity,[status(thm)],[1553, 1551])).
% 0.93/1.12 tff(1555,plain,
% 0.93/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(1556,plain,
% 0.93/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 0.93/1.12 tff(1557,plain,
% 0.93/1.12 ((~c0_1(a1758)) | c1_1(a1762)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1556, 102, 387, 643, 661, 367, 642, 1550])).
% 0.93/1.12 tff(1558,plain,
% 0.93/1.12 (~c0_1(a1758)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1557, 1149])).
% 0.93/1.12 tff(1559,plain,
% 0.93/1.12 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1560,plain,
% 0.93/1.12 ((hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758))) <=> (hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1561,plain,
% 0.93/1.12 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762)))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[1560])).
% 0.93/1.12 tff(1562,plain,
% 0.93/1.12 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 0.93/1.12 inference(transitivity,[status(thm)],[1561, 1559])).
% 0.93/1.12 tff(1563,plain,
% 0.93/1.12 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(1564,plain,
% 0.93/1.12 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762)),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 0.93/1.12 tff(1565,plain,
% 0.93/1.12 (hskp17),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1564, 102, 368, 387, 643, 642, 1061, 1149, 1558])).
% 0.93/1.12 tff(1566,plain,
% 0.93/1.12 (~c1_1(a1781)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1073, 1565])).
% 0.93/1.12 tff(1567,plain,
% 0.93/1.12 (c3_1(a1781)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1089, 1565])).
% 0.93/1.12 tff(1568,plain,
% 0.93/1.12 (c2_1(a1781)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1097, 1565])).
% 0.93/1.12 tff(1569,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1570,plain,
% 0.93/1.12 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758))) <=> (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1571,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781))))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[1570])).
% 0.93/1.12 tff(1572,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 0.93/1.12 inference(transitivity,[status(thm)],[1571, 1569])).
% 0.93/1.12 tff(1573,plain,
% 0.93/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(1574,plain,
% 0.93/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 0.93/1.12 tff(1575,plain,
% 0.93/1.12 (~c0_1(a1781)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1574, 102, 1568, 1567, 661, 1566, 642, 753, 1558])).
% 0.93/1.12 tff(1576,assumption,(hskp8), introduced(assumption)).
% 0.93/1.12 tff(1577,plain,
% 0.93/1.12 (~c1_1(a1765)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[299, 1576])).
% 0.93/1.12 tff(1578,plain,
% 0.93/1.12 (c2_1(a1765)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[405, 1576])).
% 0.93/1.12 tff(1579,plain,
% 0.93/1.12 (c0_1(a1765)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[413, 1576])).
% 0.93/1.12 tff(1580,plain,
% 0.93/1.12 ($false),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[422, 102, 652, 662, 1579, 1578, 387, 254, 1577, 367, 46, 1149])).
% 0.93/1.12 tff(1581,plain,((~hskp8) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1762)) | c0_1(a1771) | c0_1(a1762) | c1_1(a1762)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.12 tff(1582,plain,
% 0.93/1.12 (~hskp8),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1581, 1149, 662, 387, 254, 367, 652])).
% 0.93/1.12 tff(1583,plain,
% 0.93/1.12 (~c3_1(a1771)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1200, 1582])).
% 0.93/1.12 tff(1584,plain,
% 0.93/1.12 (~c1_1(a1763)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[996, 1168])).
% 0.93/1.12 tff(1585,plain,
% 0.93/1.12 ($false),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1182, 1584, 1168, 662, 368, 387, 254, 1171, 1149])).
% 0.93/1.12 tff(1586,plain,((~hskp7) | (~c2_1(a1771)) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | c1_1(a1762)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.12 tff(1587,plain,
% 0.93/1.12 (~hskp7),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1586, 1583, 368, 387, 254, 662, 1149])).
% 0.93/1.12 tff(1588,plain,
% 0.93/1.12 (hskp8 | hskp4),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[293, 102, 368, 387, 367, 121])).
% 0.93/1.12 tff(1589,plain,
% 0.93/1.12 (hskp4),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1588, 1582])).
% 0.93/1.12 tff(1590,plain,
% 0.93/1.12 (~c2_1(a1759)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[881, 1589])).
% 0.93/1.12 tff(1591,plain,
% 0.93/1.12 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1592,plain,
% 0.93/1.12 ((hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1593,plain,
% 0.93/1.12 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781))))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[1592])).
% 0.93/1.12 tff(1594,plain,
% 0.93/1.12 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.12 inference(transitivity,[status(thm)],[1593, 1591])).
% 0.93/1.12 tff(1595,plain,
% 0.93/1.12 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(1596,plain,
% 0.93/1.12 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 0.93/1.12 tff(1597,plain,
% 0.93/1.12 (hskp7 | c0_1(a1759)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1596, 102, 1567, 869, 1566, 1590, 983, 1575])).
% 0.93/1.12 tff(1598,plain,
% 0.93/1.12 (c0_1(a1759)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1597, 1587])).
% 0.93/1.12 tff(1599,plain,
% 0.93/1.12 (~hskp29),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1485, 1598, 1568, 1583, 662, 1566, 254, 1567, 869, 34])).
% 0.93/1.12 tff(1600,plain,
% 0.93/1.12 (hskp30 | hskp29 | c3_1(a1771)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1502, 102, 652, 662, 1496])).
% 0.93/1.12 tff(1601,plain,
% 0.93/1.12 (hskp30),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1600, 1599, 1583])).
% 0.93/1.12 tff(1602,plain,
% 0.93/1.12 (c3_1(a1823)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1511, 1601])).
% 0.93/1.12 tff(1603,plain,
% 0.93/1.12 (c2_1(a1823)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1519, 1601])).
% 0.93/1.12 tff(1604,plain,
% 0.93/1.12 (c1_1(a1823)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1527, 1601])).
% 0.93/1.12 tff(1605,plain,
% 0.93/1.12 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1606,plain,
% 0.93/1.12 ((hskp8 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1607,plain,
% 0.93/1.12 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[1606])).
% 0.93/1.12 tff(1608,plain,
% 0.93/1.12 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 0.93/1.12 inference(transitivity,[status(thm)],[1607, 1605])).
% 0.93/1.12 tff(1609,plain,
% 0.93/1.12 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.12 inference(quant_inst,[status(thm)],[])).
% 0.93/1.12 tff(1610,plain,
% 0.93/1.12 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 0.93/1.12 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 0.93/1.12 tff(1611,plain,
% 0.93/1.12 ($false),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1610, 102, 1582, 1604, 1603, 1602, 1567, 1566, 1193, 1575])).
% 0.93/1.12 tff(1612,plain,(c1_1(a1762) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~c1_1(a1759)) | c3_1(a1759) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c2_1(a1758)) | c3_1(a1758) | (~c1_1(a1758))), inference(lemma,lemma(discharge,[]))).
% 0.93/1.12 tff(1613,plain,
% 0.93/1.12 (c1_1(a1762)),
% 0.93/1.12 inference(unit_resolution,[status(thm)],[1612, 1131, 1144, 1143, 842, 34, 1142, 1141, 1140, 1540, 1539, 1538])).
% 0.93/1.12 tff(1614,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1615,plain,
% 0.93/1.12 (((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758))) <=> (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.93/1.12 inference(rewrite,[status(thm)],[])).
% 0.93/1.12 tff(1616,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))))),
% 0.93/1.12 inference(monotonicity,[status(thm)],[1615])).
% 0.93/1.12 tff(1617,plain,
% 0.93/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 0.93/1.12 inference(transitivity,[status(thm)],[1616, 1614])).
% 0.93/1.12 tff(1618,plain,
% 0.93/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(1619,plain,
% 0.93/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 0.93/1.13 tff(1620,plain,
% 0.93/1.13 ((~c0_1(a1758)) | (~c1_1(a1762))),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1619, 102, 1142, 1141, 1538, 1540, 1539, 618])).
% 0.93/1.13 tff(1621,plain,
% 0.93/1.13 (~c0_1(a1758)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1620, 1613])).
% 0.93/1.13 tff(1622,plain,
% 0.93/1.13 (hskp17 | (~c1_1(a1762))),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1223, 102, 1142, 1141, 1140, 1217])).
% 0.93/1.13 tff(1623,plain,
% 0.93/1.13 (hskp17),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1622, 1613])).
% 0.93/1.13 tff(1624,plain,
% 0.93/1.13 (~c1_1(a1781)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1073, 1623])).
% 0.93/1.13 tff(1625,plain,
% 0.93/1.13 (c3_1(a1781)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1089, 1623])).
% 0.93/1.13 tff(1626,plain,
% 0.93/1.13 (c2_1(a1781)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1097, 1623])).
% 0.93/1.13 tff(1627,plain,
% 0.93/1.13 (~c0_1(a1781)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1574, 102, 1626, 1625, 1540, 1624, 1539, 753, 1621])).
% 0.93/1.13 tff(1628,plain,
% 0.93/1.13 (hskp8),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1281, 102, 1625, 1142, 1141, 1624, 1193, 1613, 1627])).
% 0.93/1.13 tff(1629,plain,
% 0.93/1.13 (~c1_1(a1765)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[299, 1628])).
% 0.93/1.13 tff(1630,plain,
% 0.93/1.13 (c2_1(a1765)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[405, 1628])).
% 0.93/1.13 tff(1631,plain,
% 0.93/1.13 (c0_1(a1765)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[413, 1628])).
% 0.93/1.13 tff(1632,plain,
% 0.93/1.13 ($false),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1292, 102, 1625, 1131, 1144, 1631, 1630, 1624, 1143, 1629, 46, 1627])).
% 0.93/1.13 tff(1633,plain,(c3_1(a1759) | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.93/1.13 tff(1634,plain,
% 0.93/1.13 (c3_1(a1759)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1633, 12])).
% 0.93/1.13 tff(1635,plain,
% 0.93/1.13 (((~hskp4) | (~c3_1(a1759))) <=> ((~hskp4) | (~c3_1(a1759)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1636,plain,
% 0.93/1.13 (((~c3_1(a1759)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1759)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1637,axiom,((~c3_1(a1759)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.93/1.13 tff(1638,plain,
% 0.93/1.13 ((~hskp4) | (~c3_1(a1759))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 0.93/1.13 tff(1639,plain,
% 0.93/1.13 ((~hskp4) | (~c3_1(a1759))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1638, 1635])).
% 0.93/1.13 tff(1640,plain,
% 0.93/1.13 (~hskp4),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1639, 1634])).
% 0.93/1.13 tff(1641,plain,
% 0.93/1.13 (^[U: $i] : refl((hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(1642,plain,
% 0.93/1.13 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[1641])).
% 0.93/1.13 tff(1643,plain,
% 0.93/1.13 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1644,plain,
% 0.93/1.13 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp6) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp6) <=> (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(1645,plain,
% 0.93/1.13 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp6) <=> ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[1644])).
% 0.93/1.13 tff(1646,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.93/1.13 tff(1647,plain,
% 0.93/1.13 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 0.93/1.13 tff(1648,plain,
% 0.93/1.13 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1647, 1643])).
% 0.93/1.13 tff(1649,plain,(
% 0.93/1.13 ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.13 inference(skolemize,[status(sab)],[1648])).
% 0.93/1.13 tff(1650,plain,
% 0.93/1.13 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1649, 1642])).
% 0.93/1.13 tff(1651,assumption,(hskp0), introduced(assumption)).
% 0.93/1.13 tff(1652,plain,
% 0.93/1.13 (((~hskp0) | (~c1_1(a1754))) <=> ((~hskp0) | (~c1_1(a1754)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1653,plain,
% 0.93/1.13 (((~c1_1(a1754)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a1754)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1654,axiom,((~c1_1(a1754)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.93/1.13 tff(1655,plain,
% 0.93/1.13 ((~hskp0) | (~c1_1(a1754))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 0.93/1.13 tff(1656,plain,
% 0.93/1.13 ((~hskp0) | (~c1_1(a1754))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1655, 1652])).
% 0.93/1.13 tff(1657,plain,
% 0.93/1.13 (~c1_1(a1754)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1656, 1651])).
% 0.93/1.13 tff(1658,plain,
% 0.93/1.13 (((~hskp0) | (~c0_1(a1754))) <=> ((~hskp0) | (~c0_1(a1754)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1659,plain,
% 0.93/1.13 (((~c0_1(a1754)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1754)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1660,axiom,((~c0_1(a1754)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.93/1.13 tff(1661,plain,
% 0.93/1.13 ((~hskp0) | (~c0_1(a1754))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 0.93/1.13 tff(1662,plain,
% 0.93/1.13 ((~hskp0) | (~c0_1(a1754))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1661, 1658])).
% 0.93/1.13 tff(1663,plain,
% 0.93/1.13 (~c0_1(a1754)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1662, 1651])).
% 0.93/1.13 tff(1664,plain,
% 0.93/1.13 (((~hskp0) | c2_1(a1754)) <=> ((~hskp0) | c2_1(a1754))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1665,axiom,((~hskp0) | c2_1(a1754)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.93/1.13 tff(1666,plain,
% 0.93/1.13 ((~hskp0) | c2_1(a1754)),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 0.93/1.13 tff(1667,plain,
% 0.93/1.13 ((~hskp0) | c2_1(a1754)),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1666, 1664])).
% 0.93/1.13 tff(1668,plain,
% 0.93/1.13 ((~hskp0) | c2_1(a1754)),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1667, 1664])).
% 0.93/1.13 tff(1669,plain,
% 0.93/1.13 ((~hskp0) | c2_1(a1754)),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1668, 1664])).
% 0.93/1.13 tff(1670,plain,
% 0.93/1.13 ((~hskp0) | c2_1(a1754)),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1669, 1664])).
% 0.93/1.13 tff(1671,plain,
% 0.93/1.13 (c2_1(a1754)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1670, 1651])).
% 0.93/1.13 tff(1672,plain,
% 0.93/1.13 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1673,plain,
% 0.93/1.13 ((hskp6 | hskp4 | (~ndr1_0) | c1_1(a1754) | c0_1(a1754) | (~c2_1(a1754))) <=> (hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1674,plain,
% 0.93/1.13 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1754) | c0_1(a1754) | (~c2_1(a1754)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754))))),
% 0.93/1.13 inference(monotonicity,[status(thm)],[1673])).
% 0.93/1.13 tff(1675,plain,
% 0.93/1.13 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1754) | c0_1(a1754) | (~c2_1(a1754)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754)))),
% 0.93/1.13 inference(transitivity,[status(thm)],[1674, 1672])).
% 0.93/1.13 tff(1676,plain,
% 0.93/1.13 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1754) | c0_1(a1754) | (~c2_1(a1754)))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(1677,plain,
% 0.93/1.13 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 0.93/1.13 tff(1678,plain,
% 0.93/1.13 ($false),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1677, 102, 225, 315, 1671, 1663, 1657, 1650])).
% 0.93/1.13 tff(1679,plain,((~hskp0) | hskp6 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.93/1.13 tff(1680,plain,
% 0.93/1.13 (~hskp0),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1679, 225, 1640])).
% 0.93/1.13 tff(1681,plain,
% 0.93/1.13 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(1682,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[1681])).
% 0.93/1.13 tff(1683,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1684,plain,
% 0.93/1.13 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_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)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_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)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_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)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(1685,plain,
% 0.93/1.13 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[1684])).
% 0.93/1.13 tff(1686,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.93/1.13 tff(1687,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1686, 1685])).
% 0.93/1.13 tff(1688,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1687, 1683])).
% 0.93/1.13 tff(1689,plain,(
% 0.93/1.13 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.93/1.13 inference(skolemize,[status(sab)],[1688])).
% 0.93/1.13 tff(1690,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1689, 1682])).
% 0.93/1.13 tff(1691,plain,
% 0.93/1.13 (~hskp13),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1138, 225, 12])).
% 0.93/1.13 tff(1692,plain,
% 0.93/1.13 (~hskp2),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[110, 1691, 12])).
% 0.93/1.13 tff(1693,plain,
% 0.93/1.13 (hskp25),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[147, 1692, 1640])).
% 0.93/1.13 tff(1694,plain,
% 0.93/1.13 (~c2_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[208, 1693])).
% 0.93/1.13 tff(1695,plain,
% 0.93/1.13 (~c1_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[153, 1693])).
% 0.93/1.13 tff(1696,plain,
% 0.93/1.13 (~c0_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[159, 1693])).
% 0.93/1.13 tff(1697,plain,
% 0.93/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1698,plain,
% 0.93/1.13 ((hskp0 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1827) | c1_1(a1827) | c0_1(a1827)) <=> (hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1699,plain,
% 0.93/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827))))),
% 0.93/1.13 inference(monotonicity,[status(thm)],[1698])).
% 0.93/1.13 tff(1700,plain,
% 0.93/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827)))),
% 0.93/1.13 inference(transitivity,[status(thm)],[1699, 1697])).
% 0.93/1.13 tff(1701,plain,
% 0.93/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1827) | c1_1(a1827) | c0_1(a1827))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(1702,plain,
% 0.93/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1701, 1700])).
% 0.93/1.13 tff(1703,plain,
% 0.93/1.13 (hskp0 | (~c3_1(a1827))),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1702, 102, 1696, 1695, 1694, 1690])).
% 0.93/1.13 tff(1704,plain,
% 0.93/1.13 (~c3_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1703, 1680])).
% 0.93/1.13 tff(1705,plain,
% 0.93/1.13 (^[U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(1706,plain,
% 0.93/1.13 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[1705])).
% 0.93/1.13 tff(1707,plain,
% 0.93/1.13 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1708,plain,
% 0.93/1.13 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(1709,plain,
% 0.93/1.13 (![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[1708])).
% 0.93/1.13 tff(1710,axiom,(![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.93/1.13 tff(1711,plain,
% 0.93/1.13 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1710, 1709])).
% 0.93/1.13 tff(1712,plain,
% 0.93/1.13 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1711, 1707])).
% 0.93/1.13 tff(1713,plain,(
% 0.93/1.13 ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.93/1.13 inference(skolemize,[status(sab)],[1712])).
% 0.93/1.13 tff(1714,plain,
% 0.93/1.13 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1713, 1706])).
% 0.93/1.13 tff(1715,plain,
% 0.93/1.13 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1716,plain,
% 0.93/1.13 ((hskp11 | (~ndr1_0) | c3_1(a1827) | c2_1(a1827) | c1_1(a1827)) <=> (hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1717,plain,
% 0.93/1.13 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | (~ndr1_0) | c3_1(a1827) | c2_1(a1827) | c1_1(a1827))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827)))),
% 0.93/1.13 inference(monotonicity,[status(thm)],[1716])).
% 0.93/1.13 tff(1718,plain,
% 0.93/1.13 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | (~ndr1_0) | c3_1(a1827) | c2_1(a1827) | c1_1(a1827))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 0.93/1.13 inference(transitivity,[status(thm)],[1717, 1715])).
% 0.93/1.13 tff(1719,plain,
% 0.93/1.13 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | (~ndr1_0) | c3_1(a1827) | c2_1(a1827) | c1_1(a1827))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(1720,plain,
% 0.93/1.13 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827)),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 0.93/1.13 tff(1721,plain,
% 0.93/1.13 (hskp11 | c3_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1720, 102, 1695, 1694, 1714])).
% 0.93/1.13 tff(1722,plain,
% 0.93/1.13 (hskp11),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1721, 1704])).
% 0.93/1.13 tff(1723,plain,
% 0.93/1.13 (~c2_1(a1768)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1025, 1722])).
% 0.93/1.13 tff(1724,plain,
% 0.93/1.13 (c0_1(a1768)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1033, 1722])).
% 0.93/1.13 tff(1725,plain,
% 0.93/1.13 (~c1_1(a1768)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1040, 102, 12, 1691, 1724, 1723, 33])).
% 0.93/1.13 tff(1726,plain,
% 0.93/1.13 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(1727,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[1726])).
% 0.93/1.13 tff(1728,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1729,plain,
% 0.93/1.13 (^[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)) | (~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))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp0))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.93/1.13 inference(bind,[status(th)],[])).
% 0.93/1.13 tff(1730,plain,
% 0.93/1.13 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.93/1.13 inference(quant_intro,[status(thm)],[1729])).
% 0.93/1.13 tff(1731,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 0.93/1.13 tff(1732,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1731, 1730])).
% 0.93/1.13 tff(1733,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1732, 1728])).
% 0.93/1.13 tff(1734,plain,(
% 0.93/1.13 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.93/1.13 inference(skolemize,[status(sab)],[1733])).
% 0.93/1.13 tff(1735,plain,
% 0.93/1.13 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1734, 1727])).
% 0.93/1.13 tff(1736,plain,
% 0.93/1.13 (c3_1(a1768)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1081, 1722])).
% 0.93/1.13 tff(1737,plain,
% 0.93/1.13 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1738,plain,
% 0.93/1.13 ((hskp27 | hskp2 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827)) <=> (hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1739,plain,
% 0.93/1.13 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827)))),
% 0.93/1.13 inference(monotonicity,[status(thm)],[1738])).
% 0.93/1.13 tff(1740,plain,
% 0.93/1.13 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 0.93/1.13 inference(transitivity,[status(thm)],[1739, 1737])).
% 0.93/1.13 tff(1741,plain,
% 0.93/1.13 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(1742,plain,
% 0.93/1.13 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827)),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 0.93/1.13 tff(1743,plain,
% 0.93/1.13 (hskp27 | c3_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1742, 102, 1692, 1696, 1695, 597])).
% 0.93/1.13 tff(1744,plain,
% 0.93/1.13 (hskp27),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1743, 1704])).
% 0.93/1.13 tff(1745,plain,
% 0.93/1.13 (c3_1(a1756)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[342, 1744])).
% 0.93/1.13 tff(1746,plain,
% 0.93/1.13 (c1_1(a1756)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[350, 1744])).
% 0.93/1.13 tff(1747,plain,
% 0.93/1.13 (c0_1(a1756)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[358, 1744])).
% 0.93/1.13 tff(1748,plain,
% 0.93/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1749,plain,
% 0.93/1.13 ((hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768))) <=> (hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.93/1.13 inference(rewrite,[status(thm)],[])).
% 0.93/1.13 tff(1750,plain,
% 0.93/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 0.93/1.13 inference(monotonicity,[status(thm)],[1749])).
% 0.93/1.13 tff(1751,plain,
% 0.93/1.13 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.93/1.13 inference(transitivity,[status(thm)],[1750, 1748])).
% 0.93/1.13 tff(1752,plain,
% 0.93/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)))),
% 0.93/1.13 inference(quant_inst,[status(thm)],[])).
% 0.93/1.13 tff(1753,plain,
% 0.93/1.13 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 0.93/1.13 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 0.93/1.13 tff(1754,plain,
% 0.93/1.13 ($false),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1753, 102, 1680, 1747, 1746, 1745, 1736, 1723, 1735, 1725])).
% 0.93/1.13 tff(1755,plain,(hskp6 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.93/1.13 tff(1756,plain,
% 0.93/1.13 (hskp6),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1755, 12])).
% 0.93/1.13 tff(1757,plain,
% 0.93/1.13 (~c0_1(a1762)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[270, 1756])).
% 0.93/1.13 tff(1758,plain,
% 0.93/1.13 (c2_1(a1762)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[286, 1756])).
% 0.93/1.13 tff(1759,plain,
% 0.93/1.13 (hskp13 | (~c1_1(a1762))),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[374, 102, 1758, 1757, 22])).
% 0.93/1.13 tff(1760,plain,
% 0.93/1.13 (~c1_1(a1762)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1759, 23])).
% 0.93/1.13 tff(1761,plain,
% 0.93/1.13 (c3_1(a1762)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[278, 1756])).
% 0.93/1.13 tff(1762,assumption,(~hskp2), introduced(assumption)).
% 0.93/1.13 tff(1763,plain,
% 0.93/1.13 (hskp25),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[147, 315, 1762])).
% 0.93/1.13 tff(1764,plain,
% 0.93/1.13 (~c1_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[153, 1763])).
% 0.93/1.13 tff(1765,plain,
% 0.93/1.13 (~c0_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[159, 1763])).
% 0.93/1.13 tff(1766,plain,
% 0.93/1.13 (c3_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[166, 102, 315, 35, 1765, 1764, 131])).
% 0.93/1.13 tff(1767,plain,
% 0.93/1.13 (~c2_1(a1827)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[208, 1763])).
% 0.93/1.13 tff(1768,plain,
% 0.93/1.13 ($false),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1442, 102, 368, 387, 1764, 1767, 367, 1051, 1149, 1766])).
% 0.93/1.13 tff(1769,plain,(hskp4 | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | c1_1(a1762) | hskp3 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.93/1.13 tff(1770,plain,
% 0.93/1.13 (hskp3),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[1769, 111, 1761, 1757, 1640, 1758, 1760])).
% 0.93/1.13 tff(1771,plain,
% 0.93/1.13 (c2_1(a1758)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[556, 1770])).
% 0.93/1.13 tff(1772,plain,
% 0.93/1.13 (c1_1(a1758)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[564, 1770])).
% 0.93/1.13 tff(1773,plain,
% 0.93/1.13 (c0_1(a1758)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[571, 102, 23, 1772, 1771, 22])).
% 0.93/1.13 tff(1774,plain,
% 0.93/1.13 (~c3_1(a1758)),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[578, 1770])).
% 0.93/1.13 tff(1775,plain,
% 0.93/1.13 (hskp8),
% 0.93/1.13 inference(unit_resolution,[status(thm)],[293, 102, 1640, 1758, 1761, 1757, 121])).
% 0.93/1.13 tff(1776,plain,
% 0.93/1.14 (~c1_1(a1765)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[299, 1775])).
% 0.93/1.14 tff(1777,plain,
% 0.93/1.14 (c2_1(a1765)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[405, 1775])).
% 0.93/1.14 tff(1778,plain,
% 0.93/1.14 (c0_1(a1765)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[413, 1775])).
% 0.93/1.14 tff(1779,plain,
% 0.93/1.14 ($false),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[742, 102, 1778, 1777, 1772, 1771, 1776, 1774, 736, 1773])).
% 0.93/1.14 tff(1780,plain,(hskp13 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.93/1.14 tff(1781,plain,
% 0.93/1.14 (hskp13),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1780, 12])).
% 0.93/1.14 tff(1782,plain,
% 0.93/1.14 (c1_1(a1771)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[234, 1781])).
% 0.93/1.14 tff(1783,plain,
% 0.93/1.14 (~c0_1(a1771)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[223, 1781])).
% 0.93/1.14 tff(1784,plain,
% 0.93/1.14 (c2_1(a1771)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[242, 1781])).
% 0.93/1.14 tff(1785,plain,
% 0.93/1.14 (c1_1(a1762)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1581, 1784, 1775, 1761, 1783, 1757, 1782])).
% 0.93/1.14 tff(1786,plain,
% 0.93/1.14 (hskp3),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1328, 1784, 1640, 1783, 1756, 12, 1782])).
% 0.93/1.14 tff(1787,plain,
% 0.93/1.14 (~c3_1(a1758)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[578, 1786])).
% 0.93/1.14 tff(1788,plain,
% 0.93/1.14 (c2_1(a1758)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[556, 1786])).
% 0.93/1.14 tff(1789,plain,
% 0.93/1.14 (c1_1(a1758)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[564, 1786])).
% 0.93/1.14 tff(1790,plain,
% 0.93/1.14 (~c0_1(a1758)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1619, 102, 1758, 1761, 1789, 1788, 1787, 618, 1785])).
% 0.93/1.14 tff(1791,plain,
% 0.93/1.14 (~c3_1(a1765)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[759, 102, 1778, 1777, 1788, 1776, 1787, 753, 1790])).
% 0.93/1.14 tff(1792,plain,
% 0.93/1.14 (~hskp22),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1294, 1782, 1784, 1783, 1758, 1761, 1757])).
% 0.93/1.14 tff(1793,plain,
% 0.93/1.14 ($false),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[776, 102, 1792, 1777, 1789, 1788, 1776, 1787, 770, 1791])).
% 0.93/1.14 tff(1794,plain,(hskp19), inference(lemma,lemma(discharge,[]))).
% 0.93/1.14 tff(1795,plain,
% 0.93/1.14 (((~hskp19) | (~c0_1(a1783))) <=> ((~hskp19) | (~c0_1(a1783)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1796,plain,
% 0.93/1.14 (((~c0_1(a1783)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a1783)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1797,axiom,((~c0_1(a1783)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.93/1.14 tff(1798,plain,
% 0.93/1.14 ((~hskp19) | (~c0_1(a1783))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 0.93/1.14 tff(1799,plain,
% 0.93/1.14 ((~hskp19) | (~c0_1(a1783))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1798, 1795])).
% 0.93/1.14 tff(1800,plain,
% 0.93/1.14 (~c0_1(a1783)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1799, 1794])).
% 0.93/1.14 tff(1801,plain,
% 0.93/1.14 (((~hskp19) | c3_1(a1783)) <=> ((~hskp19) | c3_1(a1783))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1802,axiom,((~hskp19) | c3_1(a1783)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.93/1.14 tff(1803,plain,
% 0.93/1.14 ((~hskp19) | c3_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 0.93/1.14 tff(1804,plain,
% 0.93/1.14 ((~hskp19) | c3_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1803, 1801])).
% 0.93/1.14 tff(1805,plain,
% 0.93/1.14 ((~hskp19) | c3_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1804, 1801])).
% 0.93/1.14 tff(1806,plain,
% 0.93/1.14 ((~hskp19) | c3_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1805, 1801])).
% 0.93/1.14 tff(1807,plain,
% 0.93/1.14 ((~hskp19) | c3_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1806, 1801])).
% 0.93/1.14 tff(1808,plain,
% 0.93/1.14 (c3_1(a1783)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1807, 1794])).
% 0.93/1.14 tff(1809,assumption,(~c2_1(a1771)), introduced(assumption)).
% 0.93/1.14 tff(1810,plain,
% 0.93/1.14 (~hskp13),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[242, 1809])).
% 0.93/1.14 tff(1811,assumption,(hskp23), introduced(assumption)).
% 0.93/1.14 tff(1812,plain,
% 0.93/1.14 (((~hskp23) | (~c3_1(a1807))) <=> ((~hskp23) | (~c3_1(a1807)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1813,plain,
% 0.93/1.14 (((~c3_1(a1807)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1807)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1814,axiom,((~c3_1(a1807)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.93/1.14 tff(1815,plain,
% 0.93/1.14 ((~hskp23) | (~c3_1(a1807))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 0.93/1.14 tff(1816,plain,
% 0.93/1.14 ((~hskp23) | (~c3_1(a1807))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1815, 1812])).
% 0.93/1.14 tff(1817,plain,
% 0.93/1.14 (~c3_1(a1807)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1816, 1811])).
% 0.93/1.14 tff(1818,plain,
% 0.93/1.14 (((~hskp23) | (~c1_1(a1807))) <=> ((~hskp23) | (~c1_1(a1807)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1819,plain,
% 0.93/1.14 (((~c1_1(a1807)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a1807)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1820,axiom,((~c1_1(a1807)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.93/1.14 tff(1821,plain,
% 0.93/1.14 ((~hskp23) | (~c1_1(a1807))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1820, 1819])).
% 0.93/1.14 tff(1822,plain,
% 0.93/1.14 ((~hskp23) | (~c1_1(a1807))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1821, 1818])).
% 0.93/1.14 tff(1823,plain,
% 0.93/1.14 (~c1_1(a1807)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1822, 1811])).
% 0.93/1.14 tff(1824,plain,
% 0.93/1.14 (((~hskp23) | (~c0_1(a1807))) <=> ((~hskp23) | (~c0_1(a1807)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1825,plain,
% 0.93/1.14 (((~c0_1(a1807)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a1807)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1826,axiom,((~c0_1(a1807)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.93/1.14 tff(1827,plain,
% 0.93/1.14 ((~hskp23) | (~c0_1(a1807))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 0.93/1.14 tff(1828,plain,
% 0.93/1.14 ((~hskp23) | (~c0_1(a1807))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1827, 1824])).
% 0.93/1.14 tff(1829,plain,
% 0.93/1.14 (~c0_1(a1807)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1828, 1811])).
% 0.93/1.14 tff(1830,plain,
% 0.93/1.14 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1831,plain,
% 0.93/1.14 ((hskp4 | hskp3 | (~ndr1_0) | c3_1(a1807) | c1_1(a1807) | c0_1(a1807)) <=> (hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1832,plain,
% 0.93/1.14 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1807) | c1_1(a1807) | c0_1(a1807))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0)))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[1831])).
% 0.93/1.14 tff(1833,plain,
% 0.93/1.14 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1807) | c1_1(a1807) | c0_1(a1807))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0))),
% 0.93/1.14 inference(transitivity,[status(thm)],[1832, 1830])).
% 0.93/1.14 tff(1834,plain,
% 0.93/1.14 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1807) | c1_1(a1807) | c0_1(a1807))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(1835,plain,
% 0.93/1.14 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 0.93/1.14 tff(1836,plain,
% 0.93/1.14 ($false),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1835, 102, 315, 35, 1829, 1823, 1817, 131])).
% 0.93/1.14 tff(1837,plain,((~hskp23) | hskp4 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.93/1.14 tff(1838,plain,
% 0.93/1.14 (~hskp23),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1837, 35, 315])).
% 0.93/1.14 tff(1839,plain,
% 0.93/1.14 (~hskp0),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1679, 315, 225])).
% 0.93/1.14 tff(1840,plain,
% 0.93/1.14 (((~hskp19) | c1_1(a1783)) <=> ((~hskp19) | c1_1(a1783))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1841,axiom,((~hskp19) | c1_1(a1783)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.93/1.14 tff(1842,plain,
% 0.93/1.14 ((~hskp19) | c1_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 0.93/1.14 tff(1843,plain,
% 0.93/1.14 ((~hskp19) | c1_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1842, 1840])).
% 0.93/1.14 tff(1844,plain,
% 0.93/1.14 ((~hskp19) | c1_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1843, 1840])).
% 0.93/1.14 tff(1845,plain,
% 0.93/1.14 ((~hskp19) | c1_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1844, 1840])).
% 0.93/1.14 tff(1846,plain,
% 0.93/1.14 ((~hskp19) | c1_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1845, 1840])).
% 0.93/1.14 tff(1847,plain,
% 0.93/1.14 (c1_1(a1783)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1846, 1794])).
% 0.93/1.14 tff(1848,plain,
% 0.93/1.14 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1849,plain,
% 0.93/1.14 ((hskp13 | (~ndr1_0) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783))) <=> (hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1850,plain,
% 0.93/1.14 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[1849])).
% 0.93/1.14 tff(1851,plain,
% 0.93/1.14 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 0.93/1.14 inference(transitivity,[status(thm)],[1850, 1848])).
% 0.93/1.14 tff(1852,plain,
% 0.93/1.14 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(1853,plain,
% 0.93/1.14 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 0.93/1.14 tff(1854,plain,
% 0.93/1.14 (hskp13 | (~c2_1(a1783))),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1853, 102, 1847, 1800, 22])).
% 0.93/1.14 tff(1855,plain,
% 0.93/1.14 (~c2_1(a1783)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1854, 23])).
% 0.93/1.14 tff(1856,assumption,(~c2_1(a1781)), introduced(assumption)).
% 0.93/1.14 tff(1857,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1858,plain,
% 0.93/1.14 ((hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1781) | c1_1(a1781) | c3_1(a1781)) <=> (hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1859,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1781) | c1_1(a1781) | c3_1(a1781))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[1858])).
% 0.93/1.14 tff(1860,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1781) | c1_1(a1781) | c3_1(a1781))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.14 inference(transitivity,[status(thm)],[1859, 1857])).
% 0.93/1.14 tff(1861,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1781) | c1_1(a1781) | c3_1(a1781))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(1862,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 0.93/1.14 tff(1863,plain,
% 0.93/1.14 (c3_1(a1781)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1862, 102, 23, 1808, 1856, 1800, 1240, 177, 1855])).
% 0.93/1.14 tff(1864,assumption,(~hskp0), introduced(assumption)).
% 0.93/1.14 tff(1865,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1866,plain,
% 0.93/1.14 ((hskp0 | (~ndr1_0) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)) | c2_1(a1781) | c1_1(a1781) | c0_1(a1781)) <=> (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1867,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)) | c2_1(a1781) | c1_1(a1781) | c0_1(a1781))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781))))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[1866])).
% 0.93/1.14 tff(1868,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)) | c2_1(a1781) | c1_1(a1781) | c0_1(a1781))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.14 inference(transitivity,[status(thm)],[1867, 1865])).
% 0.93/1.14 tff(1869,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)) | c2_1(a1781) | c1_1(a1781) | c0_1(a1781))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(1870,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 0.93/1.14 tff(1871,plain,
% 0.93/1.14 (c0_1(a1781)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1870, 102, 1864, 1856, 1863, 1240, 1690])).
% 0.93/1.14 tff(1872,plain,
% 0.93/1.14 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(1873,plain,
% 0.93/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[1872])).
% 0.93/1.14 tff(1874,plain,
% 0.93/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1875,plain,
% 0.93/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.93/1.14 inference(bind,[status(th)],[])).
% 0.93/1.14 tff(1876,plain,
% 0.93/1.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.14 inference(quant_intro,[status(thm)],[1875])).
% 0.93/1.14 tff(1877,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.93/1.14 tff(1878,plain,
% 0.93/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 0.93/1.14 tff(1879,plain,
% 0.93/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1878, 1874])).
% 0.93/1.14 tff(1880,plain,(
% 0.93/1.14 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.14 inference(skolemize,[status(sab)],[1879])).
% 0.93/1.14 tff(1881,plain,
% 0.93/1.14 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1880, 1873])).
% 0.93/1.14 tff(1882,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1883,plain,
% 0.93/1.14 ((hskp27 | (~ndr1_0) | c2_1(a1781) | c1_1(a1781) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1884,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1781) | c1_1(a1781) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[1883])).
% 0.93/1.14 tff(1885,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1781) | c1_1(a1781) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.14 inference(transitivity,[status(thm)],[1884, 1882])).
% 0.93/1.14 tff(1886,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1781) | c1_1(a1781) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(1887,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 0.93/1.14 tff(1888,plain,
% 0.93/1.14 (hskp27 | (~c0_1(a1781))),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1887, 102, 1808, 1856, 1800, 1240, 1881, 1855])).
% 0.93/1.14 tff(1889,plain,
% 0.93/1.14 (hskp27),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1888, 1871])).
% 0.93/1.14 tff(1890,plain,
% 0.93/1.14 (c3_1(a1756)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[342, 1889])).
% 0.93/1.14 tff(1891,plain,
% 0.93/1.14 (c1_1(a1756)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[350, 1889])).
% 0.93/1.14 tff(1892,plain,
% 0.93/1.14 (c0_1(a1756)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[358, 1889])).
% 0.93/1.14 tff(1893,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1894,plain,
% 0.93/1.14 ((hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c1_1(a1781) | (~c3_1(a1781))) <=> (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1895,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[1894])).
% 0.93/1.14 tff(1896,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.93/1.14 inference(transitivity,[status(thm)],[1895, 1893])).
% 0.93/1.14 tff(1897,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(1898,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 0.93/1.14 tff(1899,plain,
% 0.93/1.14 ($false),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1898, 102, 1864, 1892, 1891, 1890, 1856, 1863, 1240, 1735])).
% 0.93/1.14 tff(1900,plain,(c2_1(a1781) | hskp0 | c1_1(a1781) | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.93/1.14 tff(1901,plain,
% 0.93/1.14 (c2_1(a1781)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1900, 1240, 1839, 1810])).
% 0.93/1.14 tff(1902,plain,
% 0.93/1.14 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1903,plain,
% 0.93/1.14 ((hskp6 | hskp4 | (~ndr1_0) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781))) <=> (hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1904,plain,
% 0.93/1.14 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781)))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[1903])).
% 0.93/1.14 tff(1905,plain,
% 0.93/1.14 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 0.93/1.14 inference(transitivity,[status(thm)],[1904, 1902])).
% 0.93/1.14 tff(1906,plain,
% 0.93/1.14 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(1907,plain,
% 0.93/1.14 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 0.93/1.14 tff(1908,plain,
% 0.93/1.14 (c0_1(a1781)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1907, 102, 225, 315, 1901, 1240, 1650])).
% 0.93/1.14 tff(1909,plain,
% 0.93/1.14 (~c2_1(a1783)),
% 0.93/1.14 inference(unit_resolution,[status(thm)],[1854, 1810])).
% 0.93/1.14 tff(1910,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1911,plain,
% 0.93/1.14 ((hskp0 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c0_1(a1771)) <=> (hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.14 inference(rewrite,[status(thm)],[])).
% 0.93/1.14 tff(1912,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c0_1(a1771))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)))),
% 0.93/1.14 inference(monotonicity,[status(thm)],[1911])).
% 0.93/1.14 tff(1913,plain,
% 0.93/1.14 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c0_1(a1771))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.14 inference(transitivity,[status(thm)],[1912, 1910])).
% 0.93/1.14 tff(1914,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c0_1(a1771))),
% 0.93/1.14 inference(quant_inst,[status(thm)],[])).
% 0.93/1.14 tff(1915,plain,
% 0.93/1.14 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)),
% 0.93/1.14 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 0.93/1.15 tff(1916,plain,
% 0.93/1.15 (hskp0 | c1_1(a1771)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1915, 102, 1808, 1809, 1800, 254, 1690, 1909])).
% 0.93/1.15 tff(1917,plain,
% 0.93/1.15 (c1_1(a1771)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1916, 1839])).
% 0.93/1.15 tff(1918,plain,
% 0.93/1.15 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.93/1.15 inference(bind,[status(th)],[])).
% 0.93/1.15 tff(1919,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.15 inference(quant_intro,[status(thm)],[1918])).
% 0.93/1.15 tff(1920,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1921,plain,
% 0.93/1.15 (^[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(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.93/1.15 inference(bind,[status(th)],[])).
% 0.93/1.15 tff(1922,plain,
% 0.93/1.15 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.15 inference(quant_intro,[status(thm)],[1921])).
% 0.93/1.15 tff(1923,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.93/1.15 tff(1924,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 0.93/1.15 tff(1925,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1924, 1920])).
% 0.93/1.15 tff(1926,plain,(
% 0.93/1.15 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.15 inference(skolemize,[status(sab)],[1925])).
% 0.93/1.15 tff(1927,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1926, 1919])).
% 0.93/1.15 tff(1928,assumption,(~hskp23), introduced(assumption)).
% 0.93/1.15 tff(1929,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1930,plain,
% 0.93/1.15 ((hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c3_1(a1781) | (~c2_1(a1781))) <=> (hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1931,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c3_1(a1781) | (~c2_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[1930])).
% 0.93/1.15 tff(1932,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c3_1(a1781) | (~c2_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(transitivity,[status(thm)],[1931, 1929])).
% 0.93/1.15 tff(1933,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c3_1(a1781) | (~c2_1(a1781)))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(1934,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1933, 1932])).
% 0.93/1.15 tff(1935,plain,
% 0.93/1.15 (c3_1(a1781)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1934, 102, 1928, 1847, 1808, 1901, 1240, 1927, 1909])).
% 0.93/1.15 tff(1936,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1937,plain,
% 0.93/1.15 ((hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1771) | c0_1(a1771) | (~c1_1(a1771))) <=> (hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1938,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781))))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[1937])).
% 0.93/1.15 tff(1939,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 0.93/1.15 inference(transitivity,[status(thm)],[1938, 1936])).
% 0.93/1.15 tff(1940,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(1941,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 0.93/1.15 tff(1942,plain,
% 0.93/1.15 (hskp11),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1941, 102, 1935, 1917, 1809, 1240, 254, 860, 1908])).
% 0.93/1.15 tff(1943,plain,
% 0.93/1.15 (~c2_1(a1768)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1025, 1942])).
% 0.93/1.15 tff(1944,plain,
% 0.93/1.15 (c0_1(a1768)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1033, 1942])).
% 0.93/1.15 tff(1945,plain,
% 0.93/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1946,plain,
% 0.93/1.15 (((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1947,plain,
% 0.93/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[1946])).
% 0.93/1.15 tff(1948,plain,
% 0.93/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.15 inference(transitivity,[status(thm)],[1947, 1945])).
% 0.93/1.15 tff(1949,plain,
% 0.93/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(1950,plain,
% 0.93/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 0.93/1.15 tff(1951,plain,
% 0.93/1.15 (~c1_1(a1768)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1950, 102, 1847, 1808, 1901, 1944, 1800, 1240, 1943, 433, 1908])).
% 0.93/1.15 tff(1952,plain,
% 0.93/1.15 (c3_1(a1768)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1081, 1942])).
% 0.93/1.15 tff(1953,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1954,plain,
% 0.93/1.15 ((hskp27 | (~ndr1_0) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1955,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[1954])).
% 0.93/1.15 tff(1956,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(transitivity,[status(thm)],[1955, 1953])).
% 0.93/1.15 tff(1957,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(1958,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783)),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 0.93/1.15 tff(1959,plain,
% 0.93/1.15 (hskp27),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1958, 102, 1808, 1944, 1800, 1943, 1881, 1909, 1951])).
% 0.93/1.15 tff(1960,plain,
% 0.93/1.15 (c3_1(a1756)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[342, 1959])).
% 0.93/1.15 tff(1961,plain,
% 0.93/1.15 (c1_1(a1756)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[350, 1959])).
% 0.93/1.15 tff(1962,plain,
% 0.93/1.15 (c0_1(a1756)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[358, 1959])).
% 0.93/1.15 tff(1963,plain,
% 0.93/1.15 ($false),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1753, 102, 1839, 1962, 1961, 1960, 1952, 1943, 1735, 1951])).
% 0.93/1.15 tff(1964,plain,(c1_1(a1781) | c2_1(a1771) | c0_1(a1771) | hskp23 | hskp6 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.93/1.15 tff(1965,plain,
% 0.93/1.15 (c1_1(a1781)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1964, 1838, 254, 1809, 225, 315])).
% 0.93/1.15 tff(1966,assumption,(c1_1(a1781)), introduced(assumption)).
% 0.93/1.15 tff(1967,assumption,(~c3_1(a1781)), introduced(assumption)).
% 0.93/1.15 tff(1968,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1969,plain,
% 0.93/1.15 ((hskp3 | (~ndr1_0) | c3_1(a1781) | (~c1_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1970,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1781) | (~c1_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[1969])).
% 0.93/1.15 tff(1971,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1781) | (~c1_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.15 inference(transitivity,[status(thm)],[1970, 1968])).
% 0.93/1.15 tff(1972,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1781) | (~c1_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(1973,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 0.93/1.15 tff(1974,plain,
% 0.93/1.15 (~c0_1(a1781)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1973, 102, 35, 1847, 1808, 1967, 1800, 1966, 1400])).
% 0.93/1.15 tff(1975,plain,
% 0.93/1.15 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.93/1.15 inference(bind,[status(th)],[])).
% 0.93/1.15 tff(1976,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.15 inference(quant_intro,[status(thm)],[1975])).
% 0.93/1.15 tff(1977,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1978,plain,
% 0.93/1.15 (^[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))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.93/1.15 inference(bind,[status(th)],[])).
% 0.93/1.15 tff(1979,plain,
% 0.93/1.15 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.15 inference(quant_intro,[status(thm)],[1978])).
% 0.93/1.15 tff(1980,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.93/1.15 tff(1981,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 0.93/1.15 tff(1982,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1981, 1977])).
% 0.93/1.15 tff(1983,plain,(
% 0.93/1.15 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.15 inference(skolemize,[status(sab)],[1982])).
% 0.93/1.15 tff(1984,plain,
% 0.93/1.15 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1983, 1976])).
% 0.93/1.15 tff(1985,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1986,plain,
% 0.93/1.15 ((hskp13 | (~ndr1_0) | c3_1(a1781) | c0_1(a1781) | (~c1_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1987,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1781) | c0_1(a1781) | (~c1_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783)))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[1986])).
% 0.93/1.15 tff(1988,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1781) | c0_1(a1781) | (~c1_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(transitivity,[status(thm)],[1987, 1985])).
% 0.93/1.15 tff(1989,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1781) | c0_1(a1781) | (~c1_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 0.93/1.15 inference(quant_inst,[status(thm)],[])).
% 0.93/1.15 tff(1990,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783)),
% 0.93/1.15 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 0.93/1.15 tff(1991,plain,
% 0.93/1.15 ($false),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1990, 102, 23, 1808, 1967, 1800, 1966, 1984, 1974, 1855])).
% 0.93/1.15 tff(1992,plain,(c3_1(a1781) | hskp13 | (~c1_1(a1781)) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.93/1.15 tff(1993,plain,
% 0.93/1.15 (c3_1(a1781)),
% 0.93/1.15 inference(unit_resolution,[status(thm)],[1992, 1965, 1810, 35])).
% 0.93/1.15 tff(1994,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1995,plain,
% 0.93/1.15 ((hskp3 | (~ndr1_0) | (~c1_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(rewrite,[status(thm)],[])).
% 0.93/1.15 tff(1996,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 0.93/1.15 inference(monotonicity,[status(thm)],[1995])).
% 0.93/1.15 tff(1997,plain,
% 0.93/1.15 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.15 inference(transitivity,[status(thm)],[1996, 1994])).
% 0.93/1.15 tff(1998,plain,
% 0.93/1.15 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(1999,plain,
% 0.93/1.16 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 0.93/1.16 tff(2000,plain,
% 0.93/1.16 ((~c0_1(a1781)) | (~c3_1(a1781))),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[1999, 102, 35, 1808, 1800, 1965, 11, 1909])).
% 0.93/1.16 tff(2001,plain,
% 0.93/1.16 (~c0_1(a1781)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2000, 1993])).
% 0.93/1.16 tff(2002,plain,
% 0.93/1.16 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2003,plain,
% 0.93/1.16 ((hskp6 | hskp3 | (~ndr1_0) | c0_1(a1781) | (~c2_1(a1781)) | (~c1_1(a1781))) <=> (hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2004,plain,
% 0.93/1.16 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1781) | (~c2_1(a1781)) | (~c1_1(a1781)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781)))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[2003])).
% 0.93/1.16 tff(2005,plain,
% 0.93/1.16 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1781) | (~c2_1(a1781)) | (~c1_1(a1781)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 0.93/1.16 inference(transitivity,[status(thm)],[2004, 2002])).
% 0.93/1.16 tff(2006,plain,
% 0.93/1.16 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1781) | (~c2_1(a1781)) | (~c1_1(a1781)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(2007,plain,
% 0.93/1.16 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 0.93/1.16 tff(2008,plain,
% 0.93/1.16 ((~c2_1(a1781)) | c0_1(a1781)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2007, 102, 225, 35, 1965, 253])).
% 0.93/1.16 tff(2009,plain,
% 0.93/1.16 (~c2_1(a1781)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2008, 2001])).
% 0.93/1.16 tff(2010,assumption,(~c0_1(a1781)), introduced(assumption)).
% 0.93/1.16 tff(2011,assumption,(hskp12), introduced(assumption)).
% 0.93/1.16 tff(2012,plain,
% 0.93/1.16 (((~hskp12) | (~c3_1(a1770))) <=> ((~hskp12) | (~c3_1(a1770)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2013,plain,
% 0.93/1.16 (((~c3_1(a1770)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a1770)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2014,axiom,((~c3_1(a1770)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.93/1.16 tff(2015,plain,
% 0.93/1.16 ((~hskp12) | (~c3_1(a1770))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 0.93/1.16 tff(2016,plain,
% 0.93/1.16 ((~hskp12) | (~c3_1(a1770))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2015, 2012])).
% 0.93/1.16 tff(2017,plain,
% 0.93/1.16 (~c3_1(a1770)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2016, 2011])).
% 0.93/1.16 tff(2018,plain,
% 0.93/1.16 (((~hskp12) | (~c0_1(a1770))) <=> ((~hskp12) | (~c0_1(a1770)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2019,plain,
% 0.93/1.16 (((~c0_1(a1770)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1770)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2020,axiom,((~c0_1(a1770)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.93/1.16 tff(2021,plain,
% 0.93/1.16 ((~hskp12) | (~c0_1(a1770))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 0.93/1.16 tff(2022,plain,
% 0.93/1.16 ((~hskp12) | (~c0_1(a1770))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2021, 2018])).
% 0.93/1.16 tff(2023,plain,
% 0.93/1.16 (~c0_1(a1770)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2022, 2011])).
% 0.93/1.16 tff(2024,plain,
% 0.93/1.16 (((~hskp12) | c1_1(a1770)) <=> ((~hskp12) | c1_1(a1770))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2025,axiom,((~hskp12) | c1_1(a1770)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.93/1.16 tff(2026,plain,
% 0.93/1.16 ((~hskp12) | c1_1(a1770)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 0.93/1.16 tff(2027,plain,
% 0.93/1.16 ((~hskp12) | c1_1(a1770)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2026, 2024])).
% 0.93/1.16 tff(2028,plain,
% 0.93/1.16 ((~hskp12) | c1_1(a1770)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2027, 2024])).
% 0.93/1.16 tff(2029,plain,
% 0.93/1.16 ((~hskp12) | c1_1(a1770)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2028, 2024])).
% 0.93/1.16 tff(2030,plain,
% 0.93/1.16 ((~hskp12) | c1_1(a1770)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2029, 2024])).
% 0.93/1.16 tff(2031,plain,
% 0.93/1.16 (c1_1(a1770)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2030, 2011])).
% 0.93/1.16 tff(2032,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2033,plain,
% 0.93/1.16 ((hskp13 | (~ndr1_0) | c3_1(a1770) | c0_1(a1770) | (~c1_1(a1770)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2034,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1770) | c0_1(a1770) | (~c1_1(a1770)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781))))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[2033])).
% 0.93/1.16 tff(2035,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1770) | c0_1(a1770) | (~c1_1(a1770)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.16 inference(transitivity,[status(thm)],[2034, 2032])).
% 0.93/1.16 tff(2036,plain,
% 0.93/1.16 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1770) | c0_1(a1770) | (~c1_1(a1770)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(2037,plain,
% 0.93/1.16 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 0.93/1.16 tff(2038,plain,
% 0.93/1.16 ($false),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2037, 102, 23, 1856, 1241, 2031, 2023, 2017, 1984, 2010])).
% 0.93/1.16 tff(2039,plain,((~hskp12) | hskp13 | c2_1(a1781) | (~c3_1(a1781)) | c0_1(a1781)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.16 tff(2040,plain,
% 0.93/1.16 (~hskp12),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2039, 2009, 1810, 1993, 2001])).
% 0.93/1.16 tff(2041,plain,
% 0.93/1.16 (^[U: $i] : refl((hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(2042,plain,
% 0.93/1.16 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[2041])).
% 0.93/1.16 tff(2043,plain,
% 0.93/1.16 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2044,plain,
% 0.93/1.16 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp12) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp12))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(2045,plain,
% 0.93/1.16 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp12) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[2044])).
% 0.93/1.16 tff(2046,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.93/1.16 tff(2047,plain,
% 0.93/1.16 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 0.93/1.16 tff(2048,plain,
% 0.93/1.16 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2047, 2043])).
% 0.93/1.16 tff(2049,plain,(
% 0.93/1.16 ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.93/1.16 inference(skolemize,[status(sab)],[2048])).
% 0.93/1.16 tff(2050,plain,
% 0.93/1.16 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2049, 2042])).
% 0.93/1.16 tff(2051,plain,
% 0.93/1.16 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2052,plain,
% 0.93/1.16 ((hskp27 | hskp12 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783))) <=> (hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2053,plain,
% 0.93/1.16 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783)))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[2052])).
% 0.93/1.16 tff(2054,plain,
% 0.93/1.16 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783))),
% 0.93/1.16 inference(transitivity,[status(thm)],[2053, 2051])).
% 0.93/1.16 tff(2055,plain,
% 0.93/1.16 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(2056,plain,
% 0.93/1.16 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2055, 2054])).
% 0.93/1.16 tff(2057,plain,
% 0.93/1.16 (hskp27 | hskp12 | c2_1(a1783)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2056, 102, 1847, 1800, 2050])).
% 0.93/1.16 tff(2058,plain,
% 0.93/1.16 (hskp27),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2057, 2040, 1909])).
% 0.93/1.16 tff(2059,plain,
% 0.93/1.16 (c3_1(a1756)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[342, 2058])).
% 0.93/1.16 tff(2060,plain,
% 0.93/1.16 (c1_1(a1756)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[350, 2058])).
% 0.93/1.16 tff(2061,plain,
% 0.93/1.16 (c0_1(a1756)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[358, 2058])).
% 0.93/1.16 tff(2062,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2063,plain,
% 0.93/1.16 ((hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2064,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[2063])).
% 0.93/1.16 tff(2065,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 0.93/1.16 inference(transitivity,[status(thm)],[2064, 2062])).
% 0.93/1.16 tff(2066,plain,
% 0.93/1.16 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(2067,plain,
% 0.93/1.16 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 0.93/1.16 tff(2068,plain,
% 0.93/1.16 ($false),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2067, 102, 35, 2061, 2060, 2059, 2009, 1993, 11, 2001])).
% 0.93/1.16 tff(2069,plain,(hskp3 | hskp6 | c0_1(a1771) | c2_1(a1771) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.93/1.16 tff(2070,plain,
% 0.93/1.16 (hskp3),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2069, 315, 254, 1809, 225])).
% 0.93/1.16 tff(2071,plain,
% 0.93/1.16 (c2_1(a1758)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[556, 2070])).
% 0.93/1.16 tff(2072,plain,
% 0.93/1.16 (c1_1(a1758)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[564, 2070])).
% 0.93/1.16 tff(2073,plain,
% 0.93/1.16 (c0_1(a1758)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[571, 102, 1810, 2072, 2071, 22])).
% 0.93/1.16 tff(2074,plain,
% 0.93/1.16 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(2075,plain,
% 0.93/1.16 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[2074])).
% 0.93/1.16 tff(2076,plain,
% 0.93/1.16 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2077,plain,
% 0.93/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.93/1.16 inference(bind,[status(th)],[])).
% 0.93/1.16 tff(2078,plain,
% 0.93/1.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.16 inference(quant_intro,[status(thm)],[2077])).
% 0.93/1.16 tff(2079,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.93/1.16 tff(2080,plain,
% 0.93/1.16 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2079, 2078])).
% 0.93/1.16 tff(2081,plain,
% 0.93/1.16 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2080, 2076])).
% 0.93/1.16 tff(2082,plain,(
% 0.93/1.16 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.16 inference(skolemize,[status(sab)],[2081])).
% 0.93/1.16 tff(2083,plain,
% 0.93/1.16 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2082, 2075])).
% 0.93/1.16 tff(2084,plain,
% 0.93/1.16 (~c3_1(a1758)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[578, 2070])).
% 0.93/1.16 tff(2085,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2086,plain,
% 0.93/1.16 ((hskp14 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2087,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[2086])).
% 0.93/1.16 tff(2088,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.16 inference(transitivity,[status(thm)],[2087, 2085])).
% 0.93/1.16 tff(2089,plain,
% 0.93/1.16 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(2090,plain,
% 0.93/1.16 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 0.93/1.16 tff(2091,plain,
% 0.93/1.16 (hskp14),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2090, 102, 1808, 2071, 1800, 2084, 2083, 1909, 2073])).
% 0.93/1.16 tff(2092,plain,
% 0.93/1.16 (((~hskp14) | (~c0_1(a1777))) <=> ((~hskp14) | (~c0_1(a1777)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2093,plain,
% 0.93/1.16 (((~c0_1(a1777)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a1777)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2094,axiom,((~c0_1(a1777)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.93/1.16 tff(2095,plain,
% 0.93/1.16 ((~hskp14) | (~c0_1(a1777))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 0.93/1.16 tff(2096,plain,
% 0.93/1.16 ((~hskp14) | (~c0_1(a1777))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2095, 2092])).
% 0.93/1.16 tff(2097,plain,
% 0.93/1.16 (~c0_1(a1777)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2096, 2091])).
% 0.93/1.16 tff(2098,plain,
% 0.93/1.16 (((~hskp14) | c2_1(a1777)) <=> ((~hskp14) | c2_1(a1777))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2099,axiom,((~hskp14) | c2_1(a1777)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.93/1.16 tff(2100,plain,
% 0.93/1.16 ((~hskp14) | c2_1(a1777)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2099, 2098])).
% 0.93/1.16 tff(2101,plain,
% 0.93/1.16 ((~hskp14) | c2_1(a1777)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2100, 2098])).
% 0.93/1.16 tff(2102,plain,
% 0.93/1.16 ((~hskp14) | c2_1(a1777)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2101, 2098])).
% 0.93/1.16 tff(2103,plain,
% 0.93/1.16 ((~hskp14) | c2_1(a1777)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2102, 2098])).
% 0.93/1.16 tff(2104,plain,
% 0.93/1.16 ((~hskp14) | c2_1(a1777)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2103, 2098])).
% 0.93/1.16 tff(2105,plain,
% 0.93/1.16 (c2_1(a1777)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2104, 2091])).
% 0.93/1.16 tff(2106,plain,
% 0.93/1.16 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2107,plain,
% 0.93/1.16 ((hskp13 | (~ndr1_0) | c0_1(a1777) | (~c2_1(a1777)) | (~c1_1(a1777))) <=> (hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777)))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2108,plain,
% 0.93/1.16 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1777) | (~c2_1(a1777)) | (~c1_1(a1777)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777))))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[2107])).
% 0.93/1.16 tff(2109,plain,
% 0.93/1.16 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1777) | (~c2_1(a1777)) | (~c1_1(a1777)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777)))),
% 0.93/1.16 inference(transitivity,[status(thm)],[2108, 2106])).
% 0.93/1.16 tff(2110,plain,
% 0.93/1.16 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1777) | (~c2_1(a1777)) | (~c1_1(a1777)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(2111,plain,
% 0.93/1.16 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777))),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2110, 2109])).
% 0.93/1.16 tff(2112,plain,
% 0.93/1.16 (~c1_1(a1777)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2111, 102, 1810, 2105, 2097, 22])).
% 0.93/1.16 tff(2113,plain,
% 0.93/1.16 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2114,plain,
% 0.93/1.16 ((hskp6 | hskp4 | (~ndr1_0) | c1_1(a1777) | c0_1(a1777) | (~c2_1(a1777))) <=> (hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2115,plain,
% 0.93/1.16 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777)))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[2114])).
% 0.93/1.16 tff(2116,plain,
% 0.93/1.16 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777))),
% 0.93/1.16 inference(transitivity,[status(thm)],[2115, 2113])).
% 0.93/1.16 tff(2117,plain,
% 0.93/1.16 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))),
% 0.93/1.16 inference(quant_inst,[status(thm)],[])).
% 0.93/1.16 tff(2118,plain,
% 0.93/1.16 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777)),
% 0.93/1.16 inference(modus_ponens,[status(thm)],[2117, 2116])).
% 0.93/1.16 tff(2119,plain,
% 0.93/1.16 ($false),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2118, 102, 225, 315, 2105, 2097, 1650, 2112])).
% 0.93/1.16 tff(2120,plain,(hskp4 | hskp6 | c0_1(a1771) | c2_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.16 tff(2121,plain,
% 0.93/1.16 (hskp4),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[2120, 1809, 254, 225])).
% 0.93/1.16 tff(2122,plain,
% 0.93/1.16 (~c3_1(a1759)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[1639, 2121])).
% 0.93/1.16 tff(2123,plain,
% 0.93/1.16 (c1_1(a1759)),
% 0.93/1.16 inference(unit_resolution,[status(thm)],[138, 2121])).
% 0.93/1.16 tff(2124,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2125,plain,
% 0.93/1.16 ((hskp13 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.16 inference(rewrite,[status(thm)],[])).
% 0.93/1.16 tff(2126,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783)))),
% 0.93/1.16 inference(monotonicity,[status(thm)],[2125])).
% 0.93/1.16 tff(2127,plain,
% 0.93/1.16 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783))),
% 0.93/1.16 inference(transitivity,[status(thm)],[2126, 2124])).
% 0.93/1.16 tff(2128,plain,
% 0.93/1.16 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(2129,plain,
% 0.93/1.17 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 0.93/1.17 tff(2130,plain,
% 0.93/1.17 (c0_1(a1759)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2129, 102, 1810, 1808, 2123, 1800, 2122, 1984, 1909])).
% 0.93/1.17 tff(2131,assumption,(hskp19), introduced(assumption)).
% 0.93/1.17 tff(2132,plain,
% 0.93/1.17 (c1_1(a1783)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[1846, 2131])).
% 0.93/1.17 tff(2133,plain,
% 0.93/1.17 (c3_1(a1783)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[1807, 2131])).
% 0.93/1.17 tff(2134,assumption,(~c0_1(a1783)), introduced(assumption)).
% 0.93/1.17 tff(2135,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2136,plain,
% 0.93/1.17 ((hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2137,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[2136])).
% 0.93/1.17 tff(2138,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.17 inference(transitivity,[status(thm)],[2137, 2135])).
% 0.93/1.17 tff(2139,plain,
% 0.93/1.17 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(2140,plain,
% 0.93/1.17 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 0.93/1.17 tff(2141,plain,
% 0.93/1.17 ((~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2140, 35, 2134, 34, 1400])).
% 0.93/1.17 tff(2142,plain,
% 0.93/1.17 ($false),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2141, 2133, 2132, 226, 869, 1465])).
% 0.93/1.17 tff(2143,plain,((~hskp19) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | hskp3 | c0_1(a1783) | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.17 tff(2144,plain,
% 0.93/1.17 ((~hskp19) | (~c1_1(a1759)) | (~c0_1(a1759)) | hskp3 | c0_1(a1783) | c3_1(a1759)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2143, 102])).
% 0.93/1.17 tff(2145,plain,
% 0.93/1.17 ((~c1_1(a1759)) | (~c0_1(a1759)) | hskp3 | c3_1(a1759)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2144, 1794, 1800])).
% 0.93/1.17 tff(2146,plain,
% 0.93/1.17 (hskp3),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2145, 2130, 2123, 2122])).
% 0.93/1.17 tff(2147,plain,
% 0.93/1.17 (c2_1(a1758)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[556, 2146])).
% 0.93/1.17 tff(2148,plain,
% 0.93/1.17 (c1_1(a1758)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[564, 2146])).
% 0.93/1.17 tff(2149,plain,
% 0.93/1.17 (c0_1(a1758)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[571, 102, 1810, 2148, 2147, 22])).
% 0.93/1.17 tff(2150,plain,
% 0.93/1.17 (~c3_1(a1758)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[578, 2146])).
% 0.93/1.17 tff(2151,plain,
% 0.93/1.17 (hskp14),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2090, 102, 1808, 2147, 1800, 2150, 2083, 1909, 2149])).
% 0.93/1.17 tff(2152,plain,
% 0.93/1.17 (~c0_1(a1777)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2096, 2151])).
% 0.93/1.17 tff(2153,plain,
% 0.93/1.17 (c2_1(a1777)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2104, 2151])).
% 0.93/1.17 tff(2154,plain,
% 0.93/1.17 (~c1_1(a1777)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2111, 102, 1810, 2153, 2152, 22])).
% 0.93/1.17 tff(2155,plain,
% 0.93/1.17 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(2156,plain,
% 0.93/1.17 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[2155])).
% 0.93/1.17 tff(2157,plain,
% 0.93/1.17 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2158,plain,
% 0.93/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(2159,plain,
% 0.93/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[2158])).
% 0.93/1.17 tff(2160,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.93/1.17 tff(2161,plain,
% 0.93/1.17 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2160, 2159])).
% 0.93/1.17 tff(2162,plain,
% 0.93/1.17 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2161, 2157])).
% 0.93/1.17 tff(2163,plain,(
% 0.93/1.17 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.17 inference(skolemize,[status(sab)],[2162])).
% 0.93/1.17 tff(2164,plain,
% 0.93/1.17 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2163, 2156])).
% 0.93/1.17 tff(2165,plain,
% 0.93/1.17 (((~hskp14) | (~c3_1(a1777))) <=> ((~hskp14) | (~c3_1(a1777)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2166,plain,
% 0.93/1.17 (((~c3_1(a1777)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a1777)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2167,axiom,((~c3_1(a1777)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.93/1.17 tff(2168,plain,
% 0.93/1.17 ((~hskp14) | (~c3_1(a1777))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 0.93/1.17 tff(2169,plain,
% 0.93/1.17 ((~hskp14) | (~c3_1(a1777))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2168, 2165])).
% 0.93/1.17 tff(2170,plain,
% 0.93/1.17 (~c3_1(a1777)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2169, 2151])).
% 0.93/1.17 tff(2171,plain,
% 0.93/1.17 (^[U: $i] : refl((hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(2172,plain,
% 0.93/1.17 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[2171])).
% 0.93/1.17 tff(2173,plain,
% 0.93/1.17 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2174,plain,
% 0.93/1.17 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) | hskp6) <=> ((hskp20 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp20 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) | hskp6) <=> (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(2175,plain,
% 0.93/1.17 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) | hskp6) <=> ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[2174])).
% 0.93/1.17 tff(2176,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.93/1.17 tff(2177,plain,
% 0.93/1.17 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2176, 2175])).
% 0.93/1.17 tff(2178,plain,
% 0.93/1.17 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2177, 2173])).
% 0.93/1.17 tff(2179,plain,(
% 0.93/1.17 ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.17 inference(skolemize,[status(sab)],[2178])).
% 0.93/1.17 tff(2180,plain,
% 0.93/1.17 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2179, 2172])).
% 0.93/1.17 tff(2181,plain,
% 0.93/1.17 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2182,plain,
% 0.93/1.17 ((hskp20 | hskp6 | (~ndr1_0) | c3_1(a1777) | c0_1(a1777) | (~c2_1(a1777))) <=> (hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2183,plain,
% 0.93/1.17 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777))))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[2182])).
% 0.93/1.17 tff(2184,plain,
% 0.93/1.17 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)))),
% 0.93/1.17 inference(transitivity,[status(thm)],[2183, 2181])).
% 0.93/1.17 tff(2185,plain,
% 0.93/1.17 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(2186,plain,
% 0.93/1.17 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2185, 2184])).
% 0.93/1.17 tff(2187,plain,
% 0.93/1.17 (hskp20),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2186, 102, 225, 2153, 2152, 2170, 2180])).
% 0.93/1.17 tff(2188,plain,
% 0.93/1.17 (((~hskp20) | (~c3_1(a1786))) <=> ((~hskp20) | (~c3_1(a1786)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2189,plain,
% 0.93/1.17 (((~c3_1(a1786)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a1786)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2190,axiom,((~c3_1(a1786)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.93/1.17 tff(2191,plain,
% 0.93/1.17 ((~hskp20) | (~c3_1(a1786))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 0.93/1.17 tff(2192,plain,
% 0.93/1.17 ((~hskp20) | (~c3_1(a1786))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2191, 2188])).
% 0.93/1.17 tff(2193,plain,
% 0.93/1.17 (~c3_1(a1786)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2192, 2187])).
% 0.93/1.17 tff(2194,plain,
% 0.93/1.17 (((~hskp20) | c1_1(a1786)) <=> ((~hskp20) | c1_1(a1786))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2195,axiom,((~hskp20) | c1_1(a1786)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.93/1.17 tff(2196,plain,
% 0.93/1.17 ((~hskp20) | c1_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 0.93/1.17 tff(2197,plain,
% 0.93/1.17 ((~hskp20) | c1_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2196, 2194])).
% 0.93/1.17 tff(2198,plain,
% 0.93/1.17 ((~hskp20) | c1_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2197, 2194])).
% 0.93/1.17 tff(2199,plain,
% 0.93/1.17 ((~hskp20) | c1_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2198, 2194])).
% 0.93/1.17 tff(2200,plain,
% 0.93/1.17 ((~hskp20) | c1_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2199, 2194])).
% 0.93/1.17 tff(2201,plain,
% 0.93/1.17 (c1_1(a1786)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2200, 2187])).
% 0.93/1.17 tff(2202,plain,
% 0.93/1.17 (((~hskp20) | c0_1(a1786)) <=> ((~hskp20) | c0_1(a1786))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2203,axiom,((~hskp20) | c0_1(a1786)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.93/1.17 tff(2204,plain,
% 0.93/1.17 ((~hskp20) | c0_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2203, 2202])).
% 0.93/1.17 tff(2205,plain,
% 0.93/1.17 ((~hskp20) | c0_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2204, 2202])).
% 0.93/1.17 tff(2206,plain,
% 0.93/1.17 ((~hskp20) | c0_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2205, 2202])).
% 0.93/1.17 tff(2207,plain,
% 0.93/1.17 ((~hskp20) | c0_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2206, 2202])).
% 0.93/1.17 tff(2208,plain,
% 0.93/1.17 ((~hskp20) | c0_1(a1786)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2207, 2202])).
% 0.93/1.17 tff(2209,plain,
% 0.93/1.17 (c0_1(a1786)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2208, 2187])).
% 0.93/1.17 tff(2210,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2211,plain,
% 0.93/1.17 ((hskp15 | (~ndr1_0) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777))) <=> (hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2212,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786))))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[2211])).
% 0.93/1.17 tff(2213,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 0.93/1.17 inference(transitivity,[status(thm)],[2212, 2210])).
% 0.93/1.17 tff(2214,plain,
% 0.93/1.17 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(2215,plain,
% 0.93/1.17 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2214, 2213])).
% 0.93/1.17 tff(2216,plain,
% 0.93/1.17 (hskp15),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2215, 102, 2209, 2201, 2153, 2193, 2170, 2164, 2154])).
% 0.93/1.17 tff(2217,plain,
% 0.93/1.17 (((~hskp15) | (~c3_1(a1779))) <=> ((~hskp15) | (~c3_1(a1779)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2218,plain,
% 0.93/1.17 (((~c3_1(a1779)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a1779)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2219,axiom,((~c3_1(a1779)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.93/1.17 tff(2220,plain,
% 0.93/1.17 ((~hskp15) | (~c3_1(a1779))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2219, 2218])).
% 0.93/1.17 tff(2221,plain,
% 0.93/1.17 ((~hskp15) | (~c3_1(a1779))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2220, 2217])).
% 0.93/1.17 tff(2222,plain,
% 0.93/1.17 (~c3_1(a1779)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2221, 2216])).
% 0.93/1.17 tff(2223,plain,
% 0.93/1.17 (((~hskp15) | (~c2_1(a1779))) <=> ((~hskp15) | (~c2_1(a1779)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2224,plain,
% 0.93/1.17 (((~c2_1(a1779)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a1779)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2225,axiom,((~c2_1(a1779)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.93/1.17 tff(2226,plain,
% 0.93/1.17 ((~hskp15) | (~c2_1(a1779))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 0.93/1.17 tff(2227,plain,
% 0.93/1.17 ((~hskp15) | (~c2_1(a1779))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2226, 2223])).
% 0.93/1.17 tff(2228,plain,
% 0.93/1.17 (~c2_1(a1779)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2227, 2216])).
% 0.93/1.17 tff(2229,plain,
% 0.93/1.17 (((~hskp15) | c0_1(a1779)) <=> ((~hskp15) | c0_1(a1779))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2230,axiom,((~hskp15) | c0_1(a1779)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.93/1.17 tff(2231,plain,
% 0.93/1.17 ((~hskp15) | c0_1(a1779)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 0.93/1.17 tff(2232,plain,
% 0.93/1.17 ((~hskp15) | c0_1(a1779)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2231, 2229])).
% 0.93/1.17 tff(2233,plain,
% 0.93/1.17 ((~hskp15) | c0_1(a1779)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2232, 2229])).
% 0.93/1.17 tff(2234,plain,
% 0.93/1.17 ((~hskp15) | c0_1(a1779)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2233, 2229])).
% 0.93/1.17 tff(2235,plain,
% 0.93/1.17 ((~hskp15) | c0_1(a1779)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2234, 2229])).
% 0.93/1.17 tff(2236,plain,
% 0.93/1.17 (c0_1(a1779)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2235, 2216])).
% 0.93/1.17 tff(2237,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2238,plain,
% 0.93/1.17 ((hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777))) <=> (hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2239,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777)))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[2238])).
% 0.93/1.17 tff(2240,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777))),
% 0.93/1.17 inference(transitivity,[status(thm)],[2239, 2237])).
% 0.93/1.17 tff(2241,plain,
% 0.93/1.17 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(2242,plain,
% 0.93/1.17 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777)),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 0.93/1.17 tff(2243,plain,
% 0.93/1.17 (hskp22),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2242, 102, 2153, 2148, 2147, 2170, 2150, 770, 2154])).
% 0.93/1.17 tff(2244,plain,
% 0.93/1.17 (~c2_1(a1799)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[494, 2243])).
% 0.93/1.17 tff(2245,plain,
% 0.93/1.17 (~c0_1(a1799)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[500, 2243])).
% 0.93/1.17 tff(2246,plain,
% 0.93/1.17 (c3_1(a1799)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[508, 2243])).
% 0.93/1.17 tff(2247,assumption,(hskp18), introduced(assumption)).
% 0.93/1.17 tff(2248,plain,
% 0.93/1.17 (((~hskp18) | (~c3_1(a1782))) <=> ((~hskp18) | (~c3_1(a1782)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2249,plain,
% 0.93/1.17 (((~c3_1(a1782)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a1782)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2250,axiom,((~c3_1(a1782)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.93/1.17 tff(2251,plain,
% 0.93/1.17 ((~hskp18) | (~c3_1(a1782))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 0.93/1.17 tff(2252,plain,
% 0.93/1.17 ((~hskp18) | (~c3_1(a1782))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2251, 2248])).
% 0.93/1.17 tff(2253,plain,
% 0.93/1.17 (~c3_1(a1782)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2252, 2247])).
% 0.93/1.17 tff(2254,plain,
% 0.93/1.17 (((~hskp18) | (~c2_1(a1782))) <=> ((~hskp18) | (~c2_1(a1782)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2255,plain,
% 0.93/1.17 (((~c2_1(a1782)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a1782)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2256,axiom,((~c2_1(a1782)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.93/1.17 tff(2257,plain,
% 0.93/1.17 ((~hskp18) | (~c2_1(a1782))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 0.93/1.17 tff(2258,plain,
% 0.93/1.17 ((~hskp18) | (~c2_1(a1782))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2257, 2254])).
% 0.93/1.17 tff(2259,plain,
% 0.93/1.17 (~c2_1(a1782)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2258, 2247])).
% 0.93/1.17 tff(2260,plain,
% 0.93/1.17 (((~hskp18) | (~c1_1(a1782))) <=> ((~hskp18) | (~c1_1(a1782)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2261,plain,
% 0.93/1.17 (((~c1_1(a1782)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a1782)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2262,axiom,((~c1_1(a1782)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.93/1.17 tff(2263,plain,
% 0.93/1.17 ((~hskp18) | (~c1_1(a1782))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2262, 2261])).
% 0.93/1.17 tff(2264,plain,
% 0.93/1.17 ((~hskp18) | (~c1_1(a1782))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2263, 2260])).
% 0.93/1.17 tff(2265,plain,
% 0.93/1.17 (~c1_1(a1782)),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2264, 2247])).
% 0.93/1.17 tff(2266,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2267,plain,
% 0.93/1.17 ((hskp13 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782)) <=> (hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2268,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799))))),
% 0.93/1.17 inference(monotonicity,[status(thm)],[2267])).
% 0.93/1.17 tff(2269,plain,
% 0.93/1.17 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799)))),
% 0.93/1.17 inference(transitivity,[status(thm)],[2268, 2266])).
% 0.93/1.17 tff(2270,plain,
% 0.93/1.17 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782))),
% 0.93/1.17 inference(quant_inst,[status(thm)],[])).
% 0.93/1.17 tff(2271,plain,
% 0.93/1.17 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799))),
% 0.93/1.17 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 0.93/1.17 tff(2272,plain,
% 0.93/1.17 ($false),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2271, 102, 23, 1151, 1159, 1150, 2265, 2259, 2253, 177])).
% 0.93/1.17 tff(2273,plain,((~hskp18) | hskp13 | (~c3_1(a1799)) | c0_1(a1799) | c2_1(a1799)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.17 tff(2274,plain,
% 0.93/1.17 (~hskp18),
% 0.93/1.17 inference(unit_resolution,[status(thm)],[2273, 1810, 2246, 2245, 2244])).
% 0.93/1.17 tff(2275,plain,
% 0.93/1.17 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.93/1.17 inference(bind,[status(th)],[])).
% 0.93/1.17 tff(2276,plain,
% 0.93/1.17 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.93/1.17 inference(quant_intro,[status(thm)],[2275])).
% 0.93/1.17 tff(2277,plain,
% 0.93/1.17 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.93/1.17 inference(rewrite,[status(thm)],[])).
% 0.93/1.17 tff(2278,plain,
% 0.93/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.93/1.18 inference(bind,[status(th)],[])).
% 0.93/1.18 tff(2279,plain,
% 0.93/1.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.93/1.18 inference(quant_intro,[status(thm)],[2278])).
% 0.93/1.18 tff(2280,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.93/1.18 tff(2281,plain,
% 0.93/1.18 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[2280, 2279])).
% 0.93/1.18 tff(2282,plain,
% 0.93/1.18 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[2281, 2277])).
% 0.93/1.18 tff(2283,plain,(
% 0.93/1.18 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.93/1.18 inference(skolemize,[status(sab)],[2282])).
% 0.93/1.18 tff(2284,plain,
% 0.93/1.18 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[2283, 2276])).
% 0.93/1.18 tff(2285,assumption,(~c3_1(a1779)), introduced(assumption)).
% 0.93/1.18 tff(2286,assumption,(~c2_1(a1779)), introduced(assumption)).
% 0.93/1.18 tff(2287,assumption,(c0_1(a1779)), introduced(assumption)).
% 0.93/1.18 tff(2288,assumption,(~hskp18), introduced(assumption)).
% 0.93/1.18 tff(2289,plain,
% 0.93/1.18 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.93/1.18 inference(rewrite,[status(thm)],[])).
% 0.93/1.18 tff(2290,plain,
% 0.93/1.18 ((hskp18 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c2_1(a1779) | c3_1(a1779) | (~c0_1(a1779))) <=> (hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.93/1.18 inference(rewrite,[status(thm)],[])).
% 0.93/1.18 tff(2291,plain,
% 0.93/1.18 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c2_1(a1779) | c3_1(a1779) | (~c0_1(a1779)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))))),
% 0.93/1.18 inference(monotonicity,[status(thm)],[2290])).
% 0.93/1.18 tff(2292,plain,
% 0.93/1.18 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c2_1(a1779) | c3_1(a1779) | (~c0_1(a1779)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 0.93/1.18 inference(transitivity,[status(thm)],[2291, 2289])).
% 0.93/1.18 tff(2293,plain,
% 0.93/1.18 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c2_1(a1779) | c3_1(a1779) | (~c0_1(a1779)))),
% 0.93/1.18 inference(quant_inst,[status(thm)],[])).
% 0.93/1.18 tff(2294,plain,
% 0.93/1.18 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 0.93/1.18 tff(2295,plain,
% 0.93/1.18 ($false),
% 0.93/1.18 inference(unit_resolution,[status(thm)],[2294, 102, 2288, 1469, 1468, 1467, 2287, 2286, 2285, 2284])).
% 0.93/1.18 tff(2296,plain,((~hskp29) | hskp18 | (~c0_1(a1779)) | c2_1(a1779) | c3_1(a1779)), inference(lemma,lemma(discharge,[]))).
% 0.93/1.18 tff(2297,plain,
% 0.93/1.18 (~hskp29),
% 0.93/1.18 inference(unit_resolution,[status(thm)],[2296, 2274, 2236, 2228, 2222])).
% 0.93/1.18 tff(2298,plain,
% 0.93/1.18 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 0.93/1.18 inference(rewrite,[status(thm)],[])).
% 0.93/1.18 tff(2299,plain,
% 0.93/1.18 ((hskp30 | hskp29 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758))) <=> (hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 0.93/1.18 inference(rewrite,[status(thm)],[])).
% 0.93/1.18 tff(2300,plain,
% 0.93/1.18 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758))))),
% 0.93/1.18 inference(monotonicity,[status(thm)],[2299])).
% 0.93/1.18 tff(2301,plain,
% 0.93/1.18 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 0.93/1.18 inference(transitivity,[status(thm)],[2300, 2298])).
% 0.93/1.18 tff(2302,plain,
% 0.93/1.18 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 0.93/1.18 inference(quant_inst,[status(thm)],[])).
% 0.93/1.18 tff(2303,plain,
% 0.93/1.18 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758))),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 0.93/1.18 tff(2304,plain,
% 0.93/1.18 (hskp30 | hskp29),
% 0.93/1.18 inference(unit_resolution,[status(thm)],[2303, 102, 2148, 2147, 2150, 1496])).
% 0.93/1.18 tff(2305,plain,
% 0.93/1.18 (hskp30),
% 0.93/1.18 inference(unit_resolution,[status(thm)],[2304, 2297])).
% 0.93/1.18 tff(2306,plain,
% 0.93/1.18 (c2_1(a1823)),
% 0.93/1.18 inference(unit_resolution,[status(thm)],[1519, 2305])).
% 0.93/1.18 tff(2307,plain,
% 0.93/1.18 (c1_1(a1823)),
% 0.93/1.18 inference(unit_resolution,[status(thm)],[1527, 2305])).
% 0.93/1.18 tff(2308,plain,
% 0.93/1.18 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823))),
% 0.93/1.18 inference(rewrite,[status(thm)],[])).
% 0.93/1.18 tff(2309,plain,
% 0.93/1.18 ((hskp13 | (~ndr1_0) | c0_1(a1823) | (~c2_1(a1823)) | (~c1_1(a1823))) <=> (hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823))),
% 0.93/1.18 inference(rewrite,[status(thm)],[])).
% 0.93/1.18 tff(2310,plain,
% 0.93/1.18 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1823) | (~c2_1(a1823)) | (~c1_1(a1823)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823)))),
% 0.93/1.18 inference(monotonicity,[status(thm)],[2309])).
% 0.93/1.18 tff(2311,plain,
% 0.93/1.18 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1823) | (~c2_1(a1823)) | (~c1_1(a1823)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823))),
% 0.93/1.18 inference(transitivity,[status(thm)],[2310, 2308])).
% 0.93/1.18 tff(2312,plain,
% 0.93/1.18 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1823) | (~c2_1(a1823)) | (~c1_1(a1823)))),
% 0.93/1.18 inference(quant_inst,[status(thm)],[])).
% 0.93/1.18 tff(2313,plain,
% 0.93/1.18 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823)),
% 0.93/1.18 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 0.93/1.18 tff(2314,plain,
% 0.93/1.18 (c0_1(a1823)),
% 0.93/1.18 inference(unit_resolution,[status(thm)],[2313, 102, 1810, 2307, 2306, 22])).
% 0.93/1.18 tff(2315,plain,
% 0.93/1.18 (c3_1(a1823)),
% 0.93/1.18 inference(unit_resolution,[status(thm)],[1511, 2305])).
% 0.93/1.18 tff(2316,plain,
% 0.93/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823)))),
% 0.93/1.18 inference(rewrite,[status(thm)],[])).
% 0.93/1.18 tff(2317,plain,
% 0.93/1.18 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c0_1(a1823)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786))) <=> (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823)))),
% 0.93/1.18 inference(rewrite,[status(thm)],[])).
% 0.93/1.18 tff(2318,plain,
% 0.93/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c0_1(a1823)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823))))),
% 0.93/1.18 inference(monotonicity,[status(thm)],[2317])).
% 0.93/1.18 tff(2319,plain,
% 0.93/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c0_1(a1823)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823)))),
% 1.02/1.18 inference(transitivity,[status(thm)],[2318, 2316])).
% 1.02/1.18 tff(2320,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c0_1(a1823)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(2321,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 1.02/1.18 tff(2322,plain,
% 1.02/1.18 ($false),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2321, 102, 2307, 2306, 2315, 2209, 2201, 2193, 618, 2314])).
% 1.02/1.18 tff(2323,plain,(c2_1(a1771) | hskp6 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.02/1.18 tff(2324,plain,
% 1.02/1.18 (c2_1(a1771)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2323, 254, 225])).
% 1.02/1.18 tff(2325,plain,
% 1.02/1.18 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(2326,plain,
% 1.02/1.18 ((hskp13 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(2327,plain,
% 1.02/1.18 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[2326])).
% 1.02/1.18 tff(2328,plain,
% 1.02/1.18 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.02/1.18 inference(transitivity,[status(thm)],[2327, 2325])).
% 1.02/1.18 tff(2329,plain,
% 1.02/1.18 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(2330,plain,
% 1.02/1.18 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[2329, 2328])).
% 1.02/1.18 tff(2331,plain,
% 1.02/1.18 (hskp13 | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2330, 102, 254, 22])).
% 1.02/1.18 tff(2332,plain,
% 1.02/1.18 (~c1_1(a1771)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2331, 23, 2324])).
% 1.02/1.18 tff(2333,plain,
% 1.02/1.18 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(2334,plain,
% 1.02/1.18 ((hskp6 | hskp4 | (~ndr1_0) | c1_1(a1771) | c0_1(a1771) | (~c2_1(a1771))) <=> (hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(2335,plain,
% 1.02/1.18 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771))))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[2334])).
% 1.02/1.18 tff(2336,plain,
% 1.02/1.18 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771)))),
% 1.02/1.18 inference(transitivity,[status(thm)],[2335, 2333])).
% 1.02/1.18 tff(2337,plain,
% 1.02/1.18 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(2338,plain,
% 1.02/1.18 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 1.02/1.18 tff(2339,plain,
% 1.02/1.18 (hskp4 | c1_1(a1771) | (~c2_1(a1771))),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2338, 102, 225, 254, 1650])).
% 1.02/1.18 tff(2340,plain,
% 1.02/1.18 (hskp4),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2339, 2332, 2324])).
% 1.02/1.18 tff(2341,plain,
% 1.02/1.18 (~c3_1(a1759)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[1639, 2340])).
% 1.02/1.18 tff(2342,plain,
% 1.02/1.18 (c1_1(a1759)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[138, 2340])).
% 1.02/1.18 tff(2343,plain,
% 1.02/1.18 (c0_1(a1759)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2129, 102, 23, 1808, 2342, 1800, 2341, 1984, 1855])).
% 1.02/1.18 tff(2344,plain,
% 1.02/1.18 (hskp3),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2140, 102, 1847, 1808, 2342, 1800, 2341, 1400, 2343])).
% 1.02/1.18 tff(2345,plain,
% 1.02/1.18 (c2_1(a1758)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[556, 2344])).
% 1.02/1.18 tff(2346,plain,
% 1.02/1.18 (c1_1(a1758)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[564, 2344])).
% 1.02/1.18 tff(2347,plain,
% 1.02/1.18 (c0_1(a1758)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[571, 102, 23, 2346, 2345, 22])).
% 1.02/1.18 tff(2348,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(2349,plain,
% 1.02/1.18 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | c1_1(a1771) | (~c3_1(a1771))) <=> (c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(2350,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771))))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[2349])).
% 1.02/1.18 tff(2351,plain,
% 1.02/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)))),
% 1.02/1.18 inference(transitivity,[status(thm)],[2350, 2348])).
% 1.02/1.18 tff(2352,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(2353,plain,
% 1.02/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[2352, 2351])).
% 1.02/1.18 tff(2354,plain,
% 1.02/1.18 (~c3_1(a1771)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2353, 102, 2332, 2342, 2346, 2345, 254, 2341, 1550, 2343, 2347])).
% 1.02/1.18 tff(2355,plain,
% 1.02/1.18 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(2356,plain,
% 1.02/1.18 ((hskp20 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771))) <=> (hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(2357,plain,
% 1.02/1.18 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771))))),
% 1.02/1.18 inference(monotonicity,[status(thm)],[2356])).
% 1.02/1.18 tff(2358,plain,
% 1.02/1.18 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.18 inference(transitivity,[status(thm)],[2357, 2355])).
% 1.02/1.18 tff(2359,plain,
% 1.02/1.18 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.18 inference(quant_inst,[status(thm)],[])).
% 1.02/1.18 tff(2360,plain,
% 1.02/1.18 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[2359, 2358])).
% 1.02/1.18 tff(2361,plain,
% 1.02/1.18 (hskp20 | c3_1(a1771) | (~c2_1(a1771))),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2360, 102, 225, 254, 2180])).
% 1.02/1.18 tff(2362,plain,
% 1.02/1.18 (hskp20),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2361, 2354, 2324])).
% 1.02/1.18 tff(2363,plain,
% 1.02/1.18 (~c3_1(a1786)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2192, 2362])).
% 1.02/1.18 tff(2364,plain,
% 1.02/1.18 (c1_1(a1786)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2200, 2362])).
% 1.02/1.18 tff(2365,plain,
% 1.02/1.18 (c0_1(a1786)),
% 1.02/1.18 inference(unit_resolution,[status(thm)],[2208, 2362])).
% 1.02/1.18 tff(2366,plain,
% 1.02/1.18 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.02/1.18 inference(bind,[status(th)],[])).
% 1.02/1.18 tff(2367,plain,
% 1.02/1.18 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.02/1.18 inference(quant_intro,[status(thm)],[2366])).
% 1.02/1.18 tff(2368,plain,
% 1.02/1.18 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.02/1.18 inference(rewrite,[status(thm)],[])).
% 1.02/1.18 tff(2369,plain,
% 1.02/1.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.02/1.18 inference(bind,[status(th)],[])).
% 1.02/1.18 tff(2370,plain,
% 1.02/1.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.02/1.18 inference(quant_intro,[status(thm)],[2369])).
% 1.02/1.18 tff(2371,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.02/1.18 tff(2372,plain,
% 1.02/1.18 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 1.02/1.18 tff(2373,plain,
% 1.02/1.18 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.02/1.18 inference(modus_ponens,[status(thm)],[2372, 2368])).
% 1.02/1.19 tff(2374,plain,(
% 1.02/1.19 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.02/1.19 inference(skolemize,[status(sab)],[2373])).
% 1.02/1.19 tff(2375,plain,
% 1.02/1.19 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2374, 2367])).
% 1.02/1.19 tff(2376,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2377,plain,
% 1.02/1.19 ((hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2378,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[2377])).
% 1.02/1.19 tff(2379,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.02/1.19 inference(transitivity,[status(thm)],[2378, 2376])).
% 1.02/1.19 tff(2380,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(2381,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 1.02/1.19 tff(2382,plain,
% 1.02/1.19 (hskp28),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2381, 102, 1847, 1808, 2346, 2345, 2375, 1855, 2347])).
% 1.02/1.19 tff(2383,plain,
% 1.02/1.19 (((~hskp28) | c2_1(a1795)) <=> ((~hskp28) | c2_1(a1795))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2384,axiom,((~hskp28) | c2_1(a1795)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.02/1.19 tff(2385,plain,
% 1.02/1.19 ((~hskp28) | c2_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.02/1.19 tff(2386,plain,
% 1.02/1.19 ((~hskp28) | c2_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2385, 2383])).
% 1.02/1.19 tff(2387,plain,
% 1.02/1.19 ((~hskp28) | c2_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2386, 2383])).
% 1.02/1.19 tff(2388,plain,
% 1.02/1.19 ((~hskp28) | c2_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2387, 2383])).
% 1.02/1.19 tff(2389,plain,
% 1.02/1.19 ((~hskp28) | c2_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2388, 2383])).
% 1.02/1.19 tff(2390,plain,
% 1.02/1.19 (c2_1(a1795)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2389, 2382])).
% 1.02/1.19 tff(2391,plain,
% 1.02/1.19 (((~hskp28) | c1_1(a1795)) <=> ((~hskp28) | c1_1(a1795))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2392,axiom,((~hskp28) | c1_1(a1795)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.02/1.19 tff(2393,plain,
% 1.02/1.19 ((~hskp28) | c1_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 1.02/1.19 tff(2394,plain,
% 1.02/1.19 ((~hskp28) | c1_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2393, 2391])).
% 1.02/1.19 tff(2395,plain,
% 1.02/1.19 ((~hskp28) | c1_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2394, 2391])).
% 1.02/1.19 tff(2396,plain,
% 1.02/1.19 ((~hskp28) | c1_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2395, 2391])).
% 1.02/1.19 tff(2397,plain,
% 1.02/1.19 ((~hskp28) | c1_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2396, 2391])).
% 1.02/1.19 tff(2398,plain,
% 1.02/1.19 (c1_1(a1795)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2397, 2382])).
% 1.02/1.19 tff(2399,plain,
% 1.02/1.19 (((~hskp28) | c0_1(a1795)) <=> ((~hskp28) | c0_1(a1795))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2400,axiom,((~hskp28) | c0_1(a1795)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.02/1.19 tff(2401,plain,
% 1.02/1.19 ((~hskp28) | c0_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 1.02/1.19 tff(2402,plain,
% 1.02/1.19 ((~hskp28) | c0_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2401, 2399])).
% 1.02/1.19 tff(2403,plain,
% 1.02/1.19 ((~hskp28) | c0_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2402, 2399])).
% 1.02/1.19 tff(2404,plain,
% 1.02/1.19 ((~hskp28) | c0_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2403, 2399])).
% 1.02/1.19 tff(2405,plain,
% 1.02/1.19 ((~hskp28) | c0_1(a1795)),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2404, 2399])).
% 1.02/1.19 tff(2406,plain,
% 1.02/1.19 (c0_1(a1795)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2405, 2382])).
% 1.02/1.19 tff(2407,plain,
% 1.02/1.19 (~c3_1(a1758)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[578, 2344])).
% 1.02/1.19 tff(2408,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2409,plain,
% 1.02/1.19 ((hskp15 | (~ndr1_0) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771))) <=> (hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2410,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[2409])).
% 1.02/1.19 tff(2411,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[2410, 2408])).
% 1.02/1.19 tff(2412,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(2413,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2412, 2411])).
% 1.02/1.19 tff(2414,plain,
% 1.02/1.19 (hskp15),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2413, 102, 2332, 2324, 2346, 2407, 2164, 2354, 2347])).
% 1.02/1.19 tff(2415,plain,
% 1.02/1.19 (~c3_1(a1779)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2221, 2414])).
% 1.02/1.19 tff(2416,plain,
% 1.02/1.19 (~c2_1(a1779)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2227, 2414])).
% 1.02/1.19 tff(2417,plain,
% 1.02/1.19 (c0_1(a1779)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2235, 2414])).
% 1.02/1.19 tff(2418,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2419,plain,
% 1.02/1.19 ((hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771))) <=> (hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(2420,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771))))),
% 1.02/1.19 inference(monotonicity,[status(thm)],[2419])).
% 1.02/1.19 tff(2421,plain,
% 1.02/1.19 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.19 inference(transitivity,[status(thm)],[2420, 2418])).
% 1.02/1.19 tff(2422,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.02/1.19 inference(quant_inst,[status(thm)],[])).
% 1.02/1.19 tff(2423,plain,
% 1.02/1.19 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.02/1.19 tff(2424,plain,
% 1.02/1.19 (hskp22),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2423, 102, 2332, 2324, 2346, 2345, 2407, 770, 2354])).
% 1.02/1.19 tff(2425,plain,
% 1.02/1.19 (~c2_1(a1799)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[494, 2424])).
% 1.02/1.19 tff(2426,plain,
% 1.02/1.19 (~c0_1(a1799)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[500, 2424])).
% 1.02/1.19 tff(2427,plain,
% 1.02/1.19 (c3_1(a1799)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[508, 2424])).
% 1.02/1.19 tff(2428,plain,
% 1.02/1.19 (~hskp18),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2273, 2427, 23, 2426, 2425])).
% 1.02/1.19 tff(2429,plain,
% 1.02/1.19 (~hskp29),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2296, 2428, 2417, 2416, 2415])).
% 1.02/1.19 tff(2430,plain,
% 1.02/1.19 (hskp30 | hskp29),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2303, 102, 2346, 2345, 2407, 1496])).
% 1.02/1.19 tff(2431,plain,
% 1.02/1.19 (hskp30),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[2430, 2429])).
% 1.02/1.19 tff(2432,plain,
% 1.02/1.19 (c3_1(a1823)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1511, 2431])).
% 1.02/1.19 tff(2433,plain,
% 1.02/1.19 (c2_1(a1823)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1519, 2431])).
% 1.02/1.19 tff(2434,plain,
% 1.02/1.19 (c1_1(a1823)),
% 1.02/1.19 inference(unit_resolution,[status(thm)],[1527, 2431])).
% 1.03/1.19 tff(2435,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2436,plain,
% 1.03/1.19 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786))) <=> (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2437,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[2436])).
% 1.03/1.19 tff(2438,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[2437, 2435])).
% 1.03/1.19 tff(2439,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(2440,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[2439, 2438])).
% 1.03/1.19 tff(2441,plain,
% 1.03/1.19 ($false),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2440, 102, 2434, 2433, 2432, 2406, 2398, 2390, 2365, 2364, 2363, 618])).
% 1.03/1.19 tff(2442,plain,(hskp13 | hskp6 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.19 tff(2443,plain,
% 1.03/1.19 (hskp13),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2442, 254, 225])).
% 1.03/1.19 tff(2444,plain,
% 1.03/1.19 (hskp3),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[264, 2443, 225, 254])).
% 1.03/1.19 tff(2445,plain,
% 1.03/1.19 (c1_1(a1758)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[564, 2444])).
% 1.03/1.19 tff(2446,plain,
% 1.03/1.19 (~c3_1(a1758)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[578, 2444])).
% 1.03/1.19 tff(2447,plain,
% 1.03/1.19 (c1_1(a1771)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[234, 2443])).
% 1.03/1.19 tff(2448,assumption,(~hskp17), introduced(assumption)).
% 1.03/1.19 tff(2449,plain,
% 1.03/1.19 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2450,plain,
% 1.03/1.19 ((hskp17 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2451,plain,
% 1.03/1.19 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[2450])).
% 1.03/1.19 tff(2452,plain,
% 1.03/1.19 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[2451, 2449])).
% 1.03/1.19 tff(2453,plain,
% 1.03/1.19 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(2454,plain,
% 1.03/1.19 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[2453, 2452])).
% 1.03/1.19 tff(2455,plain,
% 1.03/1.19 (hskp17 | (~c3_1(a1771)) | (~c1_1(a1771))),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2454, 102, 1847, 1808, 2324, 1800, 1217])).
% 1.03/1.19 tff(2456,plain,
% 1.03/1.19 (~c3_1(a1771)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2455, 2448, 2447])).
% 1.03/1.19 tff(2457,plain,
% 1.03/1.19 (hskp20),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2361, 2456, 2324])).
% 1.03/1.19 tff(2458,plain,
% 1.03/1.19 (~c3_1(a1786)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2192, 2457])).
% 1.03/1.19 tff(2459,plain,
% 1.03/1.19 (c1_1(a1786)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2200, 2457])).
% 1.03/1.19 tff(2460,plain,
% 1.03/1.19 (c0_1(a1786)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2208, 2457])).
% 1.03/1.19 tff(2461,assumption,(hskp30), introduced(assumption)).
% 1.03/1.19 tff(2462,plain,
% 1.03/1.19 (c3_1(a1823)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1511, 2461])).
% 1.03/1.19 tff(2463,plain,
% 1.03/1.19 (c2_1(a1823)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1519, 2461])).
% 1.03/1.19 tff(2464,plain,
% 1.03/1.19 (c1_1(a1823)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1527, 2461])).
% 1.03/1.19 tff(2465,plain,
% 1.03/1.19 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2466,plain,
% 1.03/1.19 ((hskp17 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2467,plain,
% 1.03/1.19 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[2466])).
% 1.03/1.19 tff(2468,plain,
% 1.03/1.19 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[2467, 2465])).
% 1.03/1.19 tff(2469,plain,
% 1.03/1.19 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(2470,plain,
% 1.03/1.19 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[2469, 2468])).
% 1.03/1.19 tff(2471,plain,
% 1.03/1.19 ($false),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2470, 102, 2448, 2464, 2463, 2462, 1847, 1808, 1800, 1217])).
% 1.03/1.19 tff(2472,plain,((~hskp30) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.03/1.19 tff(2473,plain,
% 1.03/1.19 (~hskp30),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2472, 2448])).
% 1.03/1.19 tff(2474,plain,
% 1.03/1.19 (hskp30 | hskp29 | c3_1(a1771) | (~c1_1(a1771))),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[1502, 102, 2324, 1496])).
% 1.03/1.19 tff(2475,plain,
% 1.03/1.19 (hskp29),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2474, 2473, 2447, 2456])).
% 1.03/1.19 tff(2476,plain,
% 1.03/1.19 (c3_1(a1805)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[907, 2475])).
% 1.03/1.19 tff(2477,plain,
% 1.03/1.19 (c2_1(a1805)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[924, 2475])).
% 1.03/1.19 tff(2478,plain,
% 1.03/1.19 (c0_1(a1805)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[916, 2475])).
% 1.03/1.19 tff(2479,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2480,plain,
% 1.03/1.19 (((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786))) <=> (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2481,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[2480])).
% 1.03/1.19 tff(2482,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[2481, 2479])).
% 1.03/1.19 tff(2483,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(2484,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[2483, 2482])).
% 1.03/1.19 tff(2485,plain,
% 1.03/1.19 (~c1_1(a1805)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2484, 102, 2478, 2477, 2476, 2460, 2459, 2458, 618])).
% 1.03/1.19 tff(2486,plain,
% 1.03/1.19 (c2_1(a1758)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[556, 2444])).
% 1.03/1.19 tff(2487,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2488,plain,
% 1.03/1.19 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805))) <=> (c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2489,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[2488])).
% 1.03/1.19 tff(2490,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[2489, 2487])).
% 1.03/1.19 tff(2491,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.03/1.19 inference(quant_inst,[status(thm)],[])).
% 1.03/1.19 tff(2492,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))),
% 1.03/1.19 inference(modus_ponens,[status(thm)],[2491, 2490])).
% 1.03/1.19 tff(2493,plain,
% 1.03/1.19 (~c0_1(a1758)),
% 1.03/1.19 inference(unit_resolution,[status(thm)],[2492, 102, 2478, 2477, 2460, 2459, 2445, 2486, 2458, 736, 2485])).
% 1.03/1.19 tff(2494,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2495,plain,
% 1.03/1.19 (((~ndr1_0) | c1_1(a1805) | (~c2_1(a1805)) | (~c3_1(a1805)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758))) <=> (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.03/1.19 inference(rewrite,[status(thm)],[])).
% 1.03/1.19 tff(2496,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1805) | (~c2_1(a1805)) | (~c3_1(a1805)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))))),
% 1.03/1.19 inference(monotonicity,[status(thm)],[2495])).
% 1.03/1.19 tff(2497,plain,
% 1.03/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1805) | (~c2_1(a1805)) | (~c3_1(a1805)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.03/1.19 inference(transitivity,[status(thm)],[2496, 2494])).
% 1.03/1.19 tff(2498,plain,
% 1.03/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1805) | (~c2_1(a1805)) | (~c3_1(a1805)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2499,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2498, 2497])).
% 1.03/1.20 tff(2500,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2499, 102, 2478, 2477, 2476, 2486, 2446, 753, 2493, 2485])).
% 1.03/1.20 tff(2501,plain,(hskp17 | hskp6 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2502,plain,
% 1.03/1.20 (hskp17),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2501, 254, 225])).
% 1.03/1.20 tff(2503,plain,
% 1.03/1.20 (~c1_1(a1781)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1073, 2502])).
% 1.03/1.20 tff(2504,plain,
% 1.03/1.20 (c3_1(a1781)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1089, 2502])).
% 1.03/1.20 tff(2505,plain,
% 1.03/1.20 (c2_1(a1781)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1097, 2502])).
% 1.03/1.20 tff(2506,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2507,plain,
% 1.03/1.20 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781))) <=> (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2508,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2507])).
% 1.03/1.20 tff(2509,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2508, 2506])).
% 1.03/1.20 tff(2510,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2511,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 1.03/1.20 tff(2512,plain,
% 1.03/1.20 ((~c0_1(a1758)) | (~c0_1(a1781))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2511, 102, 1242, 643, 661, 1240, 642, 736])).
% 1.03/1.20 tff(2513,plain,
% 1.03/1.20 (~c0_1(a1758)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2512, 1229])).
% 1.03/1.20 tff(2514,plain,
% 1.03/1.20 (c0_1(a1758) | (~c0_1(a1781))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1574, 102, 1242, 1241, 661, 1240, 642, 753])).
% 1.03/1.20 tff(2515,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2514, 2513, 1229])).
% 1.03/1.20 tff(2516,plain,((~c0_1(a1781)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1758)) | c1_1(a1781) | c3_1(a1758) | (~c1_1(a1758))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2517,plain,
% 1.03/1.20 (~c0_1(a1781)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2516, 2505, 2504, 2486, 2503, 2446, 2445])).
% 1.03/1.20 tff(2518,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2519,plain,
% 1.03/1.20 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781))) <=> (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2520,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2519])).
% 1.03/1.20 tff(2521,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2520, 2518])).
% 1.03/1.20 tff(2522,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2523,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 1.03/1.20 tff(2524,plain,
% 1.03/1.20 (~c0_1(a1758)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2523, 102, 2504, 2445, 2486, 2503, 2446, 1550, 2517])).
% 1.03/1.20 tff(2525,assumption,(~c0_1(a1758)), introduced(assumption)).
% 1.03/1.20 tff(2526,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2527,plain,
% 1.03/1.20 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758))) <=> (c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2528,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2527])).
% 1.03/1.20 tff(2529,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2528, 2526])).
% 1.03/1.20 tff(2530,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2531,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2530, 2529])).
% 1.03/1.20 tff(2532,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2531, 102, 1242, 1241, 1169, 1170, 661, 1240, 1584, 642, 753, 2525])).
% 1.03/1.20 tff(2533,plain,((~hskp7) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1758)) | c1_1(a1781) | c3_1(a1758) | c0_1(a1758)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2534,plain,
% 1.03/1.20 (~hskp7),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2533, 2505, 2504, 2486, 2503, 2446, 2524])).
% 1.03/1.20 tff(2535,assumption,(~hskp7), introduced(assumption)).
% 1.03/1.20 tff(2536,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2537,plain,
% 1.03/1.20 ((hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2538,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2537])).
% 1.03/1.20 tff(2539,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2538, 2536])).
% 1.03/1.20 tff(2540,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2541,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 1.03/1.20 tff(2542,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2541, 102, 2535, 1847, 1241, 1800, 1240, 983, 2010, 1])).
% 1.03/1.20 tff(2543,plain,(c2_1(a1783) | hskp7 | (~c3_1(a1781)) | c1_1(a1781) | c0_1(a1781)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2544,plain,
% 1.03/1.20 (c2_1(a1783)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2543, 2534, 2504, 2503, 2517])).
% 1.03/1.20 tff(2545,plain,
% 1.03/1.20 (hskp4 | c0_1(a1781)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1907, 102, 225, 2505, 2503, 1650])).
% 1.03/1.20 tff(2546,plain,
% 1.03/1.20 (hskp4),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2545, 2517])).
% 1.03/1.20 tff(2547,plain,
% 1.03/1.20 (~c2_1(a1759)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[881, 2546])).
% 1.03/1.20 tff(2548,plain,
% 1.03/1.20 (c1_1(a1759)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[138, 2546])).
% 1.03/1.20 tff(2549,plain,
% 1.03/1.20 (hskp7 | c0_1(a1759)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1596, 102, 2504, 2548, 2503, 2547, 983, 2517])).
% 1.03/1.20 tff(2550,plain,
% 1.03/1.20 (c0_1(a1759)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2549, 2534])).
% 1.03/1.20 tff(2551,plain,
% 1.03/1.20 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(2552,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[2551])).
% 1.03/1.20 tff(2553,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2554,plain,
% 1.03/1.20 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(2555,plain,
% 1.03/1.20 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[2554])).
% 1.03/1.20 tff(2556,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.03/1.20 tff(2557,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 1.03/1.20 tff(2558,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2557, 2553])).
% 1.03/1.20 tff(2559,plain,(
% 1.03/1.20 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.03/1.20 inference(skolemize,[status(sab)],[2558])).
% 1.03/1.20 tff(2560,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2559, 2552])).
% 1.03/1.20 tff(2561,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2562,plain,
% 1.03/1.20 ((hskp18 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758))) <=> (hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2563,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2562])).
% 1.03/1.20 tff(2564,plain,
% 1.03/1.20 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2563, 2561])).
% 1.03/1.20 tff(2565,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2566,plain,
% 1.03/1.20 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2565, 2564])).
% 1.03/1.20 tff(2567,plain,
% 1.03/1.20 (hskp18 | (~c0_1(a1759))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2566, 102, 2548, 2445, 2547, 2446, 2560, 2524])).
% 1.03/1.20 tff(2568,plain,
% 1.03/1.20 (hskp18),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2567, 2550])).
% 1.03/1.20 tff(2569,plain,
% 1.03/1.20 (~c3_1(a1782)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2252, 2568])).
% 1.03/1.20 tff(2570,plain,
% 1.03/1.20 (~c2_1(a1782)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2258, 2568])).
% 1.03/1.20 tff(2571,plain,
% 1.03/1.20 (~c1_1(a1782)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2264, 2568])).
% 1.03/1.20 tff(2572,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2573,plain,
% 1.03/1.20 (((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782) | c3_1(a1782) | c2_1(a1782) | c0_1(a1782)) <=> (c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2574,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782) | c3_1(a1782) | c2_1(a1782) | c0_1(a1782))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2573])).
% 1.03/1.20 tff(2575,plain,
% 1.03/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782) | c3_1(a1782) | c2_1(a1782) | c0_1(a1782))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2574, 2572])).
% 1.03/1.20 tff(2576,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782) | c3_1(a1782) | c2_1(a1782) | c0_1(a1782))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2577,plain,
% 1.03/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2576, 2575])).
% 1.03/1.20 tff(2578,plain,
% 1.03/1.20 (c0_1(a1782)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2577, 102, 1847, 1808, 2571, 2570, 2569, 1453, 2544])).
% 1.03/1.20 tff(2579,plain,
% 1.03/1.20 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.03/1.20 inference(bind,[status(th)],[])).
% 1.03/1.20 tff(2580,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/1.20 inference(quant_intro,[status(thm)],[2579])).
% 1.03/1.20 tff(2581,plain,
% 1.03/1.20 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2582,plain,
% 1.03/1.20 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_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) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(2583,plain,
% 1.03/1.21 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[2582])).
% 1.03/1.21 tff(2584,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.03/1.21 tff(2585,plain,
% 1.03/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 1.03/1.21 tff(2586,plain,
% 1.03/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2585, 2581])).
% 1.03/1.21 tff(2587,plain,(
% 1.03/1.21 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/1.21 inference(skolemize,[status(sab)],[2586])).
% 1.03/1.21 tff(2588,plain,
% 1.03/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2587, 2580])).
% 1.03/1.21 tff(2589,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2590,plain,
% 1.03/1.21 ((hskp5 | (~ndr1_0) | c2_1(a1782) | c1_1(a1782) | (~c0_1(a1782)) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781))) <=> (hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2591,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1782) | c1_1(a1782) | (~c0_1(a1782)) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2590])).
% 1.03/1.21 tff(2592,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1782) | c1_1(a1782) | (~c0_1(a1782)) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2591, 2589])).
% 1.03/1.21 tff(2593,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1782) | c1_1(a1782) | (~c0_1(a1782)) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2594,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 1.03/1.21 tff(2595,plain,
% 1.03/1.21 (hskp5 | (~c0_1(a1782))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2594, 102, 2505, 2571, 2570, 2503, 2588, 2517])).
% 1.03/1.21 tff(2596,plain,
% 1.03/1.21 (hskp5),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2595, 2578])).
% 1.03/1.21 tff(2597,plain,
% 1.03/1.21 (((~hskp5) | (~c3_1(a1760))) <=> ((~hskp5) | (~c3_1(a1760)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2598,plain,
% 1.03/1.21 (((~c3_1(a1760)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1760)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2599,axiom,((~c3_1(a1760)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.03/1.21 tff(2600,plain,
% 1.03/1.21 ((~hskp5) | (~c3_1(a1760))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2599, 2598])).
% 1.03/1.21 tff(2601,plain,
% 1.03/1.21 ((~hskp5) | (~c3_1(a1760))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2600, 2597])).
% 1.03/1.21 tff(2602,plain,
% 1.03/1.21 (~c3_1(a1760)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2601, 2596])).
% 1.03/1.21 tff(2603,plain,
% 1.03/1.21 (((~hskp5) | (~c2_1(a1760))) <=> ((~hskp5) | (~c2_1(a1760)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2604,plain,
% 1.03/1.21 (((~c2_1(a1760)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1760)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2605,axiom,((~c2_1(a1760)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.03/1.21 tff(2606,plain,
% 1.03/1.21 ((~hskp5) | (~c2_1(a1760))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 1.03/1.21 tff(2607,plain,
% 1.03/1.21 ((~hskp5) | (~c2_1(a1760))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2606, 2603])).
% 1.03/1.21 tff(2608,plain,
% 1.03/1.21 (~c2_1(a1760)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2607, 2596])).
% 1.03/1.21 tff(2609,plain,
% 1.03/1.21 (((~hskp5) | (~c0_1(a1760))) <=> ((~hskp5) | (~c0_1(a1760)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2610,plain,
% 1.03/1.21 (((~c0_1(a1760)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1760)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2611,axiom,((~c0_1(a1760)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.03/1.21 tff(2612,plain,
% 1.03/1.21 ((~hskp5) | (~c0_1(a1760))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2611, 2610])).
% 1.03/1.21 tff(2613,plain,
% 1.03/1.21 ((~hskp5) | (~c0_1(a1760))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2612, 2609])).
% 1.03/1.21 tff(2614,plain,
% 1.03/1.21 (~c0_1(a1760)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2613, 2596])).
% 1.03/1.21 tff(2615,plain,
% 1.03/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2616,plain,
% 1.03/1.21 (((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1760) | c1_1(a1760) | c3_1(a1760) | c3_1(a1760) | c2_1(a1760) | c0_1(a1760)) <=> (c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2617,plain,
% 1.03/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1760) | c1_1(a1760) | c3_1(a1760) | c3_1(a1760) | c2_1(a1760) | c0_1(a1760))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2616])).
% 1.03/1.21 tff(2618,plain,
% 1.03/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1760) | c1_1(a1760) | c3_1(a1760) | c3_1(a1760) | c2_1(a1760) | c0_1(a1760))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2617, 2615])).
% 1.03/1.21 tff(2619,plain,
% 1.03/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1760) | c1_1(a1760) | c3_1(a1760) | c3_1(a1760) | c2_1(a1760) | c0_1(a1760))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2620,plain,
% 1.03/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2619, 2618])).
% 1.03/1.21 tff(2621,plain,
% 1.03/1.21 (c1_1(a1760)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2620, 102, 1847, 1808, 2614, 2608, 2602, 1453, 2544])).
% 1.03/1.21 tff(2622,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2623,plain,
% 1.03/1.21 ((hskp7 | (~ndr1_0) | c2_1(a1760) | c0_1(a1760) | (~c1_1(a1760)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2624,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1760) | c0_1(a1760) | (~c1_1(a1760)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2623])).
% 1.03/1.21 tff(2625,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1760) | c0_1(a1760) | (~c1_1(a1760)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2624, 2622])).
% 1.03/1.21 tff(2626,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1760) | c0_1(a1760) | (~c1_1(a1760)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2627,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 1.03/1.21 tff(2628,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2627, 102, 2534, 2504, 2503, 2614, 2608, 983, 2517, 2621])).
% 1.03/1.21 tff(2629,plain,(c0_1(a1771) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2630,plain,
% 1.03/1.21 (c0_1(a1771)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2629, 225])).
% 1.03/1.21 tff(2631,plain,
% 1.03/1.21 (~hskp13),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[223, 2630])).
% 1.03/1.21 tff(2632,assumption,(hskp4), introduced(assumption)).
% 1.03/1.21 tff(2633,plain,
% 1.03/1.21 (~c3_1(a1759)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1639, 2632])).
% 1.03/1.21 tff(2634,plain,
% 1.03/1.21 (c1_1(a1759)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[138, 2632])).
% 1.03/1.21 tff(2635,plain,
% 1.03/1.21 (~c0_1(a1759)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2145, 2634, 35, 2633])).
% 1.03/1.21 tff(2636,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2129, 102, 23, 1808, 2634, 1800, 2633, 1984, 2635, 1855])).
% 1.03/1.21 tff(2637,plain,((~hskp4) | hskp13 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2638,plain,
% 1.03/1.21 (~hskp4),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2637, 35, 2631])).
% 1.03/1.21 tff(2639,plain,
% 1.03/1.21 (~hskp23),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1837, 2638, 35])).
% 1.03/1.21 tff(2640,assumption,(c0_1(a1771)), introduced(assumption)).
% 1.03/1.21 tff(2641,plain,
% 1.03/1.21 (~hskp13),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[223, 2640])).
% 1.03/1.21 tff(2642,plain,
% 1.03/1.21 (~c2_1(a1783)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1854, 2641])).
% 1.03/1.21 tff(2643,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2644,plain,
% 1.03/1.21 ((hskp3 | (~ndr1_0) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2645,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2644])).
% 1.03/1.21 tff(2646,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2645, 2643])).
% 1.03/1.21 tff(2647,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2648,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 1.03/1.21 tff(2649,plain,
% 1.03/1.21 (~c3_1(a1771)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2648, 102, 35, 1808, 652, 1800, 2640, 11, 2642])).
% 1.03/1.21 tff(2650,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2651,plain,
% 1.03/1.21 ((hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2652,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2651])).
% 1.03/1.21 tff(2653,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2652, 2650])).
% 1.03/1.21 tff(2654,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2655,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2654, 2653])).
% 1.03/1.21 tff(2656,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2655, 102, 35, 1847, 1808, 652, 1800, 2640, 1400, 2649])).
% 1.03/1.21 tff(2657,plain,((~c1_1(a1771)) | hskp3 | (~c0_1(a1771))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2658,plain,
% 1.03/1.21 (~c1_1(a1771)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2657, 35, 2630])).
% 1.03/1.21 tff(2659,plain,
% 1.03/1.21 (~hskp0),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1679, 2638, 225])).
% 1.03/1.21 tff(2660,assumption,(~c1_1(a1771)), introduced(assumption)).
% 1.03/1.21 tff(2661,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2662,plain,
% 1.03/1.21 ((hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c3_1(a1771)) <=> (hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2663,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c3_1(a1771))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2662])).
% 1.03/1.21 tff(2664,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c3_1(a1771))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2663, 2661])).
% 1.03/1.21 tff(2665,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c3_1(a1771))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2666,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2665, 2664])).
% 1.03/1.21 tff(2667,plain,
% 1.03/1.21 (c1_1(a1771) | c3_1(a1771)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2666, 102, 2641, 1808, 1809, 1800, 177, 2642])).
% 1.03/1.21 tff(2668,plain,
% 1.03/1.21 (c3_1(a1771)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2667, 2660])).
% 1.03/1.21 tff(2669,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2670,plain,
% 1.03/1.21 ((hskp27 | (~ndr1_0) | c2_1(a1771) | c1_1(a1771) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2671,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1771) | c1_1(a1771) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2670])).
% 1.03/1.21 tff(2672,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1771) | c1_1(a1771) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2671, 2669])).
% 1.03/1.21 tff(2673,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1771) | c1_1(a1771) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2674,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 1.03/1.21 tff(2675,plain,
% 1.03/1.21 (hskp27 | c1_1(a1771)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2674, 102, 1808, 1809, 1800, 2640, 1881, 2642])).
% 1.03/1.21 tff(2676,plain,
% 1.03/1.21 (hskp27),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2675, 2660])).
% 1.03/1.21 tff(2677,plain,
% 1.03/1.21 (c3_1(a1756)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[342, 2676])).
% 1.03/1.21 tff(2678,plain,
% 1.03/1.21 (c1_1(a1756)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[350, 2676])).
% 1.03/1.21 tff(2679,plain,
% 1.03/1.21 (c0_1(a1756)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[358, 2676])).
% 1.03/1.21 tff(2680,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2681,plain,
% 1.03/1.21 ((hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1771) | c1_1(a1771) | (~c3_1(a1771))) <=> (hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2682,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2681])).
% 1.03/1.21 tff(2683,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.03/1.21 tff(2684,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2685,plain,
% 1.03/1.21 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.03/1.21 tff(2686,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2685, 102, 1864, 2679, 2678, 2677, 2660, 1809, 1735, 2668])).
% 1.03/1.21 tff(2687,plain,(c1_1(a1771) | hskp0 | c2_1(a1771) | (~c0_1(a1771))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2688,plain,
% 1.03/1.21 (c2_1(a1771)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2687, 2659, 2658, 2630])).
% 1.03/1.21 tff(2689,plain,
% 1.03/1.21 (~c2_1(a1783)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1854, 2631])).
% 1.03/1.21 tff(2690,plain,
% 1.03/1.21 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2691,plain,
% 1.03/1.21 ((hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771))) <=> (hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2692,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2691])).
% 1.03/1.22 tff(2693,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2692, 2690])).
% 1.03/1.22 tff(2694,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2695,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 1.03/1.22 tff(2696,plain,
% 1.03/1.22 (hskp23 | c3_1(a1771) | (~c2_1(a1771))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2695, 102, 1847, 1808, 2658, 1927, 2689])).
% 1.03/1.22 tff(2697,plain,
% 1.03/1.22 (c3_1(a1771)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2696, 2688, 2639])).
% 1.03/1.22 tff(2698,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2699,plain,
% 1.03/1.22 ((hskp11 | (~ndr1_0) | c1_1(a1771) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783))) <=> (hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2700,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1771) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2699])).
% 1.03/1.22 tff(2701,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1771) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2700, 2698])).
% 1.03/1.22 tff(2702,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1771) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2703,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.03/1.22 tff(2704,plain,
% 1.03/1.22 (hskp11 | (~c3_1(a1771))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2703, 102, 1847, 2658, 1800, 2630, 860, 2689])).
% 1.03/1.22 tff(2705,plain,
% 1.03/1.22 (hskp11),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2704, 2697])).
% 1.03/1.22 tff(2706,plain,
% 1.03/1.22 (~c2_1(a1768)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1025, 2705])).
% 1.03/1.22 tff(2707,plain,
% 1.03/1.22 (c0_1(a1768)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1033, 2705])).
% 1.03/1.22 tff(2708,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2709,plain,
% 1.03/1.22 (((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1771) | (~c2_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2710,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1771) | (~c2_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2709])).
% 1.03/1.22 tff(2711,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1771) | (~c2_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2710, 2708])).
% 1.03/1.22 tff(2712,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1771) | (~c2_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2713,plain,
% 1.03/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2712, 2711])).
% 1.03/1.22 tff(2714,plain,
% 1.03/1.22 (~c1_1(a1768)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2713, 102, 1847, 1808, 2658, 2688, 2707, 1800, 2630, 2706, 433])).
% 1.03/1.22 tff(2715,plain,
% 1.03/1.22 (c3_1(a1768)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1081, 2705])).
% 1.03/1.22 tff(2716,plain,
% 1.03/1.22 (hskp27),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1958, 102, 1808, 2707, 1800, 2706, 1881, 2689, 2714])).
% 1.03/1.22 tff(2717,plain,
% 1.03/1.22 (c3_1(a1756)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[342, 2716])).
% 1.03/1.22 tff(2718,plain,
% 1.03/1.22 (c1_1(a1756)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[350, 2716])).
% 1.03/1.22 tff(2719,plain,
% 1.03/1.22 (c0_1(a1756)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[358, 2716])).
% 1.03/1.22 tff(2720,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1753, 102, 2659, 2719, 2718, 2717, 2715, 2706, 1735, 2714])).
% 1.03/1.22 tff(2721,plain,(hskp3 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(2722,plain,
% 1.03/1.22 (hskp3),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2721, 225])).
% 1.03/1.22 tff(2723,plain,
% 1.03/1.22 (c2_1(a1758)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[556, 2722])).
% 1.03/1.22 tff(2724,plain,
% 1.03/1.22 (c1_1(a1758)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[564, 2722])).
% 1.03/1.22 tff(2725,plain,
% 1.03/1.22 (c0_1(a1758)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[571, 102, 2631, 2724, 2723, 22])).
% 1.03/1.22 tff(2726,plain,
% 1.03/1.22 (~c3_1(a1758)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[578, 2722])).
% 1.03/1.22 tff(2727,plain,
% 1.03/1.22 (hskp14),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2090, 102, 1808, 2723, 1800, 2726, 2083, 2689, 2725])).
% 1.03/1.22 tff(2728,plain,
% 1.03/1.22 (~c0_1(a1777)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2096, 2727])).
% 1.03/1.22 tff(2729,plain,
% 1.03/1.22 (c2_1(a1777)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2104, 2727])).
% 1.03/1.22 tff(2730,plain,
% 1.03/1.22 (~c1_1(a1777)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2111, 102, 2631, 2729, 2728, 22])).
% 1.03/1.22 tff(2731,plain,
% 1.03/1.22 (~c3_1(a1777)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2169, 2727])).
% 1.03/1.22 tff(2732,plain,
% 1.03/1.22 (hskp20),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2186, 102, 225, 2729, 2728, 2731, 2180])).
% 1.03/1.22 tff(2733,plain,
% 1.03/1.22 (~c3_1(a1786)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2192, 2732])).
% 1.03/1.22 tff(2734,plain,
% 1.03/1.22 (c1_1(a1786)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2200, 2732])).
% 1.03/1.22 tff(2735,plain,
% 1.03/1.22 (c0_1(a1786)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2208, 2732])).
% 1.03/1.22 tff(2736,plain,
% 1.03/1.22 (hskp15),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2215, 102, 2735, 2734, 2729, 2733, 2731, 2164, 2730])).
% 1.03/1.22 tff(2737,plain,
% 1.03/1.22 (~c3_1(a1779)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2221, 2736])).
% 1.03/1.22 tff(2738,plain,
% 1.03/1.22 (~c2_1(a1779)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2227, 2736])).
% 1.03/1.22 tff(2739,plain,
% 1.03/1.22 (c0_1(a1779)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2235, 2736])).
% 1.03/1.22 tff(2740,plain,
% 1.03/1.22 (hskp22),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2242, 102, 2729, 2724, 2723, 2731, 2726, 770, 2730])).
% 1.03/1.22 tff(2741,plain,
% 1.03/1.22 (~c2_1(a1799)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[494, 2740])).
% 1.03/1.22 tff(2742,plain,
% 1.03/1.22 (~c0_1(a1799)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[500, 2740])).
% 1.03/1.22 tff(2743,plain,
% 1.03/1.22 (c3_1(a1799)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[508, 2740])).
% 1.03/1.22 tff(2744,plain,
% 1.03/1.22 (~hskp18),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2273, 2743, 2631, 2742, 2741])).
% 1.03/1.22 tff(2745,plain,
% 1.03/1.22 (~hskp29),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2296, 2744, 2739, 2738, 2737])).
% 1.03/1.22 tff(2746,plain,
% 1.03/1.22 (hskp30 | hskp29),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2303, 102, 2724, 2723, 2726, 1496])).
% 1.03/1.22 tff(2747,plain,
% 1.03/1.22 (hskp30),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2746, 2745])).
% 1.03/1.22 tff(2748,plain,
% 1.03/1.22 (hskp17),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2472, 2747])).
% 1.03/1.22 tff(2749,plain,
% 1.03/1.22 (c3_1(a1781)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1089, 2748])).
% 1.03/1.22 tff(2750,plain,
% 1.03/1.22 (~c1_1(a1781)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1073, 2748])).
% 1.03/1.22 tff(2751,plain,
% 1.03/1.22 (c2_1(a1781)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1097, 2748])).
% 1.03/1.22 tff(2752,plain,
% 1.03/1.22 (~c0_1(a1781)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2516, 2749, 2751, 2723, 2750, 2726, 2724])).
% 1.03/1.22 tff(2753,plain,
% 1.03/1.22 (hskp7),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2543, 2752, 2689, 2750, 2749])).
% 1.03/1.22 tff(2754,plain,
% 1.03/1.22 (~c1_1(a1763)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[996, 2753])).
% 1.03/1.22 tff(2755,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2756,plain,
% 1.03/1.22 ((hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777))) <=> (hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2757,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2756])).
% 1.03/1.22 tff(2758,plain,
% 1.03/1.22 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2757, 2755])).
% 1.03/1.22 tff(2759,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2760,plain,
% 1.03/1.22 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 1.03/1.22 tff(2761,plain,
% 1.03/1.22 (hskp23),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2760, 102, 1847, 1808, 2729, 2731, 1927, 2689, 2730])).
% 1.03/1.22 tff(2762,plain,
% 1.03/1.22 (~c3_1(a1807)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1816, 2761])).
% 1.03/1.22 tff(2763,plain,
% 1.03/1.22 (~c0_1(a1807)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1828, 2761])).
% 1.03/1.22 tff(2764,plain,
% 1.03/1.22 (c3_1(a1763)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1004, 2753])).
% 1.03/1.22 tff(2765,plain,
% 1.03/1.22 (c0_1(a1763)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1012, 2753])).
% 1.03/1.22 tff(2766,plain,
% 1.03/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2767,plain,
% 1.03/1.22 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1807) | c0_1(a1807) | (~c2_1(a1807))) <=> (c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(2768,plain,
% 1.07/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1807) | c0_1(a1807) | (~c2_1(a1807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807))))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[2767])).
% 1.07/1.22 tff(2769,plain,
% 1.07/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1807) | c0_1(a1807) | (~c2_1(a1807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807)))),
% 1.07/1.22 inference(transitivity,[status(thm)],[2768, 2766])).
% 1.07/1.22 tff(2770,plain,
% 1.07/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1807) | c0_1(a1807) | (~c2_1(a1807)))),
% 1.07/1.22 inference(quant_inst,[status(thm)],[])).
% 1.07/1.22 tff(2771,plain,
% 1.07/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807))),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 1.07/1.22 tff(2772,plain,
% 1.07/1.22 (~c2_1(a1807)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2771, 102, 2751, 2749, 2765, 2764, 2763, 2762, 2750, 2754, 753])).
% 1.07/1.22 tff(2773,plain,
% 1.07/1.22 (hskp28),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2381, 102, 1847, 1808, 2724, 2723, 2375, 2689, 2725])).
% 1.07/1.22 tff(2774,plain,
% 1.07/1.22 (c2_1(a1795)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2389, 2773])).
% 1.07/1.22 tff(2775,plain,
% 1.07/1.22 (c1_1(a1795)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2397, 2773])).
% 1.07/1.22 tff(2776,plain,
% 1.07/1.22 (c0_1(a1795)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2405, 2773])).
% 1.07/1.22 tff(2777,plain,
% 1.07/1.22 (c3_1(a1823)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1511, 2747])).
% 1.07/1.22 tff(2778,plain,
% 1.07/1.22 (c2_1(a1823)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1519, 2747])).
% 1.07/1.22 tff(2779,plain,
% 1.07/1.22 (c1_1(a1823)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[1527, 2747])).
% 1.07/1.22 tff(2780,plain,
% 1.07/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(2781,plain,
% 1.07/1.22 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1779) | (~c1_1(a1779)) | (~c0_1(a1779))) <=> (c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(2782,plain,
% 1.07/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1779) | (~c1_1(a1779)) | (~c0_1(a1779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[2781])).
% 1.07/1.22 tff(2783,plain,
% 1.07/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1779) | (~c1_1(a1779)) | (~c0_1(a1779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.07/1.22 inference(transitivity,[status(thm)],[2782, 2780])).
% 1.07/1.22 tff(2784,plain,
% 1.07/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1779) | (~c1_1(a1779)) | (~c0_1(a1779)))),
% 1.07/1.22 inference(quant_inst,[status(thm)],[])).
% 1.07/1.22 tff(2785,plain,
% 1.07/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[2784, 2783])).
% 1.07/1.22 tff(2786,plain,
% 1.07/1.22 (~c1_1(a1779)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2785, 102, 2779, 2778, 2777, 2776, 2775, 2774, 2739, 2737, 618])).
% 1.07/1.22 tff(2787,plain,
% 1.07/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(2788,plain,
% 1.07/1.22 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1779) | c1_1(a1779) | c3_1(a1779) | c3_1(a1807) | c2_1(a1807) | c0_1(a1807)) <=> (c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(2789,plain,
% 1.07/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1779) | c1_1(a1779) | c3_1(a1779) | c3_1(a1807) | c2_1(a1807) | c0_1(a1807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[2788])).
% 1.07/1.22 tff(2790,plain,
% 1.07/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1779) | c1_1(a1779) | c3_1(a1779) | c3_1(a1807) | c2_1(a1807) | c0_1(a1807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.07/1.22 inference(transitivity,[status(thm)],[2789, 2787])).
% 1.07/1.22 tff(2791,plain,
% 1.07/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1779) | c1_1(a1779) | c3_1(a1779) | c3_1(a1807) | c2_1(a1807) | c0_1(a1807))),
% 1.07/1.22 inference(quant_inst,[status(thm)],[])).
% 1.07/1.22 tff(2792,plain,
% 1.07/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.07/1.22 inference(modus_ponens,[status(thm)],[2791, 2790])).
% 1.07/1.22 tff(2793,plain,
% 1.07/1.22 ($false),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2792, 102, 2779, 2778, 2777, 2763, 2762, 2738, 2737, 1453, 2786, 2772])).
% 1.07/1.22 tff(2794,plain,(hskp6), inference(lemma,lemma(discharge,[]))).
% 1.07/1.22 tff(2795,plain,
% 1.07/1.22 (~c0_1(a1762)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[270, 2794])).
% 1.07/1.22 tff(2796,plain,
% 1.07/1.22 (c2_1(a1762)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[286, 2794])).
% 1.07/1.22 tff(2797,plain,
% 1.07/1.22 (hskp13 | (~c1_1(a1762))),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[374, 102, 2796, 2795, 22])).
% 1.07/1.22 tff(2798,plain,
% 1.07/1.22 (~c1_1(a1762)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[2797, 23])).
% 1.07/1.22 tff(2799,plain,
% 1.07/1.22 (c3_1(a1762)),
% 1.07/1.22 inference(unit_resolution,[status(thm)],[278, 2794])).
% 1.07/1.22 tff(2800,plain,
% 1.07/1.22 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(2801,plain,
% 1.07/1.22 ((hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762))) <=> (hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.07/1.22 inference(rewrite,[status(thm)],[])).
% 1.07/1.22 tff(2802,plain,
% 1.07/1.22 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.07/1.22 inference(monotonicity,[status(thm)],[2801])).
% 1.07/1.22 tff(2803,plain,
% 1.07/1.22 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.07/1.22 inference(transitivity,[status(thm)],[2802, 2800])).
% 1.07/1.22 tff(2804,plain,
% 1.07/1.22 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2805,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2804, 2803])).
% 1.07/1.23 tff(2806,plain,
% 1.07/1.23 (hskp7),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2805, 102, 1847, 2799, 1800, 2795, 983, 2798, 1855])).
% 1.07/1.23 tff(2807,plain,
% 1.07/1.23 (~c1_1(a1763)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[996, 2806])).
% 1.07/1.23 tff(2808,plain,
% 1.07/1.23 (c3_1(a1763)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1004, 2806])).
% 1.07/1.23 tff(2809,plain,
% 1.07/1.23 (c0_1(a1763)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1012, 2806])).
% 1.07/1.23 tff(2810,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2811,plain,
% 1.07/1.23 ((hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783))) <=> (hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2812,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2811])).
% 1.07/1.23 tff(2813,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2812, 2810])).
% 1.07/1.23 tff(2814,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2815,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2814, 2813])).
% 1.07/1.23 tff(2816,plain,
% 1.07/1.23 (hskp11),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2815, 102, 1847, 2809, 2808, 1800, 2807, 860, 1855])).
% 1.07/1.23 tff(2817,plain,
% 1.07/1.23 (~c2_1(a1768)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1025, 2816])).
% 1.07/1.23 tff(2818,plain,
% 1.07/1.23 (c3_1(a1768)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1081, 2816])).
% 1.07/1.23 tff(2819,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2820,plain,
% 1.07/1.23 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2821,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2820])).
% 1.07/1.23 tff(2822,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2821, 2819])).
% 1.07/1.23 tff(2823,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2824,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2823, 2822])).
% 1.07/1.23 tff(2825,plain,
% 1.07/1.23 (c1_1(a1768)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2824, 102, 2818, 2796, 2799, 2817, 2795, 1051, 2798])).
% 1.07/1.23 tff(2826,plain,
% 1.07/1.23 (c0_1(a1768)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1033, 2816])).
% 1.07/1.23 tff(2827,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2828,plain,
% 1.07/1.23 (((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1763) | (~c2_1(a1763)) | (~c0_1(a1763)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2829,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1763) | (~c2_1(a1763)) | (~c0_1(a1763)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2828])).
% 1.07/1.23 tff(2830,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1763) | (~c2_1(a1763)) | (~c0_1(a1763)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2829, 2827])).
% 1.07/1.23 tff(2831,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1763) | (~c2_1(a1763)) | (~c0_1(a1763)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2832,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2831, 2830])).
% 1.07/1.23 tff(2833,plain,
% 1.07/1.23 ((~c2_1(a1763)) | (~c1_1(a1768))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2832, 102, 1847, 1808, 2826, 2809, 1800, 2817, 2807, 433])).
% 1.07/1.23 tff(2834,plain,
% 1.07/1.23 (~c2_1(a1763)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2833, 2825])).
% 1.07/1.23 tff(2835,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2836,plain,
% 1.07/1.23 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1763) | c1_1(a1763) | (~c3_1(a1763)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2837,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1763) | c1_1(a1763) | (~c3_1(a1763)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2836])).
% 1.07/1.23 tff(2838,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1763) | c1_1(a1763) | (~c3_1(a1763)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2837, 2835])).
% 1.07/1.23 tff(2839,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1763) | c1_1(a1763) | (~c3_1(a1763)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2840,plain,
% 1.07/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2839, 2838])).
% 1.07/1.23 tff(2841,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2840, 102, 2808, 2796, 2799, 2807, 2795, 1051, 2798, 2834])).
% 1.07/1.23 tff(2842,plain,(hskp13), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(2843,plain,
% 1.07/1.23 (c1_1(a1771)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[234, 2842])).
% 1.07/1.23 tff(2844,plain,
% 1.07/1.23 (~c0_1(a1771)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[223, 2842])).
% 1.07/1.23 tff(2845,plain,
% 1.07/1.23 (c2_1(a1771)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[242, 2842])).
% 1.07/1.23 tff(2846,plain,
% 1.07/1.23 ((~hskp22) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1294, 2796, 2799, 2795])).
% 1.07/1.23 tff(2847,plain,
% 1.07/1.23 (~hskp22),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2846, 2845, 2844, 2843])).
% 1.07/1.23 tff(2848,plain,
% 1.07/1.23 (hskp27 | hskp22),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[334, 102, 2796, 2799, 2795, 327])).
% 1.07/1.23 tff(2849,plain,
% 1.07/1.23 (hskp27),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2848, 2847])).
% 1.07/1.23 tff(2850,plain,
% 1.07/1.23 (c3_1(a1756)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[342, 2849])).
% 1.07/1.23 tff(2851,plain,
% 1.07/1.23 (c1_1(a1756)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[350, 2849])).
% 1.07/1.23 tff(2852,plain,
% 1.07/1.23 (c0_1(a1756)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[358, 2849])).
% 1.07/1.23 tff(2853,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2854,plain,
% 1.07/1.23 ((hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2855,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2854])).
% 1.07/1.23 tff(2856,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2855, 2853])).
% 1.07/1.23 tff(2857,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2858,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2857, 2856])).
% 1.07/1.23 tff(2859,plain,
% 1.07/1.23 (hskp3),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2858, 102, 2852, 2851, 2850, 1808, 1800, 11, 1])).
% 1.07/1.23 tff(2860,plain,
% 1.07/1.23 (c1_1(a1758)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[564, 2859])).
% 1.07/1.23 tff(2861,plain,
% 1.07/1.23 (~c3_1(a1758)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[578, 2859])).
% 1.07/1.23 tff(2862,plain,
% 1.07/1.23 (c2_1(a1758)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[556, 2859])).
% 1.07/1.23 tff(2863,assumption,(c1_1(a1762)), introduced(assumption)).
% 1.07/1.23 tff(2864,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2865,plain,
% 1.07/1.23 ((hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2866,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2865])).
% 1.07/1.23 tff(2867,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2866, 2864])).
% 1.07/1.23 tff(2868,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2869,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2868, 2867])).
% 1.07/1.23 tff(2870,plain,
% 1.07/1.23 (hskp17 | (~c1_1(a1762))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2869, 102, 1847, 1808, 2796, 2799, 1800, 1217])).
% 1.07/1.23 tff(2871,plain,
% 1.07/1.23 (hskp17),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2870, 2863])).
% 1.07/1.23 tff(2872,plain,
% 1.07/1.23 (c3_1(a1781)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1089, 2871])).
% 1.07/1.23 tff(2873,plain,
% 1.07/1.23 (~c1_1(a1781)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1073, 2871])).
% 1.07/1.23 tff(2874,plain,
% 1.07/1.23 (c2_1(a1781)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1097, 2871])).
% 1.07/1.23 tff(2875,plain,
% 1.07/1.23 (~c0_1(a1781)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2516, 2872, 2874, 2862, 2873, 2861, 2860])).
% 1.07/1.23 tff(2876,plain,
% 1.07/1.23 ((~c0_1(a1758)) | (~c1_1(a1762))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1619, 102, 2796, 2799, 2860, 2862, 2861, 618])).
% 1.07/1.23 tff(2877,plain,
% 1.07/1.23 (~c0_1(a1758)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2876, 2863])).
% 1.07/1.23 tff(2878,plain,
% 1.07/1.23 (~hskp7),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2533, 2872, 2877, 2862, 2873, 2861, 2874])).
% 1.07/1.23 tff(2879,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2543, 2878, 2875, 1, 2873, 2872])).
% 1.07/1.23 tff(2880,plain,((~c1_1(a1762)) | c2_1(a1783)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(2881,plain,
% 1.07/1.23 (~c1_1(a1762)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2880, 1])).
% 1.07/1.23 tff(2882,plain,
% 1.07/1.23 ((~hskp8) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | c1_1(a1762)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1581, 2799, 2795])).
% 1.07/1.23 tff(2883,plain,
% 1.07/1.23 (~hskp8),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2882, 2881, 2845, 2844, 2843])).
% 1.07/1.23 tff(2884,plain,
% 1.07/1.23 (hskp8 | hskp4),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[293, 102, 2796, 2799, 2795, 121])).
% 1.07/1.23 tff(2885,plain,
% 1.07/1.23 (hskp4),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2884, 2883])).
% 1.07/1.23 tff(2886,plain,
% 1.07/1.23 (c1_1(a1759)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[138, 2885])).
% 1.07/1.23 tff(2887,plain,
% 1.07/1.23 (~c3_1(a1759)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1639, 2885])).
% 1.07/1.23 tff(2888,plain,
% 1.07/1.23 (c1_1(a1762) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~c1_1(a1759)) | c3_1(a1759) | (~c2_1(a1758)) | c3_1(a1758) | (~c1_1(a1758))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1612, 2796, 2799, 2795])).
% 1.07/1.23 tff(2889,plain,
% 1.07/1.23 ($false),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2888, 2887, 2886, 2845, 2843, 2844, 2881, 2862, 2861, 2860])).
% 1.07/1.23 tff(2890,plain,(c2_1(a1783)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.23 tff(2891,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2892,plain,
% 1.07/1.23 ((hskp17 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2893,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2892])).
% 1.07/1.23 tff(2894,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2893, 2891])).
% 1.07/1.23 tff(2895,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2896,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2895, 2894])).
% 1.07/1.23 tff(2897,plain,
% 1.07/1.23 (hskp17),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2896, 102, 1847, 1808, 1800, 1217, 2890])).
% 1.07/1.23 tff(2898,plain,
% 1.07/1.23 (~c1_1(a1781)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1073, 2897])).
% 1.07/1.23 tff(2899,plain,
% 1.07/1.23 (c3_1(a1781)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[1089, 2897])).
% 1.07/1.23 tff(2900,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2901,plain,
% 1.07/1.23 ((hskp8 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(2902,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[2901])).
% 1.07/1.23 tff(2903,plain,
% 1.07/1.23 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[2902, 2900])).
% 1.07/1.23 tff(2904,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(2905,plain,
% 1.07/1.23 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[2904, 2903])).
% 1.07/1.23 tff(2906,plain,
% 1.07/1.23 (hskp8 | c0_1(a1781)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2905, 102, 1847, 1808, 2899, 2898, 1193, 2890])).
% 1.07/1.23 tff(2907,plain,
% 1.07/1.23 (hskp8),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[2906, 2010])).
% 1.07/1.23 tff(2908,plain,
% 1.07/1.23 (~c1_1(a1765)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[299, 2907])).
% 1.07/1.23 tff(2909,plain,
% 1.07/1.23 (c2_1(a1765)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[405, 2907])).
% 1.07/1.23 tff(2910,plain,
% 1.07/1.23 (c0_1(a1765)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[413, 2907])).
% 1.07/1.23 tff(2911,plain,
% 1.07/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2912,plain,
% 1.07/1.24 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781))) <=> (c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2913,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2912])).
% 1.07/1.24 tff(2914,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2913, 2911])).
% 1.07/1.24 tff(2915,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2916,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2915, 2914])).
% 1.07/1.24 tff(2917,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2916, 102, 1847, 2899, 2910, 2909, 1800, 2898, 2908, 46, 2010, 2890])).
% 1.07/1.24 tff(2918,plain,(c0_1(a1781)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(2919,plain,
% 1.07/1.24 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2920,plain,
% 1.07/1.24 ((hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783))) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2921,plain,
% 1.07/1.24 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2920])).
% 1.07/1.24 tff(2922,plain,
% 1.07/1.24 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2921, 2919])).
% 1.07/1.24 tff(2923,plain,
% 1.07/1.24 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2924,plain,
% 1.07/1.24 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 1.07/1.24 tff(2925,plain,
% 1.07/1.24 (hskp22 | hskp16 | (~c2_1(a1783))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2924, 102, 1847, 1808, 443])).
% 1.07/1.24 tff(2926,plain,
% 1.07/1.24 (hskp16),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2925, 2890, 2847])).
% 1.07/1.24 tff(2927,plain,
% 1.07/1.24 (~c2_1(a1780)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[456, 2926])).
% 1.07/1.24 tff(2928,plain,
% 1.07/1.24 (c1_1(a1780)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[464, 2926])).
% 1.07/1.24 tff(2929,plain,
% 1.07/1.24 (c2_1(a1781)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[1097, 2897])).
% 1.07/1.24 tff(2930,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2931,plain,
% 1.07/1.24 (((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2932,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2931])).
% 1.07/1.24 tff(2933,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2932, 2930])).
% 1.07/1.24 tff(2934,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2935,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 1.07/1.24 tff(2936,plain,
% 1.07/1.24 ((~c0_1(a1780)) | (~c0_1(a1781))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2935, 102, 1847, 1808, 2929, 2928, 1800, 2898, 2927, 433])).
% 1.07/1.24 tff(2937,plain,
% 1.07/1.24 (~c0_1(a1780)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2936, 2918])).
% 1.07/1.24 tff(2938,plain,
% 1.07/1.24 (c3_1(a1780)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[479, 2926])).
% 1.07/1.24 tff(2939,plain,
% 1.07/1.24 (hskp3 | c0_1(a1780)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[486, 102, 2852, 2851, 2850, 2938, 2927, 11])).
% 1.07/1.24 tff(2940,plain,
% 1.07/1.24 (hskp3),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2939, 2937])).
% 1.07/1.24 tff(2941,plain,
% 1.07/1.24 (c1_1(a1758)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[564, 2940])).
% 1.07/1.24 tff(2942,plain,
% 1.07/1.24 (c2_1(a1758)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[556, 2940])).
% 1.07/1.24 tff(2943,plain,
% 1.07/1.24 (~c3_1(a1758)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[578, 2940])).
% 1.07/1.24 tff(2944,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2516, 2943, 2942, 2929, 2899, 2898, 2918, 2941])).
% 1.07/1.24 % SZS output end Proof
% 1.07/1.25 % E exiting
%------------------------------------------------------------------------------