%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN480-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 1.19s 1.38s
% Output : Proof 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN480-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:38:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.19/1.38 % SZS status Unsatisfiable
% 1.19/1.38 % SZS output start Proof
% 1.19/1.38 tff(c1_1_type, type, (
% 1.19/1.38 c1_1: $i > $o)).
% 1.19/1.38 tff(a1542_type, type, (
% 1.19/1.38 a1542: $i)).
% 1.19/1.38 tff(hskp28_type, type, (
% 1.19/1.38 hskp28: $o)).
% 1.19/1.38 tff(a1534_type, type, (
% 1.19/1.38 a1534: $i)).
% 1.19/1.38 tff(hskp10_type, type, (
% 1.19/1.38 hskp10: $o)).
% 1.19/1.38 tff(c0_1_type, type, (
% 1.19/1.38 c0_1: $i > $o)).
% 1.19/1.38 tff(c3_1_type, type, (
% 1.19/1.38 c3_1: $i > $o)).
% 1.19/1.38 tff(ndr1_0_type, type, (
% 1.19/1.38 ndr1_0: $o)).
% 1.19/1.38 tff(a1543_type, type, (
% 1.19/1.38 a1543: $i)).
% 1.19/1.38 tff(a1565_type, type, (
% 1.19/1.38 a1565: $i)).
% 1.19/1.38 tff(c2_1_type, type, (
% 1.19/1.38 c2_1: $i > $o)).
% 1.19/1.38 tff(a1574_type, type, (
% 1.19/1.38 a1574: $i)).
% 1.19/1.38 tff(hskp20_type, type, (
% 1.19/1.38 hskp20: $o)).
% 1.19/1.38 tff(a1562_type, type, (
% 1.19/1.38 a1562: $i)).
% 1.19/1.38 tff(hskp31_type, type, (
% 1.19/1.38 hskp31: $o)).
% 1.19/1.38 tff(hskp7_type, type, (
% 1.19/1.38 hskp7: $o)).
% 1.19/1.38 tff(a1545_type, type, (
% 1.19/1.38 a1545: $i)).
% 1.19/1.38 tff(a1539_type, type, (
% 1.19/1.38 a1539: $i)).
% 1.19/1.38 tff(a1538_type, type, (
% 1.19/1.38 a1538: $i)).
% 1.19/1.38 tff(hskp4_type, type, (
% 1.19/1.38 hskp4: $o)).
% 1.19/1.38 tff(a1558_type, type, (
% 1.19/1.38 a1558: $i)).
% 1.19/1.38 tff(hskp1_type, type, (
% 1.19/1.38 hskp1: $o)).
% 1.19/1.38 tff(a1581_type, type, (
% 1.19/1.38 a1581: $i)).
% 1.19/1.38 tff(hskp5_type, type, (
% 1.19/1.38 hskp5: $o)).
% 1.19/1.38 tff(hskp14_type, type, (
% 1.19/1.38 hskp14: $o)).
% 1.19/1.38 tff(hskp22_type, type, (
% 1.19/1.38 hskp22: $o)).
% 1.19/1.38 tff(a1549_type, type, (
% 1.19/1.38 a1549: $i)).
% 1.19/1.38 tff(hskp15_type, type, (
% 1.19/1.38 hskp15: $o)).
% 1.19/1.38 tff(a1548_type, type, (
% 1.19/1.38 a1548: $i)).
% 1.19/1.38 tff(a1536_type, type, (
% 1.19/1.38 a1536: $i)).
% 1.19/1.38 tff(hskp3_type, type, (
% 1.19/1.38 hskp3: $o)).
% 1.19/1.38 tff(hskp23_type, type, (
% 1.19/1.38 hskp23: $o)).
% 1.19/1.38 tff(a1624_type, type, (
% 1.19/1.38 a1624: $i)).
% 1.19/1.38 tff(hskp26_type, type, (
% 1.19/1.38 hskp26: $o)).
% 1.19/1.38 tff(a1547_type, type, (
% 1.19/1.38 a1547: $i)).
% 1.19/1.38 tff(hskp8_type, type, (
% 1.19/1.38 hskp8: $o)).
% 1.19/1.38 tff(a1593_type, type, (
% 1.19/1.38 a1593: $i)).
% 1.19/1.38 tff(a1570_type, type, (
% 1.19/1.38 a1570: $i)).
% 1.19/1.38 tff(hskp17_type, type, (
% 1.19/1.38 hskp17: $o)).
% 1.19/1.38 tff(a1575_type, type, (
% 1.19/1.38 a1575: $i)).
% 1.19/1.38 tff(hskp21_type, type, (
% 1.19/1.38 hskp21: $o)).
% 1.19/1.38 tff(a1553_type, type, (
% 1.19/1.38 a1553: $i)).
% 1.19/1.38 tff(hskp2_type, type, (
% 1.19/1.38 hskp2: $o)).
% 1.19/1.38 tff(a1535_type, type, (
% 1.19/1.38 a1535: $i)).
% 1.19/1.38 tff(hskp6_type, type, (
% 1.19/1.38 hskp6: $o)).
% 1.19/1.38 tff(hskp11_type, type, (
% 1.19/1.38 hskp11: $o)).
% 1.19/1.38 tff(a1554_type, type, (
% 1.19/1.38 a1554: $i)).
% 1.19/1.38 tff(hskp12_type, type, (
% 1.19/1.38 hskp12: $o)).
% 1.19/1.38 tff(a1566_type, type, (
% 1.19/1.38 a1566: $i)).
% 1.19/1.38 tff(hskp16_type, type, (
% 1.19/1.38 hskp16: $o)).
% 1.19/1.38 tff(hskp9_type, type, (
% 1.19/1.38 hskp9: $o)).
% 1.19/1.38 tff(a1544_type, type, (
% 1.19/1.38 a1544: $i)).
% 1.19/1.38 tff(hskp29_type, type, (
% 1.19/1.38 hskp29: $o)).
% 1.19/1.38 tff(a1533_type, type, (
% 1.19/1.38 a1533: $i)).
% 1.19/1.38 tff(hskp0_type, type, (
% 1.19/1.38 hskp0: $o)).
% 1.19/1.38 tff(1,plain,
% 1.19/1.38 (^[U: $i] : refl((hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(2,plain,
% 1.19/1.38 (![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[1])).
% 1.19/1.38 tff(3,plain,
% 1.19/1.38 (![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(4,plain,
% 1.19/1.38 (^[U: $i] : 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)) | hskp10) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(5,plain,
% 1.19/1.38 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> ![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[4])).
% 1.19/1.38 tff(6,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.19/1.38 tff(7,plain,
% 1.19/1.38 (![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.19/1.38 tff(8,plain,
% 1.19/1.38 (![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.19/1.38 tff(9,plain,(
% 1.19/1.38 ![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(skolemize,[status(sab)],[8])).
% 1.19/1.38 tff(10,plain,
% 1.19/1.38 (![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.19/1.38 tff(11,assumption,(~hskp10), introduced(assumption)).
% 1.19/1.38 tff(12,assumption,(~hskp28), introduced(assumption)).
% 1.19/1.38 tff(13,plain,
% 1.19/1.38 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(14,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[13])).
% 1.19/1.38 tff(15,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(16,plain,
% 1.19/1.38 (^[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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(17,plain,
% 1.19/1.38 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[16])).
% 1.19/1.38 tff(18,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.19/1.38 tff(19,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.19/1.38 tff(20,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.19/1.38 tff(21,plain,(
% 1.19/1.38 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.38 inference(skolemize,[status(sab)],[20])).
% 1.19/1.38 tff(22,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.19/1.38 tff(23,assumption,(~c0_1(a1545)), introduced(assumption)).
% 1.19/1.38 tff(24,assumption,(~c3_1(a1545)), introduced(assumption)).
% 1.19/1.38 tff(25,assumption,(~c0_1(a1565)), introduced(assumption)).
% 1.19/1.38 tff(26,plain,
% 1.19/1.38 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_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)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(27,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[26])).
% 1.19/1.38 tff(28,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(29,plain,
% 1.19/1.38 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(30,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_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) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[29])).
% 1.19/1.38 tff(31,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.19/1.38 tff(32,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.19/1.38 tff(33,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 1.19/1.38 tff(34,plain,(
% 1.19/1.38 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.38 inference(skolemize,[status(sab)],[33])).
% 1.19/1.38 tff(35,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[34, 27])).
% 1.19/1.38 tff(36,assumption,(~hskp4), introduced(assumption)).
% 1.19/1.38 tff(37,plain,
% 1.19/1.38 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(38,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[37])).
% 1.19/1.38 tff(39,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(40,plain,
% 1.19/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_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)) | (~c1_1(V))) | (~c3_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)) | (~c1_1(V))) | (~c3_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)) | (~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)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~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)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(41,plain,
% 1.19/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[40])).
% 1.19/1.38 tff(42,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.19/1.38 tff(43,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.19/1.38 tff(44,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.19/1.38 tff(45,plain,(
% 1.19/1.38 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.38 inference(skolemize,[status(sab)],[44])).
% 1.19/1.38 tff(46,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[45, 38])).
% 1.19/1.38 tff(47,assumption,(~hskp1), introduced(assumption)).
% 1.19/1.38 tff(48,plain,
% 1.19/1.38 ((hskp14 | hskp4 | hskp1) <=> (hskp14 | hskp4 | hskp1)),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(49,plain,
% 1.19/1.38 (((hskp14 | hskp1) | hskp4) <=> (hskp14 | hskp4 | hskp1)),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(50,plain,
% 1.19/1.38 ((hskp14 | hskp1) <=> (hskp14 | hskp1)),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(51,plain,
% 1.19/1.38 (((hskp14 | hskp1) | hskp4) <=> ((hskp14 | hskp1) | hskp4)),
% 1.19/1.38 inference(monotonicity,[status(thm)],[50])).
% 1.19/1.38 tff(52,plain,
% 1.19/1.38 (((hskp14 | hskp1) | hskp4) <=> (hskp14 | hskp4 | hskp1)),
% 1.19/1.38 inference(transitivity,[status(thm)],[51, 49])).
% 1.19/1.38 tff(53,axiom,((hskp14 | hskp1) | hskp4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.19/1.38 tff(54,plain,
% 1.19/1.38 (hskp14 | hskp4 | hskp1),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.19/1.38 tff(55,plain,
% 1.19/1.38 (hskp14 | hskp4 | hskp1),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[54, 48])).
% 1.19/1.38 tff(56,plain,
% 1.19/1.38 (hskp14 | hskp4 | hskp1),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.19/1.38 tff(57,plain,
% 1.19/1.38 (hskp14 | hskp4 | hskp1),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[56, 48])).
% 1.19/1.38 tff(58,plain,
% 1.19/1.38 (hskp14 | hskp4 | hskp1),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[57, 48])).
% 1.19/1.38 tff(59,plain,
% 1.19/1.38 (hskp14),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[58, 47, 36])).
% 1.19/1.38 tff(60,plain,
% 1.19/1.38 (((~hskp14) | (~c2_1(a1558))) <=> ((~hskp14) | (~c2_1(a1558)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(61,plain,
% 1.19/1.38 (((~c2_1(a1558)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1558)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(62,axiom,((~c2_1(a1558)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.19/1.38 tff(63,plain,
% 1.19/1.38 ((~hskp14) | (~c2_1(a1558))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.19/1.38 tff(64,plain,
% 1.19/1.38 ((~hskp14) | (~c2_1(a1558))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[63, 60])).
% 1.19/1.38 tff(65,plain,
% 1.19/1.38 (~c2_1(a1558)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[64, 59])).
% 1.19/1.38 tff(66,plain,
% 1.19/1.38 (((~hskp14) | c1_1(a1558)) <=> ((~hskp14) | c1_1(a1558))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(67,axiom,((~hskp14) | c1_1(a1558)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.19/1.38 tff(68,plain,
% 1.19/1.38 ((~hskp14) | c1_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.19/1.38 tff(69,plain,
% 1.19/1.38 ((~hskp14) | c1_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[68, 66])).
% 1.19/1.38 tff(70,plain,
% 1.19/1.38 ((~hskp14) | c1_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[69, 66])).
% 1.19/1.38 tff(71,plain,
% 1.19/1.38 ((~hskp14) | c1_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.19/1.38 tff(72,plain,
% 1.19/1.38 ((~hskp14) | c1_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[71, 66])).
% 1.19/1.38 tff(73,plain,
% 1.19/1.38 (c1_1(a1558)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[72, 59])).
% 1.19/1.38 tff(74,plain,
% 1.19/1.38 (((~hskp14) | c0_1(a1558)) <=> ((~hskp14) | c0_1(a1558))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(75,axiom,((~hskp14) | c0_1(a1558)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.19/1.38 tff(76,plain,
% 1.19/1.38 ((~hskp14) | c0_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.19/1.38 tff(77,plain,
% 1.19/1.38 ((~hskp14) | c0_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[76, 74])).
% 1.19/1.38 tff(78,plain,
% 1.19/1.38 ((~hskp14) | c0_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[77, 74])).
% 1.19/1.38 tff(79,plain,
% 1.19/1.38 ((~hskp14) | c0_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[78, 74])).
% 1.19/1.38 tff(80,plain,
% 1.19/1.38 ((~hskp14) | c0_1(a1558)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[79, 74])).
% 1.19/1.38 tff(81,plain,
% 1.19/1.38 (c0_1(a1558)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[80, 59])).
% 1.19/1.38 tff(82,plain,
% 1.19/1.38 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(83,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[82])).
% 1.19/1.38 tff(84,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(85,plain,
% 1.19/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(86,plain,
% 1.19/1.38 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[85])).
% 1.19/1.38 tff(87,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.19/1.38 tff(88,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.19/1.38 tff(89,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[88, 84])).
% 1.19/1.38 tff(90,plain,(
% 1.19/1.38 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.38 inference(skolemize,[status(sab)],[89])).
% 1.19/1.38 tff(91,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[90, 83])).
% 1.19/1.38 tff(92,plain,
% 1.19/1.38 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(93,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[92])).
% 1.19/1.38 tff(94,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(95,plain,
% 1.19/1.38 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(96,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[95])).
% 1.19/1.39 tff(97,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 1.19/1.39 tff(98,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.19/1.39 tff(99,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.19/1.39 tff(100,plain,(
% 1.19/1.39 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.19/1.39 inference(skolemize,[status(sab)],[99])).
% 1.19/1.39 tff(101,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[100, 93])).
% 1.19/1.39 tff(102,plain,
% 1.19/1.39 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(103,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[102])).
% 1.19/1.39 tff(104,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(105,plain,
% 1.19/1.39 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(106,plain,
% 1.19/1.39 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[105])).
% 1.19/1.39 tff(107,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.19/1.39 tff(108,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.19/1.39 tff(109,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[108, 104])).
% 1.19/1.39 tff(110,plain,(
% 1.19/1.39 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(skolemize,[status(sab)],[109])).
% 1.19/1.39 tff(111,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[110, 103])).
% 1.19/1.39 tff(112,plain,
% 1.19/1.39 (^[U: $i] : refl((hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(113,plain,
% 1.19/1.39 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[112])).
% 1.19/1.39 tff(114,plain,
% 1.19/1.39 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(115,plain,
% 1.19/1.39 (^[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)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp4) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp4))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp4) <=> (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp4) <=> (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(116,plain,
% 1.19/1.39 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp4) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[115])).
% 1.19/1.39 tff(117,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.19/1.39 tff(118,plain,
% 1.19/1.39 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.19/1.39 tff(119,plain,
% 1.19/1.39 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[118, 114])).
% 1.19/1.39 tff(120,plain,(
% 1.19/1.39 ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.19/1.39 inference(skolemize,[status(sab)],[119])).
% 1.19/1.39 tff(121,plain,
% 1.19/1.39 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[120, 113])).
% 1.19/1.39 tff(122,plain,
% 1.19/1.39 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(123,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[122])).
% 1.19/1.39 tff(124,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(125,plain,
% 1.19/1.39 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_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)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_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)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_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)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(126,plain,
% 1.19/1.39 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[125])).
% 1.19/1.39 tff(127,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.19/1.39 tff(128,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.19/1.39 tff(129,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[128, 124])).
% 1.19/1.39 tff(130,plain,(
% 1.19/1.39 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.39 inference(skolemize,[status(sab)],[129])).
% 1.19/1.39 tff(131,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[130, 123])).
% 1.19/1.39 tff(132,assumption,(~hskp15), introduced(assumption)).
% 1.19/1.39 tff(133,assumption,(hskp4), introduced(assumption)).
% 1.19/1.39 tff(134,plain,
% 1.19/1.39 (((~hskp4) | (~c2_1(a1538))) <=> ((~hskp4) | (~c2_1(a1538)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(135,plain,
% 1.19/1.39 (((~c2_1(a1538)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a1538)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(136,axiom,((~c2_1(a1538)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.19/1.39 tff(137,plain,
% 1.19/1.39 ((~hskp4) | (~c2_1(a1538))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.19/1.39 tff(138,plain,
% 1.19/1.39 ((~hskp4) | (~c2_1(a1538))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[137, 134])).
% 1.19/1.39 tff(139,plain,
% 1.19/1.39 (~c2_1(a1538)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[138, 133])).
% 1.19/1.39 tff(140,plain,
% 1.19/1.39 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(141,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[140])).
% 1.19/1.39 tff(142,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(143,plain,
% 1.19/1.39 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(144,plain,
% 1.19/1.39 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[143])).
% 1.19/1.39 tff(145,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.19/1.39 tff(146,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.19/1.39 tff(147,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[146, 142])).
% 1.19/1.39 tff(148,plain,(
% 1.19/1.39 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.19/1.39 inference(skolemize,[status(sab)],[147])).
% 1.19/1.39 tff(149,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[148, 141])).
% 1.19/1.39 tff(150,plain,
% 1.19/1.39 (((~hskp4) | (~c3_1(a1538))) <=> ((~hskp4) | (~c3_1(a1538)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(151,plain,
% 1.19/1.39 (((~c3_1(a1538)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1538)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(152,axiom,((~c3_1(a1538)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.19/1.39 tff(153,plain,
% 1.19/1.39 ((~hskp4) | (~c3_1(a1538))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.19/1.39 tff(154,plain,
% 1.19/1.39 ((~hskp4) | (~c3_1(a1538))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[153, 150])).
% 1.19/1.39 tff(155,plain,
% 1.19/1.39 (~c3_1(a1538)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[154, 133])).
% 1.19/1.39 tff(156,assumption,(~c2_1(a1538)), introduced(assumption)).
% 1.19/1.39 tff(157,plain,
% 1.19/1.39 (((~hskp4) | (~c1_1(a1538))) <=> ((~hskp4) | (~c1_1(a1538)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(158,plain,
% 1.19/1.39 (((~c1_1(a1538)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a1538)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(159,axiom,((~c1_1(a1538)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.19/1.39 tff(160,plain,
% 1.19/1.39 ((~hskp4) | (~c1_1(a1538))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.19/1.39 tff(161,plain,
% 1.19/1.39 ((~hskp4) | (~c1_1(a1538))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[160, 157])).
% 1.19/1.39 tff(162,plain,
% 1.19/1.39 (~c1_1(a1538)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[161, 133])).
% 1.19/1.39 tff(163,assumption,(~hskp31), introduced(assumption)).
% 1.19/1.39 tff(164,plain,
% 1.19/1.39 ((hskp31 | hskp15 | hskp7) <=> (hskp31 | hskp15 | hskp7)),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(165,plain,
% 1.19/1.39 (((hskp31 | hskp15) | hskp7) <=> (hskp31 | hskp15 | hskp7)),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(166,plain,
% 1.19/1.39 ((hskp31 | hskp15) <=> (hskp31 | hskp15)),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(167,plain,
% 1.19/1.39 (((hskp31 | hskp15) | hskp7) <=> ((hskp31 | hskp15) | hskp7)),
% 1.19/1.39 inference(monotonicity,[status(thm)],[166])).
% 1.19/1.39 tff(168,plain,
% 1.19/1.39 (((hskp31 | hskp15) | hskp7) <=> (hskp31 | hskp15 | hskp7)),
% 1.19/1.39 inference(transitivity,[status(thm)],[167, 165])).
% 1.19/1.39 tff(169,axiom,((hskp31 | hskp15) | hskp7), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.19/1.39 tff(170,plain,
% 1.19/1.39 (hskp31 | hskp15 | hskp7),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.19/1.39 tff(171,plain,
% 1.19/1.39 (hskp31 | hskp15 | hskp7),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[170, 164])).
% 1.19/1.39 tff(172,plain,
% 1.19/1.39 (hskp31 | hskp15 | hskp7),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[171, 164])).
% 1.19/1.39 tff(173,plain,
% 1.19/1.39 (hskp31 | hskp15 | hskp7),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[172, 164])).
% 1.19/1.39 tff(174,plain,
% 1.19/1.39 (hskp31 | hskp15 | hskp7),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[173, 164])).
% 1.19/1.39 tff(175,plain,
% 1.19/1.39 (hskp7),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[174, 163, 132])).
% 1.19/1.39 tff(176,plain,
% 1.19/1.39 (((~hskp7) | (~c3_1(a1545))) <=> ((~hskp7) | (~c3_1(a1545)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(177,plain,
% 1.19/1.39 (((~c3_1(a1545)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a1545)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(178,axiom,((~c3_1(a1545)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.19/1.39 tff(179,plain,
% 1.19/1.39 ((~hskp7) | (~c3_1(a1545))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.19/1.39 tff(180,plain,
% 1.19/1.39 ((~hskp7) | (~c3_1(a1545))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[179, 176])).
% 1.19/1.39 tff(181,plain,
% 1.19/1.39 (~c3_1(a1545)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[180, 175])).
% 1.19/1.39 tff(182,plain,
% 1.19/1.39 (((~hskp7) | (~c0_1(a1545))) <=> ((~hskp7) | (~c0_1(a1545)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(183,plain,
% 1.19/1.39 (((~c0_1(a1545)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a1545)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(184,axiom,((~c0_1(a1545)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.19/1.39 tff(185,plain,
% 1.19/1.39 ((~hskp7) | (~c0_1(a1545))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.19/1.39 tff(186,plain,
% 1.19/1.39 ((~hskp7) | (~c0_1(a1545))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[185, 182])).
% 1.19/1.39 tff(187,plain,
% 1.19/1.39 (~c0_1(a1545)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[186, 175])).
% 1.19/1.39 tff(188,plain,
% 1.19/1.39 (((~hskp7) | c2_1(a1545)) <=> ((~hskp7) | c2_1(a1545))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(189,axiom,((~hskp7) | c2_1(a1545)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.19/1.39 tff(190,plain,
% 1.19/1.39 ((~hskp7) | c2_1(a1545)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[189, 188])).
% 1.19/1.39 tff(191,plain,
% 1.19/1.39 ((~hskp7) | c2_1(a1545)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[190, 188])).
% 1.19/1.39 tff(192,plain,
% 1.19/1.39 ((~hskp7) | c2_1(a1545)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[191, 188])).
% 1.19/1.39 tff(193,plain,
% 1.19/1.39 ((~hskp7) | c2_1(a1545)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[192, 188])).
% 1.19/1.39 tff(194,plain,
% 1.19/1.39 ((~hskp7) | c2_1(a1545)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[193, 188])).
% 1.19/1.39 tff(195,plain,
% 1.19/1.39 (c2_1(a1545)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[194, 175])).
% 1.19/1.39 tff(196,plain,
% 1.19/1.39 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(197,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[196])).
% 1.19/1.39 tff(198,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(199,plain,
% 1.19/1.39 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_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) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp23))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(200,plain,
% 1.19/1.39 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[199])).
% 1.19/1.39 tff(201,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)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.19/1.39 tff(202,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.19/1.39 tff(203,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[202, 198])).
% 1.19/1.39 tff(204,plain,(
% 1.19/1.39 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(skolemize,[status(sab)],[203])).
% 1.19/1.39 tff(205,plain,
% 1.19/1.39 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[204, 197])).
% 1.19/1.39 tff(206,assumption,(~hskp26), introduced(assumption)).
% 1.19/1.39 tff(207,plain,
% 1.19/1.39 ((hskp26 | hskp15 | hskp1) <=> (hskp26 | hskp15 | hskp1)),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(208,plain,
% 1.19/1.39 (((hskp1 | hskp15) | hskp26) <=> (hskp26 | hskp15 | hskp1)),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(209,axiom,((hskp1 | hskp15) | hskp26), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 1.19/1.39 tff(210,plain,
% 1.19/1.39 (hskp26 | hskp15 | hskp1),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.19/1.39 tff(211,plain,
% 1.19/1.39 (hskp26 | hskp15 | hskp1),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[210, 207])).
% 1.19/1.39 tff(212,plain,
% 1.19/1.39 (hskp26 | hskp15 | hskp1),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[211, 207])).
% 1.19/1.39 tff(213,plain,
% 1.19/1.39 (hskp26 | hskp15 | hskp1),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[212, 207])).
% 1.19/1.39 tff(214,plain,
% 1.19/1.39 (hskp26 | hskp15 | hskp1),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[213, 207])).
% 1.19/1.39 tff(215,plain,
% 1.19/1.39 (hskp1),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[214, 206, 132])).
% 1.19/1.39 tff(216,plain,
% 1.19/1.39 (((~hskp1) | c2_1(a1534)) <=> ((~hskp1) | c2_1(a1534))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(217,axiom,((~hskp1) | c2_1(a1534)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.19/1.39 tff(218,plain,
% 1.19/1.39 ((~hskp1) | c2_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.19/1.39 tff(219,plain,
% 1.19/1.39 ((~hskp1) | c2_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[218, 216])).
% 1.19/1.39 tff(220,plain,
% 1.19/1.39 ((~hskp1) | c2_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[219, 216])).
% 1.19/1.39 tff(221,plain,
% 1.19/1.39 ((~hskp1) | c2_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[220, 216])).
% 1.19/1.39 tff(222,plain,
% 1.19/1.39 ((~hskp1) | c2_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[221, 216])).
% 1.19/1.39 tff(223,plain,
% 1.19/1.39 (c2_1(a1534)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[222, 215])).
% 1.19/1.39 tff(224,plain,
% 1.19/1.39 (((~hskp1) | (~c3_1(a1534))) <=> ((~hskp1) | (~c3_1(a1534)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(225,plain,
% 1.19/1.39 (((~c3_1(a1534)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a1534)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(226,axiom,((~c3_1(a1534)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.19/1.39 tff(227,plain,
% 1.19/1.39 ((~hskp1) | (~c3_1(a1534))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[226, 225])).
% 1.19/1.39 tff(228,plain,
% 1.19/1.39 ((~hskp1) | (~c3_1(a1534))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[227, 224])).
% 1.19/1.39 tff(229,plain,
% 1.19/1.39 (~c3_1(a1534)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[228, 215])).
% 1.19/1.39 tff(230,plain,
% 1.19/1.39 (((~hskp1) | c0_1(a1534)) <=> ((~hskp1) | c0_1(a1534))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(231,axiom,((~hskp1) | c0_1(a1534)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.19/1.39 tff(232,plain,
% 1.19/1.39 ((~hskp1) | c0_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.19/1.39 tff(233,plain,
% 1.19/1.39 ((~hskp1) | c0_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[232, 230])).
% 1.19/1.39 tff(234,plain,
% 1.19/1.39 ((~hskp1) | c0_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[233, 230])).
% 1.19/1.39 tff(235,plain,
% 1.19/1.39 ((~hskp1) | c0_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[234, 230])).
% 1.19/1.39 tff(236,plain,
% 1.19/1.39 ((~hskp1) | c0_1(a1534)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[235, 230])).
% 1.19/1.39 tff(237,plain,
% 1.19/1.39 (c0_1(a1534)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[236, 215])).
% 1.19/1.39 tff(238,assumption,(~hskp3), introduced(assumption)).
% 1.19/1.39 tff(239,plain,
% 1.19/1.39 ((hskp26 | hskp23 | hskp3) <=> (hskp26 | hskp23 | hskp3)),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(240,plain,
% 1.19/1.39 (((hskp23 | hskp3) | hskp26) <=> (hskp26 | hskp23 | hskp3)),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(241,axiom,((hskp23 | hskp3) | hskp26), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 1.19/1.39 tff(242,plain,
% 1.19/1.39 (hskp26 | hskp23 | hskp3),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.19/1.39 tff(243,plain,
% 1.19/1.39 (hskp26 | hskp23 | hskp3),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[242, 239])).
% 1.19/1.39 tff(244,plain,
% 1.19/1.39 (hskp26 | hskp23 | hskp3),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[243, 239])).
% 1.19/1.39 tff(245,plain,
% 1.19/1.39 (hskp26 | hskp23 | hskp3),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[244, 239])).
% 1.19/1.39 tff(246,plain,
% 1.19/1.39 (hskp26 | hskp23 | hskp3),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[245, 239])).
% 1.19/1.39 tff(247,plain,
% 1.19/1.39 (hskp23),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[246, 238, 206])).
% 1.19/1.39 tff(248,plain,
% 1.19/1.39 (((~hskp23) | c3_1(a1593)) <=> ((~hskp23) | c3_1(a1593))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(249,axiom,((~hskp23) | c3_1(a1593)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.19/1.39 tff(250,plain,
% 1.19/1.39 ((~hskp23) | c3_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[249, 248])).
% 1.19/1.39 tff(251,plain,
% 1.19/1.39 ((~hskp23) | c3_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[250, 248])).
% 1.19/1.39 tff(252,plain,
% 1.19/1.39 ((~hskp23) | c3_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[251, 248])).
% 1.19/1.39 tff(253,plain,
% 1.19/1.39 ((~hskp23) | c3_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[252, 248])).
% 1.19/1.39 tff(254,plain,
% 1.19/1.39 ((~hskp23) | c3_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[253, 248])).
% 1.19/1.39 tff(255,plain,
% 1.19/1.39 (c3_1(a1593)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[254, 247])).
% 1.19/1.39 tff(256,plain,
% 1.19/1.39 (((~hskp23) | c0_1(a1593)) <=> ((~hskp23) | c0_1(a1593))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(257,axiom,((~hskp23) | c0_1(a1593)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.19/1.39 tff(258,plain,
% 1.19/1.39 ((~hskp23) | c0_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[257, 256])).
% 1.19/1.39 tff(259,plain,
% 1.19/1.39 ((~hskp23) | c0_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[258, 256])).
% 1.19/1.39 tff(260,plain,
% 1.19/1.39 ((~hskp23) | c0_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[259, 256])).
% 1.19/1.39 tff(261,plain,
% 1.19/1.39 ((~hskp23) | c0_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[260, 256])).
% 1.19/1.39 tff(262,plain,
% 1.19/1.39 ((~hskp23) | c0_1(a1593)),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[261, 256])).
% 1.19/1.39 tff(263,plain,
% 1.19/1.39 (c0_1(a1593)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[262, 247])).
% 1.19/1.39 tff(264,assumption,(~c3_1(a1534)), introduced(assumption)).
% 1.19/1.39 tff(265,assumption,(c0_1(a1534)), introduced(assumption)).
% 1.19/1.39 tff(266,assumption,(c2_1(a1534)), introduced(assumption)).
% 1.19/1.39 tff(267,assumption,(~c1_1(a1534)), introduced(assumption)).
% 1.19/1.39 tff(268,plain,
% 1.19/1.39 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.19/1.39 inference(bind,[status(th)],[])).
% 1.19/1.39 tff(269,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_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) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.39 inference(quant_intro,[status(thm)],[268])).
% 1.19/1.39 tff(270,plain,
% 1.19/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_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) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(271,plain,
% 1.19/1.39 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(272,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[271])).
% 1.19/1.40 tff(273,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.19/1.40 tff(274,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[273, 272])).
% 1.19/1.40 tff(275,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[274, 270])).
% 1.19/1.40 tff(276,plain,(
% 1.19/1.40 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.40 inference(skolemize,[status(sab)],[275])).
% 1.19/1.40 tff(277,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[276, 269])).
% 1.19/1.40 tff(278,plain,
% 1.19/1.40 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(279,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[278])).
% 1.19/1.40 tff(280,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(281,plain,
% 1.19/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(282,plain,
% 1.19/1.40 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[281])).
% 1.19/1.40 tff(283,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.19/1.40 tff(284,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.19/1.40 tff(285,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[284, 280])).
% 1.19/1.40 tff(286,plain,(
% 1.19/1.40 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.40 inference(skolemize,[status(sab)],[285])).
% 1.19/1.40 tff(287,plain,
% 1.19/1.40 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[286, 279])).
% 1.19/1.40 tff(288,assumption,(hskp23), introduced(assumption)).
% 1.19/1.40 tff(289,plain,
% 1.19/1.40 (((~hskp23) | (~c2_1(a1593))) <=> ((~hskp23) | (~c2_1(a1593)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(290,plain,
% 1.19/1.40 (((~c2_1(a1593)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a1593)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(291,axiom,((~c2_1(a1593)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.19/1.40 tff(292,plain,
% 1.19/1.40 ((~hskp23) | (~c2_1(a1593))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[291, 290])).
% 1.19/1.40 tff(293,plain,
% 1.19/1.40 ((~hskp23) | (~c2_1(a1593))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[292, 289])).
% 1.19/1.40 tff(294,plain,
% 1.19/1.40 (~c2_1(a1593)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[293, 288])).
% 1.19/1.40 tff(295,plain,
% 1.19/1.40 (c3_1(a1593)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[254, 288])).
% 1.19/1.40 tff(296,plain,
% 1.19/1.40 (c0_1(a1593)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[262, 288])).
% 1.19/1.40 tff(297,assumption,(~ndr1_0), introduced(assumption)).
% 1.19/1.40 tff(298,plain,
% 1.19/1.40 ((ndr1_0 | (~hskp7)) <=> (ndr1_0 | (~hskp7))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(299,plain,
% 1.19/1.40 (((~hskp7) | ndr1_0) <=> (ndr1_0 | (~hskp7))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(300,axiom,((~hskp7) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause25')).
% 1.19/1.40 tff(301,plain,
% 1.19/1.40 (ndr1_0 | (~hskp7)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[300, 299])).
% 1.19/1.40 tff(302,plain,
% 1.19/1.40 (ndr1_0 | (~hskp7)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[301, 298])).
% 1.19/1.40 tff(303,plain,
% 1.19/1.40 (~hskp7),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[302, 297])).
% 1.19/1.40 tff(304,plain,
% 1.19/1.40 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(305,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.19/1.40 tff(306,plain,
% 1.19/1.40 ((~hskp31) | ndr1_0),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.19/1.40 tff(307,plain,
% 1.19/1.40 ((~hskp31) | ndr1_0),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[306, 304])).
% 1.19/1.40 tff(308,plain,
% 1.19/1.40 ((~hskp31) | ndr1_0),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[307, 304])).
% 1.19/1.40 tff(309,plain,
% 1.19/1.40 ((~hskp31) | ndr1_0),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[308, 304])).
% 1.19/1.40 tff(310,plain,
% 1.19/1.40 ((~hskp31) | ndr1_0),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[309, 304])).
% 1.19/1.40 tff(311,plain,
% 1.19/1.40 (~hskp31),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[310, 297])).
% 1.19/1.40 tff(312,plain,
% 1.19/1.40 ((ndr1_0 | (~hskp15)) <=> (ndr1_0 | (~hskp15))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(313,plain,
% 1.19/1.40 (((~hskp15) | ndr1_0) <=> (ndr1_0 | (~hskp15))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(314,axiom,((~hskp15) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 1.19/1.40 tff(315,plain,
% 1.19/1.40 (ndr1_0 | (~hskp15)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[314, 313])).
% 1.19/1.40 tff(316,plain,
% 1.19/1.40 (ndr1_0 | (~hskp15)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[315, 312])).
% 1.19/1.40 tff(317,plain,
% 1.19/1.40 (~hskp15),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[316, 297])).
% 1.19/1.40 tff(318,plain,
% 1.19/1.40 ($false),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[174, 317, 311, 303])).
% 1.19/1.40 tff(319,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.19/1.40 tff(320,plain,
% 1.19/1.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a1593) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a1593) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(321,plain,
% 1.19/1.40 ((hskp17 | (~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534))) <=> (hskp17 | c2_1(a1593) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(322,plain,
% 1.19/1.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a1593) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593))))),
% 1.19/1.40 inference(monotonicity,[status(thm)],[321])).
% 1.19/1.40 tff(323,plain,
% 1.19/1.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a1593) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)))),
% 1.19/1.40 inference(transitivity,[status(thm)],[322, 320])).
% 1.19/1.40 tff(324,plain,
% 1.19/1.40 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))),
% 1.19/1.40 inference(quant_inst,[status(thm)],[])).
% 1.19/1.40 tff(325,plain,
% 1.19/1.40 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a1593) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[324, 323])).
% 1.19/1.40 tff(326,plain,
% 1.19/1.40 (hskp17),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[325, 319, 296, 295, 265, 294, 264, 287, 267])).
% 1.19/1.40 tff(327,plain,
% 1.19/1.40 (((~hskp17) | (~c1_1(a1570))) <=> ((~hskp17) | (~c1_1(a1570)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(328,plain,
% 1.19/1.40 (((~c1_1(a1570)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1570)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(329,axiom,((~c1_1(a1570)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.19/1.40 tff(330,plain,
% 1.19/1.40 ((~hskp17) | (~c1_1(a1570))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[329, 328])).
% 1.19/1.40 tff(331,plain,
% 1.19/1.40 ((~hskp17) | (~c1_1(a1570))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[330, 327])).
% 1.19/1.40 tff(332,plain,
% 1.19/1.40 (~c1_1(a1570)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[331, 326])).
% 1.19/1.40 tff(333,plain,
% 1.19/1.40 (((~hskp17) | (~c0_1(a1570))) <=> ((~hskp17) | (~c0_1(a1570)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(334,plain,
% 1.19/1.40 (((~c0_1(a1570)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a1570)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(335,axiom,((~c0_1(a1570)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.19/1.40 tff(336,plain,
% 1.19/1.40 ((~hskp17) | (~c0_1(a1570))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[335, 334])).
% 1.19/1.40 tff(337,plain,
% 1.19/1.40 ((~hskp17) | (~c0_1(a1570))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[336, 333])).
% 1.19/1.40 tff(338,plain,
% 1.19/1.40 (~c0_1(a1570)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[337, 326])).
% 1.19/1.40 tff(339,plain,
% 1.19/1.40 (((~hskp17) | c3_1(a1570)) <=> ((~hskp17) | c3_1(a1570))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(340,axiom,((~hskp17) | c3_1(a1570)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.19/1.40 tff(341,plain,
% 1.19/1.40 ((~hskp17) | c3_1(a1570)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[340, 339])).
% 1.19/1.40 tff(342,plain,
% 1.19/1.40 ((~hskp17) | c3_1(a1570)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[341, 339])).
% 1.19/1.40 tff(343,plain,
% 1.19/1.40 ((~hskp17) | c3_1(a1570)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[342, 339])).
% 1.19/1.40 tff(344,plain,
% 1.19/1.40 ((~hskp17) | c3_1(a1570)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[343, 339])).
% 1.19/1.40 tff(345,plain,
% 1.19/1.40 ((~hskp17) | c3_1(a1570)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[344, 339])).
% 1.19/1.40 tff(346,plain,
% 1.19/1.40 (c3_1(a1570)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[345, 326])).
% 1.19/1.40 tff(347,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a1593) | c0_1(a1570) | c1_1(a1570) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)) | (~c0_1(a1593)) | c1_1(a1593))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1593) | c0_1(a1570) | c1_1(a1570) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)) | (~c0_1(a1593)) | c1_1(a1593))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(348,plain,
% 1.19/1.40 (((~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1593) | c1_1(a1593) | (~c0_1(a1593)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570))) <=> (c2_1(a1593) | c0_1(a1570) | c1_1(a1570) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)) | (~c0_1(a1593)) | c1_1(a1593))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(349,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1593) | c1_1(a1593) | (~c0_1(a1593)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a1593) | c0_1(a1570) | c1_1(a1570) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)) | (~c0_1(a1593)) | c1_1(a1593)))),
% 1.19/1.40 inference(monotonicity,[status(thm)],[348])).
% 1.19/1.40 tff(350,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1593) | c1_1(a1593) | (~c0_1(a1593)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1593) | c0_1(a1570) | c1_1(a1570) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)) | (~c0_1(a1593)) | c1_1(a1593))),
% 1.19/1.40 inference(transitivity,[status(thm)],[349, 347])).
% 1.19/1.40 tff(351,plain,
% 1.19/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1593) | c1_1(a1593) | (~c0_1(a1593)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570)))),
% 1.19/1.40 inference(quant_inst,[status(thm)],[])).
% 1.19/1.40 tff(352,plain,
% 1.19/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a1593) | c0_1(a1570) | c1_1(a1570) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)) | (~c0_1(a1593)) | c1_1(a1593)),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.19/1.40 tff(353,plain,
% 1.19/1.40 (c1_1(a1593)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[352, 319, 296, 346, 265, 266, 294, 338, 332, 277, 267])).
% 1.19/1.40 tff(354,plain,
% 1.19/1.40 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(355,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[354])).
% 1.19/1.40 tff(356,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(357,plain,
% 1.19/1.40 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(358,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[357])).
% 1.19/1.40 tff(359,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 1.19/1.40 tff(360,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.19/1.40 tff(361,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[360, 356])).
% 1.19/1.40 tff(362,plain,(
% 1.19/1.40 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.40 inference(skolemize,[status(sab)],[361])).
% 1.19/1.40 tff(363,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[362, 355])).
% 1.19/1.40 tff(364,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(365,plain,
% 1.19/1.40 (((~ndr1_0) | (~c1_1(a1593)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534))) <=> (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(366,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1593)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593))))),
% 1.19/1.40 inference(monotonicity,[status(thm)],[365])).
% 1.19/1.40 tff(367,plain,
% 1.19/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1593)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593)))),
% 1.19/1.40 inference(transitivity,[status(thm)],[366, 364])).
% 1.19/1.40 tff(368,plain,
% 1.19/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1593)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))),
% 1.19/1.40 inference(quant_inst,[status(thm)],[])).
% 1.19/1.40 tff(369,plain,
% 1.19/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.19/1.40 tff(370,plain,
% 1.19/1.40 ($false),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[369, 319, 296, 295, 265, 266, 264, 363, 267, 353])).
% 1.19/1.40 tff(371,plain,((~hskp23) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.40 tff(372,plain,
% 1.19/1.40 (c1_1(a1534)),
% 1.19/1.40 inference(unit_resolution,[status(thm)],[371, 247, 266, 264, 265])).
% 1.19/1.40 tff(373,plain,
% 1.19/1.40 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(374,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[373])).
% 1.19/1.40 tff(375,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.19/1.40 inference(rewrite,[status(thm)],[])).
% 1.19/1.40 tff(376,plain,
% 1.19/1.40 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(377,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[376])).
% 1.19/1.40 tff(378,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 1.19/1.40 tff(379,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[378, 377])).
% 1.19/1.40 tff(380,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[379, 375])).
% 1.19/1.40 tff(381,plain,(
% 1.19/1.40 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.19/1.40 inference(skolemize,[status(sab)],[380])).
% 1.19/1.40 tff(382,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.19/1.40 inference(modus_ponens,[status(thm)],[381, 374])).
% 1.19/1.40 tff(383,assumption,(c1_1(a1534)), introduced(assumption)).
% 1.19/1.40 tff(384,plain,
% 1.19/1.40 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.19/1.40 inference(bind,[status(th)],[])).
% 1.19/1.40 tff(385,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_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) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.40 inference(quant_intro,[status(thm)],[384])).
% 1.19/1.40 tff(386,plain,
% 1.19/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_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) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(387,plain,
% 1.19/1.41 (^[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) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(388,plain,
% 1.19/1.41 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[387])).
% 1.19/1.41 tff(389,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.19/1.41 tff(390,plain,
% 1.19/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[389, 388])).
% 1.19/1.41 tff(391,plain,
% 1.19/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[390, 386])).
% 1.19/1.41 tff(392,plain,(
% 1.19/1.41 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.41 inference(skolemize,[status(sab)],[391])).
% 1.19/1.41 tff(393,plain,
% 1.19/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[392, 385])).
% 1.19/1.41 tff(394,plain,
% 1.19/1.41 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(395,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[394])).
% 1.19/1.41 tff(396,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(397,plain,
% 1.19/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(398,plain,
% 1.19/1.41 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[397])).
% 1.19/1.41 tff(399,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.19/1.41 tff(400,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[399, 398])).
% 1.19/1.41 tff(401,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[400, 396])).
% 1.19/1.41 tff(402,plain,(
% 1.19/1.41 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.41 inference(skolemize,[status(sab)],[401])).
% 1.19/1.41 tff(403,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[402, 395])).
% 1.19/1.41 tff(404,assumption,(hskp10), introduced(assumption)).
% 1.19/1.41 tff(405,plain,
% 1.19/1.41 (((~hskp10) | (~c1_1(a1549))) <=> ((~hskp10) | (~c1_1(a1549)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(406,plain,
% 1.19/1.41 (((~c1_1(a1549)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1549)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(407,axiom,((~c1_1(a1549)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.19/1.41 tff(408,plain,
% 1.19/1.41 ((~hskp10) | (~c1_1(a1549))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[407, 406])).
% 1.19/1.41 tff(409,plain,
% 1.19/1.41 ((~hskp10) | (~c1_1(a1549))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[408, 405])).
% 1.19/1.41 tff(410,plain,
% 1.19/1.41 (~c1_1(a1549)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[409, 404])).
% 1.19/1.41 tff(411,plain,
% 1.19/1.41 (((~hskp10) | c3_1(a1549)) <=> ((~hskp10) | c3_1(a1549))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(412,axiom,((~hskp10) | c3_1(a1549)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.19/1.41 tff(413,plain,
% 1.19/1.41 ((~hskp10) | c3_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.19/1.41 tff(414,plain,
% 1.19/1.41 ((~hskp10) | c3_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[413, 411])).
% 1.19/1.41 tff(415,plain,
% 1.19/1.41 ((~hskp10) | c3_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[414, 411])).
% 1.19/1.41 tff(416,plain,
% 1.19/1.41 ((~hskp10) | c3_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[415, 411])).
% 1.19/1.41 tff(417,plain,
% 1.19/1.41 ((~hskp10) | c3_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[416, 411])).
% 1.19/1.41 tff(418,plain,
% 1.19/1.41 (c3_1(a1549)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[417, 404])).
% 1.19/1.41 tff(419,plain,
% 1.19/1.41 (((~hskp10) | c0_1(a1549)) <=> ((~hskp10) | c0_1(a1549))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(420,axiom,((~hskp10) | c0_1(a1549)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.19/1.41 tff(421,plain,
% 1.19/1.41 ((~hskp10) | c0_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[420, 419])).
% 1.19/1.41 tff(422,plain,
% 1.19/1.41 ((~hskp10) | c0_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[421, 419])).
% 1.19/1.41 tff(423,plain,
% 1.19/1.41 ((~hskp10) | c0_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[422, 419])).
% 1.19/1.41 tff(424,plain,
% 1.19/1.41 ((~hskp10) | c0_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[423, 419])).
% 1.19/1.41 tff(425,plain,
% 1.19/1.41 ((~hskp10) | c0_1(a1549)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[424, 419])).
% 1.19/1.41 tff(426,plain,
% 1.19/1.41 (c0_1(a1549)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[425, 404])).
% 1.19/1.41 tff(427,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a1549) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1549)) | (~c0_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a1549) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1549)) | (~c0_1(a1549)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(428,plain,
% 1.19/1.41 ((hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549))) <=> (hskp21 | c1_1(a1549) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1549)) | (~c0_1(a1549)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(429,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a1549) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1549)) | (~c0_1(a1549))))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[428])).
% 1.19/1.41 tff(430,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a1549) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1549)) | (~c0_1(a1549)))),
% 1.19/1.41 inference(transitivity,[status(thm)],[429, 427])).
% 1.19/1.41 tff(431,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(432,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a1549) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1549)) | (~c0_1(a1549))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[431, 430])).
% 1.19/1.41 tff(433,plain,
% 1.19/1.41 (hskp21),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[432, 319, 426, 418, 266, 410, 264, 403, 383])).
% 1.19/1.41 tff(434,plain,
% 1.19/1.41 (((~hskp21) | (~c1_1(a1575))) <=> ((~hskp21) | (~c1_1(a1575)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(435,plain,
% 1.19/1.41 (((~c1_1(a1575)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1575)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(436,axiom,((~c1_1(a1575)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.19/1.41 tff(437,plain,
% 1.19/1.41 ((~hskp21) | (~c1_1(a1575))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[436, 435])).
% 1.19/1.41 tff(438,plain,
% 1.19/1.41 ((~hskp21) | (~c1_1(a1575))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[437, 434])).
% 1.19/1.41 tff(439,plain,
% 1.19/1.41 (~c1_1(a1575)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[438, 433])).
% 1.19/1.41 tff(440,plain,
% 1.19/1.41 (((~hskp21) | (~c0_1(a1575))) <=> ((~hskp21) | (~c0_1(a1575)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(441,plain,
% 1.19/1.41 (((~c0_1(a1575)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1575)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(442,axiom,((~c0_1(a1575)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.19/1.41 tff(443,plain,
% 1.19/1.41 ((~hskp21) | (~c0_1(a1575))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[442, 441])).
% 1.19/1.41 tff(444,plain,
% 1.19/1.41 ((~hskp21) | (~c0_1(a1575))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[443, 440])).
% 1.19/1.41 tff(445,plain,
% 1.19/1.41 (~c0_1(a1575)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[444, 433])).
% 1.19/1.41 tff(446,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1575)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1575)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(447,plain,
% 1.19/1.41 (((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1575))) <=> (c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1575)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(448,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1575)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1575))))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[447])).
% 1.19/1.41 tff(449,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1575)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1575)))),
% 1.19/1.41 inference(transitivity,[status(thm)],[448, 446])).
% 1.19/1.41 tff(450,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1575)))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(451,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1575))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[450, 449])).
% 1.19/1.41 tff(452,plain,
% 1.19/1.41 (~c3_1(a1575)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[451, 319, 265, 266, 445, 439, 264, 393, 383])).
% 1.19/1.41 tff(453,plain,
% 1.19/1.41 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(454,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[453])).
% 1.19/1.41 tff(455,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(456,plain,
% 1.19/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(457,plain,
% 1.19/1.41 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[456])).
% 1.19/1.41 tff(458,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.19/1.41 tff(459,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[458, 457])).
% 1.19/1.41 tff(460,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[459, 455])).
% 1.19/1.41 tff(461,plain,(
% 1.19/1.41 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.41 inference(skolemize,[status(sab)],[460])).
% 1.19/1.41 tff(462,plain,
% 1.19/1.41 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[461, 454])).
% 1.19/1.41 tff(463,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(464,plain,
% 1.19/1.41 ((hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575) | c1_1(a1575) | c0_1(a1575)) <=> (hskp5 | c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(465,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575) | c1_1(a1575) | c0_1(a1575))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575)))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[464])).
% 1.19/1.41 tff(466,plain,
% 1.19/1.41 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575) | c1_1(a1575) | c0_1(a1575))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575))),
% 1.19/1.41 inference(transitivity,[status(thm)],[465, 463])).
% 1.19/1.41 tff(467,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575) | c1_1(a1575) | c0_1(a1575))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(468,plain,
% 1.19/1.41 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a1575) | c1_1(a1575) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1575)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.19/1.41 tff(469,plain,
% 1.19/1.41 (hskp5),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[468, 319, 265, 445, 439, 264, 462, 383, 452])).
% 1.19/1.41 tff(470,plain,
% 1.19/1.41 (((~hskp5) | (~c0_1(a1539))) <=> ((~hskp5) | (~c0_1(a1539)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(471,plain,
% 1.19/1.41 (((~c0_1(a1539)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1539)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(472,axiom,((~c0_1(a1539)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.19/1.41 tff(473,plain,
% 1.19/1.41 ((~hskp5) | (~c0_1(a1539))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.19/1.41 tff(474,plain,
% 1.19/1.41 ((~hskp5) | (~c0_1(a1539))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[473, 470])).
% 1.19/1.41 tff(475,plain,
% 1.19/1.41 (~c0_1(a1539)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[474, 469])).
% 1.19/1.41 tff(476,plain,
% 1.19/1.41 (((~hskp5) | c3_1(a1539)) <=> ((~hskp5) | c3_1(a1539))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(477,axiom,((~hskp5) | c3_1(a1539)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.19/1.41 tff(478,plain,
% 1.19/1.41 ((~hskp5) | c3_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[477, 476])).
% 1.19/1.41 tff(479,plain,
% 1.19/1.41 ((~hskp5) | c3_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[478, 476])).
% 1.19/1.41 tff(480,plain,
% 1.19/1.41 ((~hskp5) | c3_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[479, 476])).
% 1.19/1.41 tff(481,plain,
% 1.19/1.41 ((~hskp5) | c3_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[480, 476])).
% 1.19/1.41 tff(482,plain,
% 1.19/1.41 ((~hskp5) | c3_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[481, 476])).
% 1.19/1.41 tff(483,plain,
% 1.19/1.41 (c3_1(a1539)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[482, 469])).
% 1.19/1.41 tff(484,plain,
% 1.19/1.41 (((~hskp5) | c1_1(a1539)) <=> ((~hskp5) | c1_1(a1539))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(485,axiom,((~hskp5) | c1_1(a1539)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.19/1.41 tff(486,plain,
% 1.19/1.41 ((~hskp5) | c1_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.19/1.41 tff(487,plain,
% 1.19/1.41 ((~hskp5) | c1_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[486, 484])).
% 1.19/1.41 tff(488,plain,
% 1.19/1.41 ((~hskp5) | c1_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[487, 484])).
% 1.19/1.41 tff(489,plain,
% 1.19/1.41 ((~hskp5) | c1_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[488, 484])).
% 1.19/1.41 tff(490,plain,
% 1.19/1.41 ((~hskp5) | c1_1(a1539)),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[489, 484])).
% 1.19/1.41 tff(491,plain,
% 1.19/1.41 (c1_1(a1539)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[490, 469])).
% 1.19/1.41 tff(492,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1549)) | (~c0_1(a1549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1549)) | (~c0_1(a1549)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(493,plain,
% 1.19/1.41 (((~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539))) <=> (c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1549)) | (~c0_1(a1549)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(494,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1549)) | (~c0_1(a1549))))),
% 1.19/1.41 inference(monotonicity,[status(thm)],[493])).
% 1.19/1.41 tff(495,plain,
% 1.19/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1549)) | (~c0_1(a1549)))),
% 1.19/1.41 inference(transitivity,[status(thm)],[494, 492])).
% 1.19/1.41 tff(496,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539)))),
% 1.19/1.41 inference(quant_inst,[status(thm)],[])).
% 1.19/1.41 tff(497,plain,
% 1.19/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1549)) | (~c0_1(a1549))),
% 1.19/1.41 inference(modus_ponens,[status(thm)],[496, 495])).
% 1.19/1.41 tff(498,plain,
% 1.19/1.41 (~c2_1(a1539)),
% 1.19/1.41 inference(unit_resolution,[status(thm)],[497, 319, 426, 418, 491, 483, 410, 475, 382])).
% 1.19/1.41 tff(499,plain,
% 1.19/1.41 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 1.19/1.41 inference(bind,[status(th)],[])).
% 1.19/1.41 tff(500,plain,
% 1.19/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.19/1.41 inference(quant_intro,[status(thm)],[499])).
% 1.19/1.41 tff(501,plain,
% 1.19/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.19/1.41 inference(rewrite,[status(thm)],[])).
% 1.19/1.41 tff(502,plain,
% 1.19/1.41 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_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) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 1.19/1.42 inference(bind,[status(th)],[])).
% 1.19/1.42 tff(503,plain,
% 1.19/1.42 (![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))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.19/1.42 inference(quant_intro,[status(thm)],[502])).
% 1.19/1.42 tff(504,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))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 1.19/1.42 tff(505,plain,
% 1.19/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.19/1.42 tff(506,plain,
% 1.19/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[505, 501])).
% 1.19/1.42 tff(507,plain,(
% 1.19/1.42 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.19/1.42 inference(skolemize,[status(sab)],[506])).
% 1.19/1.42 tff(508,plain,
% 1.19/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[507, 500])).
% 1.19/1.42 tff(509,plain,
% 1.19/1.42 (((~hskp21) | c2_1(a1575)) <=> ((~hskp21) | c2_1(a1575))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(510,axiom,((~hskp21) | c2_1(a1575)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.19/1.42 tff(511,plain,
% 1.19/1.42 ((~hskp21) | c2_1(a1575)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[510, 509])).
% 1.19/1.42 tff(512,plain,
% 1.19/1.42 ((~hskp21) | c2_1(a1575)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[511, 509])).
% 1.19/1.42 tff(513,plain,
% 1.19/1.42 ((~hskp21) | c2_1(a1575)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[512, 509])).
% 1.19/1.42 tff(514,plain,
% 1.19/1.42 ((~hskp21) | c2_1(a1575)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[513, 509])).
% 1.19/1.42 tff(515,plain,
% 1.19/1.42 ((~hskp21) | c2_1(a1575)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[514, 509])).
% 1.19/1.42 tff(516,plain,
% 1.19/1.42 (c2_1(a1575)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[515, 433])).
% 1.19/1.42 tff(517,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c0_1(a1575) | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1575)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c0_1(a1575) | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1575)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(518,plain,
% 1.19/1.42 ((hskp28 | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575))) <=> (hskp28 | c0_1(a1575) | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1575)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(519,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c0_1(a1575) | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1575))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[518])).
% 1.19/1.42 tff(520,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c0_1(a1575) | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1575)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[519, 517])).
% 1.19/1.42 tff(521,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(522,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c0_1(a1575) | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1575))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.19/1.42 tff(523,plain,
% 1.19/1.42 (hskp28),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[522, 319, 516, 491, 483, 445, 439, 22, 498])).
% 1.19/1.42 tff(524,plain,
% 1.19/1.42 (((~hskp28) | c3_1(a1542)) <=> ((~hskp28) | c3_1(a1542))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(525,axiom,((~hskp28) | c3_1(a1542)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.19/1.42 tff(526,plain,
% 1.19/1.42 ((~hskp28) | c3_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[525, 524])).
% 1.19/1.42 tff(527,plain,
% 1.19/1.42 ((~hskp28) | c3_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[526, 524])).
% 1.19/1.42 tff(528,plain,
% 1.19/1.42 ((~hskp28) | c3_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[527, 524])).
% 1.19/1.42 tff(529,plain,
% 1.19/1.42 ((~hskp28) | c3_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[528, 524])).
% 1.19/1.42 tff(530,plain,
% 1.19/1.42 ((~hskp28) | c3_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[529, 524])).
% 1.19/1.42 tff(531,plain,
% 1.19/1.42 (c3_1(a1542)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[530, 523])).
% 1.19/1.42 tff(532,plain,
% 1.19/1.42 (((~hskp28) | c2_1(a1542)) <=> ((~hskp28) | c2_1(a1542))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(533,axiom,((~hskp28) | c2_1(a1542)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.19/1.42 tff(534,plain,
% 1.19/1.42 ((~hskp28) | c2_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.19/1.42 tff(535,plain,
% 1.19/1.42 ((~hskp28) | c2_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[534, 532])).
% 1.19/1.42 tff(536,plain,
% 1.19/1.42 ((~hskp28) | c2_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[535, 532])).
% 1.19/1.42 tff(537,plain,
% 1.19/1.42 ((~hskp28) | c2_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[536, 532])).
% 1.19/1.42 tff(538,plain,
% 1.19/1.42 ((~hskp28) | c2_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[537, 532])).
% 1.19/1.42 tff(539,plain,
% 1.19/1.42 (c2_1(a1542)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[538, 523])).
% 1.19/1.42 tff(540,plain,
% 1.19/1.42 (((~hskp28) | c1_1(a1542)) <=> ((~hskp28) | c1_1(a1542))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(541,axiom,((~hskp28) | c1_1(a1542)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.19/1.42 tff(542,plain,
% 1.19/1.42 ((~hskp28) | c1_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.19/1.42 tff(543,plain,
% 1.19/1.42 ((~hskp28) | c1_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[542, 540])).
% 1.19/1.42 tff(544,plain,
% 1.19/1.42 ((~hskp28) | c1_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[543, 540])).
% 1.19/1.42 tff(545,plain,
% 1.19/1.42 ((~hskp28) | c1_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[544, 540])).
% 1.19/1.42 tff(546,plain,
% 1.19/1.42 ((~hskp28) | c1_1(a1542)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[545, 540])).
% 1.19/1.42 tff(547,plain,
% 1.19/1.42 (c1_1(a1542)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[546, 523])).
% 1.19/1.42 tff(548,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(549,plain,
% 1.19/1.42 (((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1539) | (~c3_1(a1539)) | (~c1_1(a1539))) <=> ((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(550,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1539) | (~c3_1(a1539)) | (~c1_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[549])).
% 1.19/1.42 tff(551,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1539) | (~c3_1(a1539)) | (~c1_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[550, 548])).
% 1.19/1.42 tff(552,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1539) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(553,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[552, 551])).
% 1.19/1.42 tff(554,plain,
% 1.19/1.42 ($false),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[553, 319, 547, 539, 531, 491, 483, 265, 266, 508, 383, 498])).
% 1.19/1.42 tff(555,plain,((~hskp10) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1534)) | c3_1(a1534)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.42 tff(556,plain,
% 1.19/1.42 (~hskp10),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[555, 372, 266, 265, 264])).
% 1.19/1.42 tff(557,plain,
% 1.19/1.42 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(558,plain,
% 1.19/1.42 ((hskp10 | (~ndr1_0) | (~c1_1(a1593)) | (~c3_1(a1593)) | (~c0_1(a1593))) <=> (hskp10 | (~ndr1_0) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(559,plain,
% 1.19/1.42 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1593)) | (~c3_1(a1593)) | (~c0_1(a1593)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[558])).
% 1.19/1.42 tff(560,plain,
% 1.19/1.42 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1593)) | (~c3_1(a1593)) | (~c0_1(a1593)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[559, 557])).
% 1.19/1.42 tff(561,plain,
% 1.19/1.42 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1593)) | (~c3_1(a1593)) | (~c0_1(a1593)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(562,plain,
% 1.19/1.42 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c1_1(a1593))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[561, 560])).
% 1.19/1.42 tff(563,plain,
% 1.19/1.42 (~c1_1(a1593)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[562, 319, 556, 263, 255, 10])).
% 1.19/1.42 tff(564,plain,
% 1.19/1.42 (^[U: $i] : refl((hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.19/1.42 inference(bind,[status(th)],[])).
% 1.19/1.42 tff(565,plain,
% 1.19/1.42 (![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.42 inference(quant_intro,[status(thm)],[564])).
% 1.19/1.42 tff(566,plain,
% 1.19/1.42 (![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(567,plain,
% 1.19/1.42 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp31))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp3) <=> ((hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp3))), rewrite(((hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp3) <=> (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp3) <=> (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.19/1.42 inference(bind,[status(th)],[])).
% 1.19/1.42 tff(568,plain,
% 1.19/1.42 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp3) <=> ![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.42 inference(quant_intro,[status(thm)],[567])).
% 1.19/1.42 tff(569,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.19/1.42 tff(570,plain,
% 1.19/1.42 (![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[569, 568])).
% 1.19/1.42 tff(571,plain,
% 1.19/1.42 (![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[570, 566])).
% 1.19/1.42 tff(572,plain,(
% 1.19/1.42 ![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.42 inference(skolemize,[status(sab)],[571])).
% 1.19/1.42 tff(573,plain,
% 1.19/1.42 (![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[572, 565])).
% 1.19/1.42 tff(574,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(575,plain,
% 1.19/1.42 ((hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593))) <=> (hskp21 | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(576,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593)))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[575])).
% 1.19/1.42 tff(577,plain,
% 1.19/1.42 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593))),
% 1.19/1.42 inference(transitivity,[status(thm)],[576, 574])).
% 1.19/1.42 tff(578,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(579,plain,
% 1.19/1.42 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[578, 577])).
% 1.19/1.42 tff(580,plain,
% 1.19/1.42 (hskp21),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[579, 319, 263, 255, 266, 264, 403, 372, 563])).
% 1.19/1.42 tff(581,plain,
% 1.19/1.42 (~c1_1(a1575)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[438, 580])).
% 1.19/1.42 tff(582,plain,
% 1.19/1.42 (c2_1(a1575)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[515, 580])).
% 1.19/1.42 tff(583,plain,
% 1.19/1.42 (((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1575)) | (~c2_1(a1575)))) <=> ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp31 | hskp3 | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1575)) | (~c2_1(a1575)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(584,plain,
% 1.19/1.42 ((hskp31 | hskp3 | (~ndr1_0) | c1_1(a1575) | (~c3_1(a1575)) | (~c2_1(a1575))) <=> (hskp31 | hskp3 | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1575)) | (~c2_1(a1575)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(585,plain,
% 1.19/1.42 (((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | (~ndr1_0) | c1_1(a1575) | (~c3_1(a1575)) | (~c2_1(a1575)))) <=> ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1575)) | (~c2_1(a1575))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[584])).
% 1.19/1.42 tff(586,plain,
% 1.19/1.42 (((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | (~ndr1_0) | c1_1(a1575) | (~c3_1(a1575)) | (~c2_1(a1575)))) <=> ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp31 | hskp3 | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1575)) | (~c2_1(a1575)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[585, 583])).
% 1.19/1.42 tff(587,plain,
% 1.19/1.42 ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | (~ndr1_0) | c1_1(a1575) | (~c3_1(a1575)) | (~c2_1(a1575)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(588,plain,
% 1.19/1.42 ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp31 | hskp3 | c1_1(a1575) | (~ndr1_0) | (~c3_1(a1575)) | (~c2_1(a1575))),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[587, 586])).
% 1.19/1.42 tff(589,plain,
% 1.19/1.42 (~c3_1(a1575)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[588, 163, 319, 238, 582, 581, 573])).
% 1.19/1.42 tff(590,plain,
% 1.19/1.42 (~c0_1(a1575)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[444, 580])).
% 1.19/1.42 tff(591,plain,
% 1.19/1.42 (hskp5),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[468, 319, 265, 590, 581, 264, 462, 372, 589])).
% 1.19/1.42 tff(592,plain,
% 1.19/1.42 (~c0_1(a1539)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[474, 591])).
% 1.19/1.42 tff(593,plain,
% 1.19/1.42 (c3_1(a1539)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[482, 591])).
% 1.19/1.42 tff(594,plain,
% 1.19/1.42 (c1_1(a1539)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[490, 591])).
% 1.19/1.42 tff(595,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(596,plain,
% 1.19/1.42 (((~ndr1_0) | c1_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539))) <=> (c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(597,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593)))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[596])).
% 1.19/1.42 tff(598,plain,
% 1.19/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593))),
% 1.19/1.42 inference(transitivity,[status(thm)],[597, 595])).
% 1.19/1.42 tff(599,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.42 tff(600,plain,
% 1.19/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c3_1(a1593)) | (~c0_1(a1593)) | c1_1(a1593)),
% 1.19/1.42 inference(modus_ponens,[status(thm)],[599, 598])).
% 1.19/1.42 tff(601,plain,
% 1.19/1.42 (~c2_1(a1539)),
% 1.19/1.42 inference(unit_resolution,[status(thm)],[600, 319, 263, 255, 594, 593, 592, 382, 563])).
% 1.19/1.42 tff(602,plain,
% 1.19/1.42 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(603,plain,
% 1.19/1.42 ((hskp10 | hskp4 | (~ndr1_0) | c2_1(a1539) | c0_1(a1539) | (~c1_1(a1539))) <=> (hskp10 | hskp4 | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)))),
% 1.19/1.42 inference(rewrite,[status(thm)],[])).
% 1.19/1.42 tff(604,plain,
% 1.19/1.42 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1539) | c0_1(a1539) | (~c1_1(a1539)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539))))),
% 1.19/1.42 inference(monotonicity,[status(thm)],[603])).
% 1.19/1.42 tff(605,plain,
% 1.19/1.42 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1539) | c0_1(a1539) | (~c1_1(a1539)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)))),
% 1.19/1.42 inference(transitivity,[status(thm)],[604, 602])).
% 1.19/1.42 tff(606,plain,
% 1.19/1.42 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1539) | c0_1(a1539) | (~c1_1(a1539)))),
% 1.19/1.42 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(607,plain,
% 1.19/1.43 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[606, 605])).
% 1.19/1.43 tff(608,plain,
% 1.19/1.43 (hskp4 | c2_1(a1539)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[607, 319, 556, 594, 592, 121])).
% 1.19/1.43 tff(609,plain,
% 1.19/1.43 (hskp4),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[608, 601])).
% 1.19/1.43 tff(610,plain,
% 1.19/1.43 (~c3_1(a1538)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[154, 609])).
% 1.19/1.43 tff(611,assumption,(c2_1(a1545)), introduced(assumption)).
% 1.19/1.43 tff(612,assumption,(hskp17), introduced(assumption)).
% 1.19/1.43 tff(613,plain,
% 1.19/1.43 (~c1_1(a1570)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[331, 612])).
% 1.19/1.43 tff(614,plain,
% 1.19/1.43 (~c0_1(a1570)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[337, 612])).
% 1.19/1.43 tff(615,plain,
% 1.19/1.43 (c3_1(a1570)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[345, 612])).
% 1.19/1.43 tff(616,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1570) | c1_1(a1570) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1570) | c1_1(a1570) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(617,plain,
% 1.19/1.43 (((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570))) <=> (c0_1(a1570) | c1_1(a1570) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(618,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1570) | c1_1(a1570) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570))))),
% 1.19/1.43 inference(monotonicity,[status(thm)],[617])).
% 1.19/1.43 tff(619,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1570) | c1_1(a1570) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570)))),
% 1.19/1.43 inference(transitivity,[status(thm)],[618, 616])).
% 1.19/1.43 tff(620,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570)))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(621,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1570) | c1_1(a1570) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1570))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[620, 619])).
% 1.19/1.43 tff(622,plain,
% 1.19/1.43 ($false),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[621, 319, 615, 265, 266, 614, 613, 264, 393, 383])).
% 1.19/1.43 tff(623,plain,((~hskp17) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | (~c1_1(a1534))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.43 tff(624,plain,
% 1.19/1.43 (~hskp17),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[623, 372, 266, 264, 265])).
% 1.19/1.43 tff(625,plain,
% 1.19/1.43 (~c1_1(a1538)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[161, 609])).
% 1.19/1.43 tff(626,plain,
% 1.19/1.43 (~c2_1(a1538)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[138, 609])).
% 1.19/1.43 tff(627,assumption,(~c3_1(a1538)), introduced(assumption)).
% 1.19/1.43 tff(628,assumption,(~hskp17), introduced(assumption)).
% 1.19/1.43 tff(629,assumption,(~c1_1(a1538)), introduced(assumption)).
% 1.19/1.43 tff(630,assumption,(~c2_1(a1593)), introduced(assumption)).
% 1.19/1.43 tff(631,plain,
% 1.19/1.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a1593) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c3_1(a1593)) | (~c0_1(a1593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a1593) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c3_1(a1593)) | (~c0_1(a1593)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(632,plain,
% 1.19/1.43 ((hskp17 | (~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538))) <=> (hskp17 | c2_1(a1593) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c3_1(a1593)) | (~c0_1(a1593)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(633,plain,
% 1.19/1.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a1593) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c3_1(a1593)) | (~c0_1(a1593))))),
% 1.19/1.43 inference(monotonicity,[status(thm)],[632])).
% 1.19/1.43 tff(634,plain,
% 1.19/1.43 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a1593) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c3_1(a1593)) | (~c0_1(a1593)))),
% 1.19/1.43 inference(transitivity,[status(thm)],[633, 631])).
% 1.19/1.43 tff(635,plain,
% 1.19/1.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(636,plain,
% 1.19/1.43 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a1593) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c3_1(a1593)) | (~c0_1(a1593))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.19/1.43 tff(637,plain,
% 1.19/1.43 ((~c0_1(a1538)) | (~c3_1(a1593)) | (~c0_1(a1593))),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[636, 319, 628, 630, 629, 627, 287])).
% 1.19/1.43 tff(638,plain,
% 1.19/1.43 (~c0_1(a1538)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[637, 295, 296])).
% 1.19/1.43 tff(639,plain,
% 1.19/1.43 (c1_1(a1534) | (~c3_1(a1593)) | (~c0_1(a1593))),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[325, 319, 628, 265, 630, 264, 287])).
% 1.19/1.43 tff(640,plain,
% 1.19/1.43 (c1_1(a1534)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[639, 295, 296])).
% 1.19/1.43 tff(641,plain,
% 1.19/1.43 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(642,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[641])).
% 1.19/1.43 tff(643,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(644,plain,
% 1.19/1.43 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(645,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[644])).
% 1.19/1.43 tff(646,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.19/1.43 tff(647,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[646, 645])).
% 1.19/1.43 tff(648,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[647, 643])).
% 1.19/1.43 tff(649,plain,(
% 1.19/1.43 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 1.19/1.43 inference(skolemize,[status(sab)],[648])).
% 1.19/1.43 tff(650,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[649, 642])).
% 1.19/1.43 tff(651,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c0_1(a1538) | (~c2_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c0_1(a1538) | (~c2_1(a1545)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(652,plain,
% 1.19/1.43 (((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538)) <=> (c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c0_1(a1538) | (~c2_1(a1545)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(653,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c0_1(a1538) | (~c2_1(a1545))))),
% 1.19/1.43 inference(monotonicity,[status(thm)],[652])).
% 1.19/1.43 tff(654,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c0_1(a1538) | (~c2_1(a1545)))),
% 1.19/1.43 inference(transitivity,[status(thm)],[653, 651])).
% 1.19/1.43 tff(655,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(656,plain,
% 1.19/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c0_1(a1538) | (~c2_1(a1545))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[655, 654])).
% 1.19/1.43 tff(657,plain,
% 1.19/1.43 ($false),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[656, 319, 611, 265, 266, 23, 24, 629, 156, 650, 640, 638])).
% 1.19/1.43 tff(658,plain,((~hskp23) | (~c2_1(a1545)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | hskp17 | c2_1(a1593) | c3_1(a1534) | c3_1(a1538)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.43 tff(659,plain,
% 1.19/1.43 ($false),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[658, 294, 288, 265, 266, 23, 24, 629, 156, 628, 611, 264, 627])).
% 1.19/1.43 tff(660,plain,((~hskp23) | (~c0_1(a1534)) | (~c2_1(a1534)) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | hskp17 | (~c2_1(a1545)) | c3_1(a1534) | c3_1(a1538)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.43 tff(661,plain,
% 1.19/1.43 ($false),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[660, 626, 625, 266, 23, 24, 247, 624, 265, 611, 264, 610])).
% 1.19/1.43 tff(662,plain,(hskp3 | (~c2_1(a1534)) | c0_1(a1545) | c3_1(a1545) | (~c0_1(a1534)) | (~c2_1(a1545)) | c3_1(a1534) | hskp31 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.19/1.43 tff(663,plain,
% 1.19/1.43 (hskp3),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[662, 223, 187, 181, 237, 195, 229, 163, 206])).
% 1.19/1.43 tff(664,plain,
% 1.19/1.43 (((~hskp3) | (~c2_1(a1536))) <=> ((~hskp3) | (~c2_1(a1536)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(665,plain,
% 1.19/1.43 (((~c2_1(a1536)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1536)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(666,axiom,((~c2_1(a1536)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.19/1.43 tff(667,plain,
% 1.19/1.43 ((~hskp3) | (~c2_1(a1536))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.19/1.43 tff(668,plain,
% 1.19/1.43 ((~hskp3) | (~c2_1(a1536))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[667, 664])).
% 1.19/1.43 tff(669,plain,
% 1.19/1.43 (~c2_1(a1536)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[668, 663])).
% 1.19/1.43 tff(670,plain,
% 1.19/1.43 (((~hskp3) | (~c0_1(a1536))) <=> ((~hskp3) | (~c0_1(a1536)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(671,plain,
% 1.19/1.43 (((~c0_1(a1536)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a1536)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(672,axiom,((~c0_1(a1536)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.19/1.43 tff(673,plain,
% 1.19/1.43 ((~hskp3) | (~c0_1(a1536))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[672, 671])).
% 1.19/1.43 tff(674,plain,
% 1.19/1.43 ((~hskp3) | (~c0_1(a1536))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[673, 670])).
% 1.19/1.43 tff(675,plain,
% 1.19/1.43 (~c0_1(a1536)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[674, 663])).
% 1.19/1.43 tff(676,plain,
% 1.19/1.43 (~hskp23),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[371, 267, 266, 264, 265])).
% 1.19/1.43 tff(677,plain,
% 1.19/1.43 (hskp3),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[246, 676, 206])).
% 1.19/1.43 tff(678,plain,
% 1.19/1.43 (((~hskp3) | c1_1(a1536)) <=> ((~hskp3) | c1_1(a1536))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(679,axiom,((~hskp3) | c1_1(a1536)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.19/1.43 tff(680,plain,
% 1.19/1.43 ((~hskp3) | c1_1(a1536)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[679, 678])).
% 1.19/1.43 tff(681,plain,
% 1.19/1.43 ((~hskp3) | c1_1(a1536)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[680, 678])).
% 1.19/1.43 tff(682,plain,
% 1.19/1.43 ((~hskp3) | c1_1(a1536)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[681, 678])).
% 1.19/1.43 tff(683,plain,
% 1.19/1.43 ((~hskp3) | c1_1(a1536)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[682, 678])).
% 1.19/1.43 tff(684,plain,
% 1.19/1.43 ((~hskp3) | c1_1(a1536)),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[683, 678])).
% 1.19/1.43 tff(685,plain,
% 1.19/1.43 (c1_1(a1536)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[684, 677])).
% 1.19/1.43 tff(686,plain,
% 1.19/1.43 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(687,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[686])).
% 1.19/1.43 tff(688,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(689,plain,
% 1.19/1.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp31) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp31))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(690,plain,
% 1.19/1.43 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[689])).
% 1.19/1.43 tff(691,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.19/1.43 tff(692,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[691, 690])).
% 1.19/1.43 tff(693,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[692, 688])).
% 1.19/1.43 tff(694,plain,(
% 1.19/1.43 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.43 inference(skolemize,[status(sab)],[693])).
% 1.19/1.43 tff(695,plain,
% 1.19/1.43 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[694, 687])).
% 1.19/1.43 tff(696,assumption,(~c0_1(a1536)), introduced(assumption)).
% 1.19/1.43 tff(697,plain,
% 1.19/1.43 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp31 | c0_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c1_1(a1536)) | (~c3_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp31 | c0_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c1_1(a1536)) | (~c3_1(a1536)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(698,plain,
% 1.19/1.43 ((hskp31 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c0_1(a1536) | (~c1_1(a1536)) | (~c3_1(a1536))) <=> (hskp31 | c0_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c1_1(a1536)) | (~c3_1(a1536)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(699,plain,
% 1.19/1.43 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp31 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c0_1(a1536) | (~c1_1(a1536)) | (~c3_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp31 | c0_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c1_1(a1536)) | (~c3_1(a1536))))),
% 1.19/1.43 inference(monotonicity,[status(thm)],[698])).
% 1.19/1.43 tff(700,plain,
% 1.19/1.43 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp31 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c0_1(a1536) | (~c1_1(a1536)) | (~c3_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp31 | c0_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c1_1(a1536)) | (~c3_1(a1536)))),
% 1.19/1.43 inference(transitivity,[status(thm)],[699, 697])).
% 1.19/1.43 tff(701,plain,
% 1.19/1.43 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp31 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c0_1(a1536) | (~c1_1(a1536)) | (~c3_1(a1536)))),
% 1.19/1.43 inference(quant_inst,[status(thm)],[])).
% 1.19/1.43 tff(702,plain,
% 1.19/1.43 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp31 | c0_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c1_1(a1536)) | (~c3_1(a1536))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[701, 700])).
% 1.19/1.43 tff(703,plain,
% 1.19/1.43 ((~c1_1(a1536)) | (~c3_1(a1536))),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[702, 163, 319, 265, 696, 264, 695, 267])).
% 1.19/1.43 tff(704,plain,
% 1.19/1.43 (~c3_1(a1536)),
% 1.19/1.43 inference(unit_resolution,[status(thm)],[703, 685])).
% 1.19/1.43 tff(705,plain,
% 1.19/1.43 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(706,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[705])).
% 1.19/1.43 tff(707,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(708,plain,
% 1.19/1.43 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 1.19/1.43 inference(bind,[status(th)],[])).
% 1.19/1.43 tff(709,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.43 inference(quant_intro,[status(thm)],[708])).
% 1.19/1.43 tff(710,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.19/1.43 tff(711,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.19/1.43 tff(712,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[711, 707])).
% 1.19/1.43 tff(713,plain,(
% 1.19/1.43 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.43 inference(skolemize,[status(sab)],[712])).
% 1.19/1.43 tff(714,plain,
% 1.19/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.19/1.43 inference(modus_ponens,[status(thm)],[713, 706])).
% 1.19/1.43 tff(715,assumption,(~c2_1(a1536)), introduced(assumption)).
% 1.19/1.43 tff(716,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1545) | c3_1(a1545) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1545) | c3_1(a1545) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1545)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(717,plain,
% 1.19/1.43 (((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536)) <=> (c0_1(a1545) | c3_1(a1545) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1545)))),
% 1.19/1.43 inference(rewrite,[status(thm)],[])).
% 1.19/1.43 tff(718,plain,
% 1.19/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1545) | c3_1(a1545) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1545))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[717])).
% 1.19/1.44 tff(719,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1545) | c3_1(a1545) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1545)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[718, 716])).
% 1.19/1.44 tff(720,plain,
% 1.19/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(721,plain,
% 1.19/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1545) | c3_1(a1545) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1545))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[720, 719])).
% 1.19/1.44 tff(722,plain,
% 1.19/1.44 ($false),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[721, 319, 611, 265, 23, 24, 696, 715, 264, 714, 267, 704])).
% 1.19/1.44 tff(723,plain,(c1_1(a1534) | (~c2_1(a1545)) | (~c0_1(a1534)) | c0_1(a1545) | c3_1(a1545) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | hskp31 | hskp26 | (~c2_1(a1534))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.44 tff(724,plain,
% 1.19/1.44 (c1_1(a1534)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[723, 675, 237, 187, 181, 195, 669, 229, 163, 206, 223])).
% 1.19/1.44 tff(725,plain,
% 1.19/1.44 (c1_1(a1536)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[684, 663])).
% 1.19/1.44 tff(726,plain,
% 1.19/1.44 (~hskp10),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[555, 724, 223, 237, 229])).
% 1.19/1.44 tff(727,plain,
% 1.19/1.44 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(728,plain,
% 1.19/1.44 ((hskp10 | hskp4 | (~ndr1_0) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536))) <=> (hskp10 | hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(729,plain,
% 1.19/1.44 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[728])).
% 1.19/1.44 tff(730,plain,
% 1.19/1.44 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[729, 727])).
% 1.19/1.44 tff(731,plain,
% 1.19/1.44 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536)))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(732,plain,
% 1.19/1.44 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[731, 730])).
% 1.19/1.44 tff(733,plain,
% 1.19/1.44 (hskp4),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[732, 319, 726, 725, 675, 669, 121])).
% 1.19/1.44 tff(734,plain,
% 1.19/1.44 (~c2_1(a1538)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[138, 733])).
% 1.19/1.44 tff(735,plain,
% 1.19/1.44 (~c1_1(a1538)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[161, 733])).
% 1.19/1.44 tff(736,plain,
% 1.19/1.44 (c0_1(a1538)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[656, 319, 195, 237, 223, 187, 181, 735, 734, 650, 724])).
% 1.19/1.44 tff(737,plain,
% 1.19/1.44 (^[U: $i] : refl((hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.19/1.44 inference(bind,[status(th)],[])).
% 1.19/1.44 tff(738,plain,
% 1.19/1.44 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[737])).
% 1.19/1.44 tff(739,plain,
% 1.19/1.44 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(740,plain,
% 1.19/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp23))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.19/1.44 inference(bind,[status(th)],[])).
% 1.19/1.44 tff(741,plain,
% 1.19/1.44 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[740])).
% 1.19/1.44 tff(742,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.19/1.44 tff(743,plain,
% 1.19/1.44 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[742, 741])).
% 1.19/1.44 tff(744,plain,
% 1.19/1.44 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[743, 739])).
% 1.19/1.44 tff(745,plain,(
% 1.19/1.44 ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(skolemize,[status(sab)],[744])).
% 1.19/1.44 tff(746,plain,
% 1.19/1.44 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[745, 738])).
% 1.19/1.44 tff(747,plain,
% 1.19/1.44 (~c3_1(a1538)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[154, 733])).
% 1.19/1.44 tff(748,plain,
% 1.19/1.44 (~hskp17),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[623, 724, 223, 229, 237])).
% 1.19/1.44 tff(749,plain,
% 1.19/1.44 (~hskp23),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[660, 734, 223, 187, 181, 735, 748, 237, 195, 229, 747])).
% 1.19/1.44 tff(750,plain,
% 1.19/1.44 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp23 | hskp8 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp23 | hskp8 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(751,plain,
% 1.19/1.44 ((hskp23 | hskp8 | (~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538))) <=> (hskp23 | hskp8 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(752,plain,
% 1.19/1.44 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp23 | hskp8 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[751])).
% 1.19/1.44 tff(753,plain,
% 1.19/1.44 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp23 | hskp8 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[752, 750])).
% 1.19/1.44 tff(754,plain,
% 1.19/1.44 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(755,plain,
% 1.19/1.44 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp23 | hskp8 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[754, 753])).
% 1.19/1.44 tff(756,plain,
% 1.19/1.44 (hskp8),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[755, 319, 749, 734, 747, 746, 736])).
% 1.19/1.44 tff(757,plain,
% 1.19/1.44 (((~hskp8) | (~c3_1(a1547))) <=> ((~hskp8) | (~c3_1(a1547)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(758,plain,
% 1.19/1.44 (((~c3_1(a1547)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a1547)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(759,axiom,((~c3_1(a1547)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.19/1.44 tff(760,plain,
% 1.19/1.44 ((~hskp8) | (~c3_1(a1547))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[759, 758])).
% 1.19/1.44 tff(761,plain,
% 1.19/1.44 ((~hskp8) | (~c3_1(a1547))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[760, 757])).
% 1.19/1.44 tff(762,plain,
% 1.19/1.44 (~c3_1(a1547)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[761, 756])).
% 1.19/1.44 tff(763,plain,
% 1.19/1.44 (((~hskp8) | c1_1(a1547)) <=> ((~hskp8) | c1_1(a1547))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(764,axiom,((~hskp8) | c1_1(a1547)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.19/1.44 tff(765,plain,
% 1.19/1.44 ((~hskp8) | c1_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[764, 763])).
% 1.19/1.44 tff(766,plain,
% 1.19/1.44 ((~hskp8) | c1_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[765, 763])).
% 1.19/1.44 tff(767,plain,
% 1.19/1.44 ((~hskp8) | c1_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[766, 763])).
% 1.19/1.44 tff(768,plain,
% 1.19/1.44 ((~hskp8) | c1_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[767, 763])).
% 1.19/1.44 tff(769,plain,
% 1.19/1.44 ((~hskp8) | c1_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[768, 763])).
% 1.19/1.44 tff(770,plain,
% 1.19/1.44 (c1_1(a1547)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[769, 756])).
% 1.19/1.44 tff(771,plain,
% 1.19/1.44 (((~hskp8) | c0_1(a1547)) <=> ((~hskp8) | c0_1(a1547))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(772,axiom,((~hskp8) | c0_1(a1547)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.19/1.44 tff(773,plain,
% 1.19/1.44 ((~hskp8) | c0_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.19/1.44 tff(774,plain,
% 1.19/1.44 ((~hskp8) | c0_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[773, 771])).
% 1.19/1.44 tff(775,plain,
% 1.19/1.44 ((~hskp8) | c0_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[774, 771])).
% 1.19/1.44 tff(776,plain,
% 1.19/1.44 ((~hskp8) | c0_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[775, 771])).
% 1.19/1.44 tff(777,plain,
% 1.19/1.44 ((~hskp8) | c0_1(a1547)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[776, 771])).
% 1.19/1.44 tff(778,plain,
% 1.19/1.44 (c0_1(a1547)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[777, 756])).
% 1.19/1.44 tff(779,plain,
% 1.19/1.44 (^[U: $i] : refl((hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.19/1.44 inference(bind,[status(th)],[])).
% 1.19/1.44 tff(780,plain,
% 1.19/1.44 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[779])).
% 1.19/1.44 tff(781,plain,
% 1.19/1.44 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(782,plain,
% 1.19/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp15) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp15))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp15) <=> (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp15) <=> (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.19/1.44 inference(bind,[status(th)],[])).
% 1.19/1.44 tff(783,plain,
% 1.19/1.44 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp15) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[782])).
% 1.19/1.44 tff(784,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.19/1.44 tff(785,plain,
% 1.19/1.44 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[784, 783])).
% 1.19/1.44 tff(786,plain,
% 1.19/1.44 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[785, 781])).
% 1.19/1.44 tff(787,plain,(
% 1.19/1.44 ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(skolemize,[status(sab)],[786])).
% 1.19/1.44 tff(788,plain,
% 1.19/1.44 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[787, 780])).
% 1.19/1.44 tff(789,plain,
% 1.19/1.44 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(790,plain,
% 1.19/1.44 ((hskp28 | hskp15 | (~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538))) <=> (hskp28 | hskp15 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(791,plain,
% 1.19/1.44 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[790])).
% 1.19/1.44 tff(792,plain,
% 1.19/1.44 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[791, 789])).
% 1.19/1.44 tff(793,plain,
% 1.19/1.44 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(794,plain,
% 1.19/1.44 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.19/1.44 tff(795,plain,
% 1.19/1.44 (hskp28),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[794, 319, 132, 734, 747, 788, 736])).
% 1.19/1.44 tff(796,plain,
% 1.19/1.44 (c3_1(a1542)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[530, 795])).
% 1.19/1.44 tff(797,plain,
% 1.19/1.44 (c2_1(a1542)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[538, 795])).
% 1.19/1.44 tff(798,plain,
% 1.19/1.44 (c1_1(a1542)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[546, 795])).
% 1.19/1.44 tff(799,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | c3_1(a1547) | (~ndr1_0) | (~c0_1(a1547)) | (~c1_1(a1547)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp23 | c3_1(a1547) | (~ndr1_0) | (~c0_1(a1547)) | (~c1_1(a1547)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(800,plain,
% 1.19/1.44 ((hskp23 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1547) | (~c1_1(a1547)) | (~c0_1(a1547))) <=> (hskp23 | c3_1(a1547) | (~ndr1_0) | (~c0_1(a1547)) | (~c1_1(a1547)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(801,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1547) | (~c1_1(a1547)) | (~c0_1(a1547)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | c3_1(a1547) | (~ndr1_0) | (~c0_1(a1547)) | (~c1_1(a1547)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[800])).
% 1.19/1.44 tff(802,plain,
% 1.19/1.44 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1547) | (~c1_1(a1547)) | (~c0_1(a1547)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp23 | c3_1(a1547) | (~ndr1_0) | (~c0_1(a1547)) | (~c1_1(a1547)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[801, 799])).
% 1.19/1.44 tff(803,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1547) | (~c1_1(a1547)) | (~c0_1(a1547)))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(804,plain,
% 1.19/1.44 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp23 | c3_1(a1547) | (~ndr1_0) | (~c0_1(a1547)) | (~c1_1(a1547)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.19/1.44 tff(805,plain,
% 1.19/1.44 ($false),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[804, 319, 749, 798, 797, 796, 778, 770, 762, 205])).
% 1.19/1.44 tff(806,plain,(hskp26 | hskp15 | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.19/1.44 tff(807,plain,
% 1.19/1.44 (hskp26),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[806, 163, 132])).
% 1.19/1.44 tff(808,plain,
% 1.19/1.44 (((~hskp26) | (~c3_1(a1624))) <=> ((~hskp26) | (~c3_1(a1624)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(809,plain,
% 1.19/1.44 (((~c3_1(a1624)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a1624)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(810,axiom,((~c3_1(a1624)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.19/1.44 tff(811,plain,
% 1.19/1.44 ((~hskp26) | (~c3_1(a1624))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.19/1.44 tff(812,plain,
% 1.19/1.44 ((~hskp26) | (~c3_1(a1624))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[811, 808])).
% 1.19/1.44 tff(813,plain,
% 1.19/1.44 (~c3_1(a1624)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[812, 807])).
% 1.19/1.44 tff(814,plain,
% 1.19/1.44 (((~hskp26) | (~c2_1(a1624))) <=> ((~hskp26) | (~c2_1(a1624)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(815,plain,
% 1.19/1.44 (((~c2_1(a1624)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a1624)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(816,axiom,((~c2_1(a1624)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.19/1.44 tff(817,plain,
% 1.19/1.44 ((~hskp26) | (~c2_1(a1624))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.19/1.44 tff(818,plain,
% 1.19/1.44 ((~hskp26) | (~c2_1(a1624))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[817, 814])).
% 1.19/1.44 tff(819,plain,
% 1.19/1.44 (~c2_1(a1624)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[818, 807])).
% 1.19/1.44 tff(820,plain,
% 1.19/1.44 (((~hskp26) | (~c0_1(a1624))) <=> ((~hskp26) | (~c0_1(a1624)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(821,plain,
% 1.19/1.44 (((~c0_1(a1624)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a1624)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(822,axiom,((~c0_1(a1624)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.19/1.44 tff(823,plain,
% 1.19/1.44 ((~hskp26) | (~c0_1(a1624))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[822, 821])).
% 1.19/1.44 tff(824,plain,
% 1.19/1.44 ((~hskp26) | (~c0_1(a1624))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[823, 820])).
% 1.19/1.44 tff(825,plain,
% 1.19/1.44 (~c0_1(a1624)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[824, 807])).
% 1.19/1.44 tff(826,plain,
% 1.19/1.44 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.19/1.44 inference(bind,[status(th)],[])).
% 1.19/1.44 tff(827,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[826])).
% 1.19/1.44 tff(828,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(829,plain,
% 1.19/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp15) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.19/1.44 inference(bind,[status(th)],[])).
% 1.19/1.44 tff(830,plain,
% 1.19/1.44 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.19/1.44 inference(quant_intro,[status(thm)],[829])).
% 1.19/1.44 tff(831,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.19/1.44 tff(832,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[831, 830])).
% 1.19/1.44 tff(833,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[832, 828])).
% 1.19/1.44 tff(834,plain,(
% 1.19/1.44 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.19/1.44 inference(skolemize,[status(sab)],[833])).
% 1.19/1.44 tff(835,plain,
% 1.19/1.44 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[834, 827])).
% 1.19/1.44 tff(836,assumption,(hskp2), introduced(assumption)).
% 1.19/1.44 tff(837,plain,
% 1.19/1.44 (((~hskp2) | c3_1(a1535)) <=> ((~hskp2) | c3_1(a1535))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(838,axiom,((~hskp2) | c3_1(a1535)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.19/1.44 tff(839,plain,
% 1.19/1.44 ((~hskp2) | c3_1(a1535)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.19/1.44 tff(840,plain,
% 1.19/1.44 ((~hskp2) | c3_1(a1535)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[839, 837])).
% 1.19/1.44 tff(841,plain,
% 1.19/1.44 ((~hskp2) | c3_1(a1535)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[840, 837])).
% 1.19/1.44 tff(842,plain,
% 1.19/1.44 ((~hskp2) | c3_1(a1535)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[841, 837])).
% 1.19/1.44 tff(843,plain,
% 1.19/1.44 ((~hskp2) | c3_1(a1535)),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[842, 837])).
% 1.19/1.44 tff(844,plain,
% 1.19/1.44 (c3_1(a1535)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[843, 836])).
% 1.19/1.44 tff(845,plain,
% 1.19/1.44 (((~hskp2) | (~c2_1(a1535))) <=> ((~hskp2) | (~c2_1(a1535)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(846,plain,
% 1.19/1.44 (((~c2_1(a1535)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1535)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(847,axiom,((~c2_1(a1535)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.19/1.44 tff(848,plain,
% 1.19/1.44 ((~hskp2) | (~c2_1(a1535))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[847, 846])).
% 1.19/1.44 tff(849,plain,
% 1.19/1.44 ((~hskp2) | (~c2_1(a1535))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[848, 845])).
% 1.19/1.44 tff(850,plain,
% 1.19/1.44 (~c2_1(a1535)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[849, 836])).
% 1.19/1.44 tff(851,assumption,(~c3_1(a1624)), introduced(assumption)).
% 1.19/1.44 tff(852,assumption,(~c2_1(a1624)), introduced(assumption)).
% 1.19/1.44 tff(853,assumption,(~c0_1(a1624)), introduced(assumption)).
% 1.19/1.44 tff(854,plain,
% 1.19/1.44 (((~hskp2) | (~c1_1(a1535))) <=> ((~hskp2) | (~c1_1(a1535)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(855,plain,
% 1.19/1.44 (((~c1_1(a1535)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a1535)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(856,axiom,((~c1_1(a1535)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.19/1.44 tff(857,plain,
% 1.19/1.44 ((~hskp2) | (~c1_1(a1535))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[856, 855])).
% 1.19/1.44 tff(858,plain,
% 1.19/1.44 ((~hskp2) | (~c1_1(a1535))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[857, 854])).
% 1.19/1.44 tff(859,plain,
% 1.19/1.44 (~c1_1(a1535)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[858, 836])).
% 1.19/1.44 tff(860,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(861,plain,
% 1.19/1.44 (((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624)) <=> (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.19/1.44 inference(rewrite,[status(thm)],[])).
% 1.19/1.44 tff(862,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538))))),
% 1.19/1.44 inference(monotonicity,[status(thm)],[861])).
% 1.19/1.44 tff(863,plain,
% 1.19/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.19/1.44 inference(transitivity,[status(thm)],[862, 860])).
% 1.19/1.44 tff(864,plain,
% 1.19/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))),
% 1.19/1.44 inference(quant_inst,[status(thm)],[])).
% 1.19/1.44 tff(865,plain,
% 1.19/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538))),
% 1.19/1.44 inference(modus_ponens,[status(thm)],[864, 863])).
% 1.19/1.44 tff(866,plain,
% 1.19/1.44 (c1_1(a1538) | (~c0_1(a1538))),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[865, 319, 853, 852, 851, 156, 627, 35])).
% 1.19/1.44 tff(867,plain,
% 1.19/1.44 (~c0_1(a1538)),
% 1.19/1.44 inference(unit_resolution,[status(thm)],[866, 629])).
% 1.19/1.44 tff(868,assumption,(c3_1(a1535)), introduced(assumption)).
% 1.19/1.45 tff(869,assumption,(~c2_1(a1535)), introduced(assumption)).
% 1.19/1.45 tff(870,assumption,(~c1_1(a1535)), introduced(assumption)).
% 1.19/1.45 tff(871,assumption,(~c0_1(a1538)), introduced(assumption)).
% 1.19/1.45 tff(872,assumption,(hskp28), introduced(assumption)).
% 1.19/1.45 tff(873,plain,
% 1.19/1.45 (c2_1(a1542)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[538, 872])).
% 1.19/1.45 tff(874,plain,
% 1.19/1.45 (c1_1(a1542)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[546, 872])).
% 1.19/1.45 tff(875,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(876,plain,
% 1.19/1.45 (((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538)) <=> (c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.19/1.45 inference(rewrite,[status(thm)],[])).
% 1.19/1.45 tff(877,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))))),
% 1.19/1.45 inference(monotonicity,[status(thm)],[876])).
% 1.19/1.45 tff(878,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.19/1.45 inference(transitivity,[status(thm)],[877, 875])).
% 1.19/1.45 tff(879,plain,
% 1.19/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))),
% 1.19/1.45 inference(quant_inst,[status(thm)],[])).
% 1.19/1.45 tff(880,plain,
% 1.19/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))),
% 1.19/1.45 inference(modus_ponens,[status(thm)],[879, 878])).
% 1.19/1.45 tff(881,plain,
% 1.19/1.45 (~c0_1(a1542)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[880, 319, 874, 873, 611, 23, 24, 629, 156, 650, 871])).
% 1.19/1.45 tff(882,plain,
% 1.19/1.45 (c3_1(a1542)),
% 1.19/1.45 inference(unit_resolution,[status(thm)],[530, 872])).
% 1.19/1.45 tff(883,plain,
% 1.19/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(884,plain,
% 1.28/1.45 (((~ndr1_0) | c1_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542))) <=> (c1_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(885,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[884])).
% 1.28/1.45 tff(886,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.28/1.45 inference(transitivity,[status(thm)],[885, 883])).
% 1.28/1.45 tff(887,plain,
% 1.28/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(888,plain,
% 1.28/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[887, 886])).
% 1.28/1.45 tff(889,plain,
% 1.28/1.45 (~c0_1(a1535)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[888, 319, 874, 873, 882, 868, 870, 382, 881])).
% 1.28/1.45 tff(890,plain,
% 1.28/1.45 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(891,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[890])).
% 1.28/1.45 tff(892,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(893,plain,
% 1.28/1.45 (^[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)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(894,plain,
% 1.28/1.45 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[893])).
% 1.28/1.45 tff(895,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.28/1.45 tff(896,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[895, 894])).
% 1.28/1.45 tff(897,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[896, 892])).
% 1.28/1.45 tff(898,plain,(
% 1.28/1.45 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.28/1.45 inference(skolemize,[status(sab)],[897])).
% 1.28/1.45 tff(899,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[898, 891])).
% 1.28/1.45 tff(900,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(901,plain,
% 1.28/1.45 ((hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624)) <=> (hskp6 | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(902,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[901])).
% 1.28/1.45 tff(903,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[902, 900])).
% 1.28/1.45 tff(904,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(905,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[904, 903])).
% 1.28/1.45 tff(906,plain,
% 1.28/1.45 (hskp6 | c0_1(a1535)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[905, 319, 868, 853, 852, 851, 869, 899])).
% 1.28/1.45 tff(907,plain,
% 1.28/1.45 (hskp6),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[906, 889])).
% 1.28/1.45 tff(908,plain,
% 1.28/1.45 (((~hskp6) | (~c2_1(a1543))) <=> ((~hskp6) | (~c2_1(a1543)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(909,plain,
% 1.28/1.45 (((~c2_1(a1543)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a1543)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(910,axiom,((~c2_1(a1543)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.28/1.45 tff(911,plain,
% 1.28/1.45 ((~hskp6) | (~c2_1(a1543))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[910, 909])).
% 1.28/1.45 tff(912,plain,
% 1.28/1.45 ((~hskp6) | (~c2_1(a1543))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[911, 908])).
% 1.28/1.45 tff(913,plain,
% 1.28/1.45 (~c2_1(a1543)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[912, 907])).
% 1.28/1.45 tff(914,plain,
% 1.28/1.45 (((~hskp6) | (~c1_1(a1543))) <=> ((~hskp6) | (~c1_1(a1543)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(915,plain,
% 1.28/1.45 (((~c1_1(a1543)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a1543)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(916,axiom,((~c1_1(a1543)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.28/1.45 tff(917,plain,
% 1.28/1.45 ((~hskp6) | (~c1_1(a1543))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[916, 915])).
% 1.28/1.45 tff(918,plain,
% 1.28/1.45 ((~hskp6) | (~c1_1(a1543))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[917, 914])).
% 1.28/1.45 tff(919,plain,
% 1.28/1.45 (~c1_1(a1543)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[918, 907])).
% 1.28/1.45 tff(920,plain,
% 1.28/1.45 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(921,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[920])).
% 1.28/1.45 tff(922,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(923,plain,
% 1.28/1.45 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_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)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_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)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_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)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_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)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.28/1.45 inference(bind,[status(th)],[])).
% 1.28/1.45 tff(924,plain,
% 1.28/1.45 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.45 inference(quant_intro,[status(thm)],[923])).
% 1.28/1.45 tff(925,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.28/1.45 tff(926,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[925, 924])).
% 1.28/1.45 tff(927,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[926, 922])).
% 1.28/1.45 tff(928,plain,(
% 1.28/1.45 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.45 inference(skolemize,[status(sab)],[927])).
% 1.28/1.45 tff(929,plain,
% 1.28/1.45 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[928, 921])).
% 1.28/1.45 tff(930,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(931,plain,
% 1.28/1.45 ((hskp11 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535))) <=> (hskp11 | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(932,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[931])).
% 1.28/1.45 tff(933,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[932, 930])).
% 1.28/1.45 tff(934,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(935,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[934, 933])).
% 1.28/1.45 tff(936,plain,
% 1.28/1.45 (hskp11 | c0_1(a1535)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[935, 319, 874, 873, 882, 868, 869, 929])).
% 1.28/1.45 tff(937,plain,
% 1.28/1.45 (hskp11),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[936, 889])).
% 1.28/1.45 tff(938,plain,
% 1.28/1.45 (((~hskp11) | (~c1_1(a1553))) <=> ((~hskp11) | (~c1_1(a1553)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(939,plain,
% 1.28/1.45 (((~c1_1(a1553)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a1553)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(940,axiom,((~c1_1(a1553)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.28/1.45 tff(941,plain,
% 1.28/1.45 ((~hskp11) | (~c1_1(a1553))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[940, 939])).
% 1.28/1.45 tff(942,plain,
% 1.28/1.45 ((~hskp11) | (~c1_1(a1553))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[941, 938])).
% 1.28/1.45 tff(943,plain,
% 1.28/1.45 (~c1_1(a1553)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[942, 937])).
% 1.28/1.45 tff(944,plain,
% 1.28/1.45 (((~hskp6) | c0_1(a1543)) <=> ((~hskp6) | c0_1(a1543))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(945,axiom,((~hskp6) | c0_1(a1543)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.28/1.45 tff(946,plain,
% 1.28/1.45 ((~hskp6) | c0_1(a1543)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[945, 944])).
% 1.28/1.45 tff(947,plain,
% 1.28/1.45 ((~hskp6) | c0_1(a1543)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[946, 944])).
% 1.28/1.45 tff(948,plain,
% 1.28/1.45 ((~hskp6) | c0_1(a1543)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[947, 944])).
% 1.28/1.45 tff(949,plain,
% 1.28/1.45 ((~hskp6) | c0_1(a1543)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[948, 944])).
% 1.28/1.45 tff(950,plain,
% 1.28/1.45 ((~hskp6) | c0_1(a1543)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[949, 944])).
% 1.28/1.45 tff(951,plain,
% 1.28/1.45 (c0_1(a1543)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[950, 907])).
% 1.28/1.45 tff(952,plain,
% 1.28/1.45 (((~hskp11) | c2_1(a1553)) <=> ((~hskp11) | c2_1(a1553))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(953,axiom,((~hskp11) | c2_1(a1553)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.28/1.45 tff(954,plain,
% 1.28/1.45 ((~hskp11) | c2_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[953, 952])).
% 1.28/1.45 tff(955,plain,
% 1.28/1.45 ((~hskp11) | c2_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[954, 952])).
% 1.28/1.45 tff(956,plain,
% 1.28/1.45 ((~hskp11) | c2_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[955, 952])).
% 1.28/1.45 tff(957,plain,
% 1.28/1.45 ((~hskp11) | c2_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[956, 952])).
% 1.28/1.45 tff(958,plain,
% 1.28/1.45 ((~hskp11) | c2_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[957, 952])).
% 1.28/1.45 tff(959,plain,
% 1.28/1.45 (c2_1(a1553)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[958, 937])).
% 1.28/1.45 tff(960,plain,
% 1.28/1.45 (((~hskp11) | c0_1(a1553)) <=> ((~hskp11) | c0_1(a1553))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(961,axiom,((~hskp11) | c0_1(a1553)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.28/1.45 tff(962,plain,
% 1.28/1.45 ((~hskp11) | c0_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[961, 960])).
% 1.28/1.45 tff(963,plain,
% 1.28/1.45 ((~hskp11) | c0_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[962, 960])).
% 1.28/1.45 tff(964,plain,
% 1.28/1.45 ((~hskp11) | c0_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[963, 960])).
% 1.28/1.45 tff(965,plain,
% 1.28/1.45 ((~hskp11) | c0_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[964, 960])).
% 1.28/1.45 tff(966,plain,
% 1.28/1.45 ((~hskp11) | c0_1(a1553)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[965, 960])).
% 1.28/1.45 tff(967,plain,
% 1.28/1.45 (c0_1(a1553)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[966, 937])).
% 1.28/1.45 tff(968,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(969,plain,
% 1.28/1.45 (((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1535) | c1_1(a1535) | (~c3_1(a1535))) <=> (c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(970,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1535) | c1_1(a1535) | (~c3_1(a1535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[969])).
% 1.28/1.45 tff(971,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1535) | c1_1(a1535) | (~c3_1(a1535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[970, 968])).
% 1.28/1.45 tff(972,plain,
% 1.28/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1535) | c1_1(a1535) | (~c3_1(a1535)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(973,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[972, 971])).
% 1.28/1.46 tff(974,plain,
% 1.28/1.46 ($false),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[973, 319, 967, 959, 951, 868, 943, 919, 913, 870, 277, 889])).
% 1.28/1.46 tff(975,plain,((~hskp28) | (~c3_1(a1535)) | c1_1(a1535) | c2_1(a1535) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | (~c2_1(a1545)) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | c0_1(a1538)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.46 tff(976,plain,
% 1.28/1.46 (~hskp28),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[975, 629, 870, 869, 853, 852, 851, 611, 23, 24, 868, 156, 867])).
% 1.28/1.46 tff(977,assumption,(~c0_1(a1539)), introduced(assumption)).
% 1.28/1.46 tff(978,assumption,(~c3_1(a1539)), introduced(assumption)).
% 1.28/1.46 tff(979,plain,
% 1.28/1.46 (~hskp5),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[482, 978])).
% 1.28/1.46 tff(980,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(981,plain,
% 1.28/1.46 ((hskp15 | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538)) <=> (hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(982,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[981])).
% 1.28/1.46 tff(983,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[982, 980])).
% 1.28/1.46 tff(984,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(985,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c2_1(a1549))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[984, 983])).
% 1.28/1.46 tff(986,plain,
% 1.28/1.46 (~c2_1(a1549)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[985, 319, 132, 426, 418, 629, 156, 627, 149])).
% 1.28/1.46 tff(987,plain,
% 1.28/1.46 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(988,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[987])).
% 1.28/1.46 tff(989,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(990,plain,
% 1.28/1.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(991,plain,
% 1.28/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[990])).
% 1.28/1.46 tff(992,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.28/1.46 tff(993,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[992, 991])).
% 1.28/1.46 tff(994,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[993, 989])).
% 1.28/1.46 tff(995,plain,(
% 1.28/1.46 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.46 inference(skolemize,[status(sab)],[994])).
% 1.28/1.46 tff(996,plain,
% 1.28/1.46 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[995, 988])).
% 1.28/1.46 tff(997,plain,
% 1.28/1.46 (^[U: $i] : refl((hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(998,plain,
% 1.28/1.46 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[997])).
% 1.28/1.46 tff(999,plain,
% 1.28/1.46 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1000,plain,
% 1.28/1.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp11) | hskp1) <=> ((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1))), rewrite(((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1) <=> (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp11) | hskp1) <=> (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(1001,plain,
% 1.28/1.46 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp11) | hskp1) <=> ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[1000])).
% 1.28/1.46 tff(1002,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp11) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.28/1.46 tff(1003,plain,
% 1.28/1.46 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 1.28/1.46 tff(1004,plain,
% 1.28/1.46 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1003, 999])).
% 1.28/1.46 tff(1005,plain,(
% 1.28/1.46 ![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.28/1.46 inference(skolemize,[status(sab)],[1004])).
% 1.28/1.46 tff(1006,plain,
% 1.28/1.46 (![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1005, 998])).
% 1.28/1.46 tff(1007,plain,
% 1.28/1.46 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | c2_1(a1549))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | c2_1(a1549))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1008,plain,
% 1.28/1.46 ((hskp11 | hskp1 | (~ndr1_0) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549))) <=> (hskp11 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | c2_1(a1549))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1009,plain,
% 1.28/1.46 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | c2_1(a1549)))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[1008])).
% 1.28/1.46 tff(1010,plain,
% 1.28/1.46 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | c2_1(a1549))),
% 1.28/1.46 inference(transitivity,[status(thm)],[1009, 1007])).
% 1.28/1.46 tff(1011,plain,
% 1.28/1.46 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(1012,plain,
% 1.28/1.46 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | c2_1(a1549)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 1.28/1.46 tff(1013,plain,
% 1.28/1.46 (hskp11 | c2_1(a1549)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1012, 319, 47, 426, 410, 1006])).
% 1.28/1.46 tff(1014,plain,
% 1.28/1.46 (hskp11),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1013, 986])).
% 1.28/1.46 tff(1015,plain,
% 1.28/1.46 (~c1_1(a1553)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[942, 1014])).
% 1.28/1.46 tff(1016,plain,
% 1.28/1.46 (c2_1(a1553)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[958, 1014])).
% 1.28/1.46 tff(1017,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a1553) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1553)) | (~c2_1(a1553)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a1553) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1018,plain,
% 1.28/1.46 ((hskp15 | (~ndr1_0) | c2_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c1_1(a1553) | (~c3_1(a1553)) | (~c2_1(a1553))) <=> (hskp15 | c1_1(a1553) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1019,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c1_1(a1553) | (~c3_1(a1553)) | (~c2_1(a1553)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a1553) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1553)) | (~c2_1(a1553))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[1018])).
% 1.28/1.46 tff(1020,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c1_1(a1553) | (~c3_1(a1553)) | (~c2_1(a1553)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a1553) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[1019, 1017])).
% 1.28/1.46 tff(1021,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c1_1(a1553) | (~c3_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(1022,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a1553) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1553)) | (~c2_1(a1553))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 1.28/1.46 tff(1023,plain,
% 1.28/1.46 (~c3_1(a1553)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1022, 319, 132, 1016, 426, 418, 1015, 996, 986])).
% 1.28/1.46 tff(1024,plain,
% 1.28/1.46 (c0_1(a1553)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[966, 1014])).
% 1.28/1.46 tff(1025,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1539) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | c3_1(a1553) | (~c0_1(a1553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1539) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | c3_1(a1553) | (~c0_1(a1553)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1026,plain,
% 1.28/1.46 (((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1539) | c0_1(a1539) | (~c2_1(a1539)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624)) <=> (c3_1(a1539) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | c3_1(a1553) | (~c0_1(a1553)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1027,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1539) | c0_1(a1539) | (~c2_1(a1539)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1539) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | c3_1(a1553) | (~c0_1(a1553))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[1026])).
% 1.28/1.46 tff(1028,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1539) | c0_1(a1539) | (~c2_1(a1539)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1539) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | c3_1(a1553) | (~c0_1(a1553)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[1027, 1025])).
% 1.28/1.46 tff(1029,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1539) | c0_1(a1539) | (~c2_1(a1539)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(1030,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1539) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | c3_1(a1553) | (~c0_1(a1553))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 1.28/1.46 tff(1031,plain,
% 1.28/1.46 (~c2_1(a1539)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1030, 319, 1024, 978, 853, 852, 851, 1015, 977, 714, 1023])).
% 1.28/1.46 tff(1032,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1539) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1539) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1033,plain,
% 1.28/1.46 (((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1539) | c2_1(a1539) | c0_1(a1539)) <=> (c3_1(a1539) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1034,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1539) | c2_1(a1539) | c0_1(a1539))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a1539) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[1033])).
% 1.28/1.46 tff(1035,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1539) | c2_1(a1539) | c0_1(a1539))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1539) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[1034, 1032])).
% 1.28/1.46 tff(1036,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1539) | c2_1(a1539) | c0_1(a1539))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(1037,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a1539) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | c2_1(a1539) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 1.28/1.46 tff(1038,plain,
% 1.28/1.46 ($false),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1037, 319, 1024, 611, 978, 1015, 23, 24, 977, 714, 1031, 1023])).
% 1.28/1.46 tff(1039,plain,((~hskp10) | (~c2_1(a1545)) | c3_1(a1539) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | hskp15 | hskp1 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.46 tff(1040,plain,
% 1.28/1.46 (~hskp10),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1039, 978, 611, 23, 24, 977, 853, 852, 851, 132, 47, 629, 156, 627])).
% 1.28/1.46 tff(1041,plain,
% 1.28/1.46 (^[U: $i] : refl((hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(1042,plain,
% 1.28/1.46 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[1041])).
% 1.28/1.46 tff(1043,plain,
% 1.28/1.46 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1044,plain,
% 1.28/1.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp5) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp5))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp5) <=> (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp5) <=> (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(1045,plain,
% 1.28/1.46 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp5) <=> ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[1044])).
% 1.28/1.46 tff(1046,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.28/1.46 tff(1047,plain,
% 1.28/1.46 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 1.28/1.46 tff(1048,plain,
% 1.28/1.46 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1047, 1043])).
% 1.28/1.46 tff(1049,plain,(
% 1.28/1.46 ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.28/1.46 inference(skolemize,[status(sab)],[1048])).
% 1.28/1.46 tff(1050,plain,
% 1.28/1.46 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1049, 1042])).
% 1.28/1.46 tff(1051,plain,
% 1.28/1.46 ((hskp12 | hskp10 | hskp3) <=> (hskp12 | hskp10 | hskp3)),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1052,plain,
% 1.28/1.46 (((hskp10 | hskp12) | hskp3) <=> (hskp12 | hskp10 | hskp3)),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1053,axiom,((hskp10 | hskp12) | hskp3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.28/1.46 tff(1054,plain,
% 1.28/1.46 (hskp12 | hskp10 | hskp3),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.28/1.46 tff(1055,plain,
% 1.28/1.46 (hskp12 | hskp10 | hskp3),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1054, 1051])).
% 1.28/1.46 tff(1056,plain,
% 1.28/1.46 (hskp12 | hskp10 | hskp3),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1055, 1051])).
% 1.28/1.46 tff(1057,plain,
% 1.28/1.46 (hskp12 | hskp10 | hskp3),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1056, 1051])).
% 1.28/1.46 tff(1058,plain,
% 1.28/1.46 (hskp12 | hskp10 | hskp3),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1057, 1051])).
% 1.28/1.46 tff(1059,plain,
% 1.28/1.46 (hskp12),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1058, 11, 238])).
% 1.28/1.46 tff(1060,plain,
% 1.28/1.46 (((~hskp12) | (~c0_1(a1554))) <=> ((~hskp12) | (~c0_1(a1554)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1061,plain,
% 1.28/1.46 (((~c0_1(a1554)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1554)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1062,axiom,((~c0_1(a1554)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.28/1.46 tff(1063,plain,
% 1.28/1.46 ((~hskp12) | (~c0_1(a1554))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.28/1.46 tff(1064,plain,
% 1.28/1.46 ((~hskp12) | (~c0_1(a1554))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1063, 1060])).
% 1.28/1.46 tff(1065,plain,
% 1.28/1.46 (~c0_1(a1554)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1064, 1059])).
% 1.28/1.46 tff(1066,plain,
% 1.28/1.46 (((~hskp12) | c2_1(a1554)) <=> ((~hskp12) | c2_1(a1554))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1067,axiom,((~hskp12) | c2_1(a1554)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.28/1.46 tff(1068,plain,
% 1.28/1.46 ((~hskp12) | c2_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 1.28/1.46 tff(1069,plain,
% 1.28/1.46 ((~hskp12) | c2_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1068, 1066])).
% 1.28/1.46 tff(1070,plain,
% 1.28/1.46 ((~hskp12) | c2_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1069, 1066])).
% 1.28/1.46 tff(1071,plain,
% 1.28/1.46 ((~hskp12) | c2_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1070, 1066])).
% 1.28/1.46 tff(1072,plain,
% 1.28/1.46 ((~hskp12) | c2_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1071, 1066])).
% 1.28/1.46 tff(1073,plain,
% 1.28/1.46 (c2_1(a1554)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1072, 1059])).
% 1.28/1.46 tff(1074,plain,
% 1.28/1.46 (((~hskp12) | c1_1(a1554)) <=> ((~hskp12) | c1_1(a1554))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1075,axiom,((~hskp12) | c1_1(a1554)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.28/1.46 tff(1076,plain,
% 1.28/1.46 ((~hskp12) | c1_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 1.28/1.46 tff(1077,plain,
% 1.28/1.46 ((~hskp12) | c1_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1076, 1074])).
% 1.28/1.46 tff(1078,plain,
% 1.28/1.46 ((~hskp12) | c1_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1077, 1074])).
% 1.28/1.46 tff(1079,plain,
% 1.28/1.46 ((~hskp12) | c1_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1078, 1074])).
% 1.28/1.46 tff(1080,plain,
% 1.28/1.46 ((~hskp12) | c1_1(a1554)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1079, 1074])).
% 1.28/1.46 tff(1081,plain,
% 1.28/1.46 (c1_1(a1554)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1080, 1059])).
% 1.28/1.46 tff(1082,assumption,(~hskp5), introduced(assumption)).
% 1.28/1.46 tff(1083,plain,
% 1.28/1.46 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp14 | hskp5 | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp14 | hskp5 | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1084,plain,
% 1.28/1.46 ((hskp14 | hskp5 | (~ndr1_0) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554))) <=> (hskp14 | hskp5 | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1085,plain,
% 1.28/1.46 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp14 | hskp5 | (~ndr1_0) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554)))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp14 | hskp5 | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[1084])).
% 1.28/1.46 tff(1086,plain,
% 1.28/1.46 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp14 | hskp5 | (~ndr1_0) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554)))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp14 | hskp5 | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[1085, 1083])).
% 1.28/1.46 tff(1087,plain,
% 1.28/1.46 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp14 | hskp5 | (~ndr1_0) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(1088,plain,
% 1.28/1.46 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp14 | hskp5 | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.28/1.46 tff(1089,plain,
% 1.28/1.46 (hskp14),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1088, 319, 1082, 1081, 1073, 1065, 1050])).
% 1.28/1.46 tff(1090,plain,
% 1.28/1.46 (c1_1(a1558)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[72, 1089])).
% 1.28/1.46 tff(1091,plain,
% 1.28/1.46 (c0_1(a1558)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[80, 1089])).
% 1.28/1.46 tff(1092,plain,
% 1.28/1.46 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(1093,plain,
% 1.28/1.46 ((hskp10 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558))) <=> (hskp10 | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1094,plain,
% 1.28/1.47 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558))))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[1093])).
% 1.28/1.47 tff(1095,plain,
% 1.28/1.47 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.28/1.47 inference(transitivity,[status(thm)],[1094, 1092])).
% 1.28/1.47 tff(1096,plain,
% 1.28/1.47 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(1097,plain,
% 1.28/1.47 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.28/1.47 tff(1098,plain,
% 1.28/1.47 (~c3_1(a1558)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1097, 319, 11, 1091, 1090, 10])).
% 1.28/1.47 tff(1099,plain,
% 1.28/1.47 (~c2_1(a1558)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[64, 1089])).
% 1.28/1.47 tff(1100,plain,
% 1.28/1.47 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1101,plain,
% 1.28/1.47 ((hskp28 | hskp15 | (~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558))) <=> (hskp28 | hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1102,plain,
% 1.28/1.47 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558))))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[1101])).
% 1.28/1.47 tff(1103,plain,
% 1.28/1.47 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)))),
% 1.28/1.47 inference(transitivity,[status(thm)],[1102, 1100])).
% 1.28/1.47 tff(1104,plain,
% 1.28/1.47 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(1105,plain,
% 1.28/1.47 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 1.28/1.47 tff(1106,plain,
% 1.28/1.47 ($false),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1105, 319, 12, 132, 1091, 1099, 788, 1098])).
% 1.28/1.47 tff(1107,plain,(hskp10 | hskp28 | hskp15 | hskp5 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.28/1.47 tff(1108,plain,
% 1.28/1.47 (hskp28),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1107, 1040, 132, 979, 238])).
% 1.28/1.47 tff(1109,plain,
% 1.28/1.47 (c2_1(a1542)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[538, 1108])).
% 1.28/1.47 tff(1110,plain,
% 1.28/1.47 (c1_1(a1542)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[546, 1108])).
% 1.28/1.47 tff(1111,plain,
% 1.28/1.47 (~c0_1(a1542)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[880, 319, 1110, 1109, 611, 23, 24, 629, 156, 650, 867])).
% 1.28/1.47 tff(1112,plain,
% 1.28/1.47 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.28/1.47 inference(bind,[status(th)],[])).
% 1.28/1.47 tff(1113,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.28/1.47 inference(quant_intro,[status(thm)],[1112])).
% 1.28/1.47 tff(1114,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1115,plain,
% 1.28/1.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~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(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_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)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.28/1.47 inference(bind,[status(th)],[])).
% 1.28/1.47 tff(1116,plain,
% 1.28/1.47 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.28/1.47 inference(quant_intro,[status(thm)],[1115])).
% 1.28/1.47 tff(1117,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.28/1.47 tff(1118,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 1.28/1.47 tff(1119,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1118, 1114])).
% 1.28/1.47 tff(1120,plain,(
% 1.28/1.47 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.28/1.47 inference(skolemize,[status(sab)],[1119])).
% 1.28/1.47 tff(1121,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1120, 1113])).
% 1.28/1.47 tff(1122,plain,
% 1.28/1.47 (hskp12),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1058, 1040, 238])).
% 1.28/1.47 tff(1123,plain,
% 1.28/1.47 (~c0_1(a1554)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1064, 1122])).
% 1.28/1.47 tff(1124,plain,
% 1.28/1.47 (c2_1(a1554)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1072, 1122])).
% 1.28/1.47 tff(1125,plain,
% 1.28/1.47 (c1_1(a1554)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1080, 1122])).
% 1.28/1.47 tff(1126,plain,
% 1.28/1.47 (hskp14),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1088, 319, 979, 1125, 1124, 1123, 1050])).
% 1.28/1.47 tff(1127,plain,
% 1.28/1.47 (~c2_1(a1558)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[64, 1126])).
% 1.28/1.47 tff(1128,plain,
% 1.28/1.47 (c1_1(a1558)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[72, 1126])).
% 1.28/1.47 tff(1129,plain,
% 1.28/1.47 (c0_1(a1558)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[80, 1126])).
% 1.28/1.47 tff(1130,plain,
% 1.28/1.47 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1558) | (~ndr1_0) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1558) | (~ndr1_0) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1131,plain,
% 1.28/1.47 ((hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542))) <=> (hskp10 | c2_1(a1558) | (~ndr1_0) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1132,plain,
% 1.28/1.47 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1558) | (~ndr1_0) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[1131])).
% 1.28/1.47 tff(1133,plain,
% 1.28/1.47 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1558) | (~ndr1_0) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.28/1.47 inference(transitivity,[status(thm)],[1132, 1130])).
% 1.28/1.47 tff(1134,plain,
% 1.28/1.47 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(1135,plain,
% 1.28/1.47 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1558) | (~ndr1_0) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 1.28/1.47 tff(1136,plain,
% 1.28/1.47 ($false),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1135, 319, 1040, 1110, 1109, 1129, 1128, 1127, 1121, 1111])).
% 1.28/1.47 tff(1137,plain,(c3_1(a1539) | (~c2_1(a1545)) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | hskp15 | hskp3 | c0_1(a1539) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | hskp1 | c3_1(a1538)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.47 tff(1138,plain,
% 1.28/1.47 (c3_1(a1539)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1137, 977, 23, 24, 629, 156, 132, 238, 611, 853, 852, 851, 47, 627])).
% 1.28/1.47 tff(1139,plain,
% 1.28/1.47 (hskp5),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1107, 12, 132, 11, 238])).
% 1.28/1.47 tff(1140,assumption,(c3_1(a1539)), introduced(assumption)).
% 1.28/1.47 tff(1141,plain,
% 1.28/1.47 (^[U: $i] : refl((hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.28/1.47 inference(bind,[status(th)],[])).
% 1.28/1.47 tff(1142,plain,
% 1.28/1.47 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.28/1.47 inference(quant_intro,[status(thm)],[1141])).
% 1.28/1.47 tff(1143,plain,
% 1.28/1.47 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1144,plain,
% 1.28/1.47 (^[U: $i] : 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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp28) <=> ((hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp28))), rewrite(((hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp28) <=> (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp28) <=> (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.28/1.47 inference(bind,[status(th)],[])).
% 1.28/1.47 tff(1145,plain,
% 1.28/1.47 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp28) <=> ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.28/1.47 inference(quant_intro,[status(thm)],[1144])).
% 1.28/1.47 tff(1146,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 1.28/1.47 tff(1147,plain,
% 1.28/1.47 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.28/1.47 tff(1148,plain,
% 1.28/1.47 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1147, 1143])).
% 1.28/1.47 tff(1149,plain,(
% 1.28/1.47 ![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.28/1.47 inference(skolemize,[status(sab)],[1148])).
% 1.28/1.47 tff(1150,plain,
% 1.28/1.47 (![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1149, 1142])).
% 1.28/1.47 tff(1151,plain,
% 1.28/1.47 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1152,plain,
% 1.28/1.47 ((hskp28 | hskp1 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539))) <=> (hskp28 | hskp1 | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1153,plain,
% 1.28/1.47 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539))))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[1152])).
% 1.28/1.47 tff(1154,plain,
% 1.28/1.47 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.28/1.47 inference(transitivity,[status(thm)],[1153, 1151])).
% 1.28/1.47 tff(1155,plain,
% 1.28/1.47 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(1156,plain,
% 1.28/1.47 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 1.28/1.47 tff(1157,plain,
% 1.28/1.47 (hskp28 | (~c3_1(a1539)) | (~c1_1(a1539))),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1156, 319, 47, 977, 1150])).
% 1.28/1.47 tff(1158,plain,
% 1.28/1.47 (~c1_1(a1539)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1157, 12, 1140])).
% 1.28/1.47 tff(1159,plain,
% 1.28/1.47 ($false),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[490, 1158, 1139])).
% 1.28/1.47 tff(1160,plain,(hskp28 | (~c3_1(a1539)) | hskp1 | c0_1(a1539) | hskp15 | hskp10 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.28/1.47 tff(1161,plain,
% 1.28/1.47 (hskp10),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1160, 977, 47, 12, 132, 1138, 238])).
% 1.28/1.47 tff(1162,plain,
% 1.28/1.47 (c3_1(a1549)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[417, 1161])).
% 1.28/1.47 tff(1163,plain,
% 1.28/1.47 (c0_1(a1549)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[425, 1161])).
% 1.28/1.47 tff(1164,plain,
% 1.28/1.47 (~c2_1(a1549)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[985, 319, 132, 1163, 1162, 629, 156, 627, 149])).
% 1.28/1.47 tff(1165,plain,
% 1.28/1.47 (~c1_1(a1549)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[409, 1161])).
% 1.28/1.47 tff(1166,plain,
% 1.28/1.47 (hskp11),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1012, 319, 47, 1163, 1165, 1006, 1164])).
% 1.28/1.47 tff(1167,plain,
% 1.28/1.47 (~c1_1(a1553)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[942, 1166])).
% 1.28/1.47 tff(1168,plain,
% 1.28/1.47 (~c1_1(a1539)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1156, 319, 12, 47, 1138, 977, 1150])).
% 1.28/1.47 tff(1169,plain,
% 1.28/1.47 (c2_1(a1553)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[958, 1166])).
% 1.28/1.47 tff(1170,plain,
% 1.28/1.47 (c0_1(a1553)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[966, 1166])).
% 1.28/1.47 tff(1171,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1539) | c1_1(a1553) | c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c0_1(a1549)) | c2_1(a1549) | (~c0_1(a1553)) | (~c2_1(a1553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1539) | c1_1(a1553) | c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c0_1(a1549)) | c2_1(a1549) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1172,plain,
% 1.28/1.47 (((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)) | c0_1(a1539) | c1_1(a1539) | (~c3_1(a1539))) <=> (c1_1(a1539) | c1_1(a1553) | c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c0_1(a1549)) | c2_1(a1549) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1173,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)) | c0_1(a1539) | c1_1(a1539) | (~c3_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1539) | c1_1(a1553) | c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c0_1(a1549)) | c2_1(a1549) | (~c0_1(a1553)) | (~c2_1(a1553))))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[1172])).
% 1.28/1.47 tff(1174,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)) | c0_1(a1539) | c1_1(a1539) | (~c3_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1539) | c1_1(a1553) | c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c0_1(a1549)) | c2_1(a1549) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.28/1.47 inference(transitivity,[status(thm)],[1173, 1171])).
% 1.28/1.47 tff(1175,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)) | c0_1(a1539) | c1_1(a1539) | (~c3_1(a1539)))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(1176,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1539) | c1_1(a1553) | c1_1(a1549) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c0_1(a1549)) | c2_1(a1549) | (~c0_1(a1553)) | (~c2_1(a1553))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 1.28/1.47 tff(1177,plain,
% 1.28/1.47 ($false),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1176, 319, 1170, 1169, 1163, 1168, 1138, 1167, 1165, 977, 277, 1164])).
% 1.28/1.47 tff(1178,plain,(c0_1(a1539) | hskp1 | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | hskp28 | hskp3 | c0_1(a1545) | c3_1(a1545) | (~c2_1(a1545)) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.47 tff(1179,plain,
% 1.28/1.47 (c0_1(a1539)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1178, 629, 132, 47, 156, 627, 976, 238, 23, 24, 611, 853, 852, 851])).
% 1.28/1.47 tff(1180,plain,
% 1.28/1.47 (~hskp5),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[474, 1179])).
% 1.28/1.47 tff(1181,plain,
% 1.28/1.47 (hskp10),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1107, 1180, 132, 976, 238])).
% 1.28/1.47 tff(1182,plain,
% 1.28/1.47 (c3_1(a1549)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[417, 1181])).
% 1.28/1.47 tff(1183,plain,
% 1.28/1.47 (c0_1(a1549)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[425, 1181])).
% 1.28/1.47 tff(1184,plain,
% 1.28/1.47 (~c2_1(a1549)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[985, 319, 132, 1183, 1182, 629, 156, 627, 149])).
% 1.28/1.47 tff(1185,plain,
% 1.28/1.47 (~c1_1(a1549)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[409, 1181])).
% 1.28/1.47 tff(1186,plain,
% 1.28/1.47 (hskp11 | c2_1(a1549)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1012, 319, 47, 1183, 1185, 1006])).
% 1.28/1.47 tff(1187,plain,
% 1.28/1.47 (hskp11),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1186, 1184])).
% 1.28/1.47 tff(1188,plain,
% 1.28/1.47 (~c1_1(a1553)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[942, 1187])).
% 1.28/1.47 tff(1189,plain,
% 1.28/1.47 (c2_1(a1553)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[958, 1187])).
% 1.28/1.47 tff(1190,plain,
% 1.28/1.47 (~c3_1(a1553)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1022, 319, 132, 1189, 1183, 1182, 1188, 996, 1184])).
% 1.28/1.47 tff(1191,plain,
% 1.28/1.47 (c0_1(a1553)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[966, 1187])).
% 1.28/1.47 tff(1192,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1193,plain,
% 1.28/1.47 (((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624)) <=> (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(1194,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553))))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[1193])).
% 1.28/1.47 tff(1195,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553)))),
% 1.28/1.47 inference(transitivity,[status(thm)],[1194, 1192])).
% 1.28/1.47 tff(1196,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(1197,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c1_1(a1553) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c3_1(a1553) | (~c0_1(a1553))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 1.28/1.47 tff(1198,plain,
% 1.28/1.47 ($false),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1197, 319, 1191, 611, 853, 852, 851, 1188, 23, 24, 714, 1190])).
% 1.28/1.47 tff(1199,plain,(c1_1(a1538) | (~c2_1(a1545)) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | c3_1(a1545) | hskp15 | hskp1 | c2_1(a1538) | c3_1(a1538) | hskp3 | c1_1(a1535) | c2_1(a1535) | (~c3_1(a1535))), inference(lemma,lemma(discharge,[]))).
% 1.28/1.47 tff(1200,plain,
% 1.28/1.47 (c1_1(a1538)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[1199, 859, 853, 852, 851, 23, 24, 132, 47, 156, 627, 238, 611, 850, 844])).
% 1.28/1.47 tff(1201,plain,
% 1.28/1.47 (~hskp4),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[161, 1200])).
% 1.28/1.47 tff(1202,plain,
% 1.28/1.47 (hskp14),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[58, 1201, 47])).
% 1.28/1.47 tff(1203,plain,
% 1.28/1.47 (c1_1(a1558)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[72, 1202])).
% 1.28/1.47 tff(1204,plain,
% 1.28/1.47 (c0_1(a1558)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[80, 1202])).
% 1.28/1.47 tff(1205,plain,
% 1.28/1.47 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~c1_1(a1538)) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | (~c1_1(a1538)) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1206,plain,
% 1.28/1.48 ((hskp15 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c3_1(a1538) | c2_1(a1538) | (~c1_1(a1538))) <=> (hskp15 | (~c1_1(a1538)) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1207,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c3_1(a1538) | c2_1(a1538) | (~c1_1(a1538)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~c1_1(a1538)) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558))))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[1206])).
% 1.28/1.48 tff(1208,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c3_1(a1538) | c2_1(a1538) | (~c1_1(a1538)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | (~c1_1(a1538)) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.28/1.48 inference(transitivity,[status(thm)],[1207, 1205])).
% 1.28/1.48 tff(1209,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c3_1(a1538) | c2_1(a1538) | (~c1_1(a1538)))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(1210,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | (~c1_1(a1538)) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 1.28/1.48 tff(1211,plain,
% 1.28/1.48 (~c3_1(a1558)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1210, 319, 132, 1204, 1203, 1200, 156, 627, 835])).
% 1.28/1.48 tff(1212,plain,
% 1.28/1.48 (~c2_1(a1558)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[64, 1202])).
% 1.28/1.48 tff(1213,plain,
% 1.28/1.48 (hskp28),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1105, 319, 132, 1204, 1212, 788, 1211])).
% 1.28/1.48 tff(1214,plain,
% 1.28/1.48 (c3_1(a1542)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[530, 1213])).
% 1.28/1.48 tff(1215,plain,
% 1.28/1.48 (c1_1(a1542)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[546, 1213])).
% 1.28/1.48 tff(1216,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1217,plain,
% 1.28/1.48 ((hskp15 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1558) | c2_1(a1558) | (~c1_1(a1558))) <=> (hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1218,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1558) | c2_1(a1558) | (~c1_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542))))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[1217])).
% 1.28/1.48 tff(1219,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1558) | c2_1(a1558) | (~c1_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.28/1.48 inference(transitivity,[status(thm)],[1218, 1216])).
% 1.28/1.48 tff(1220,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1558) | c2_1(a1558) | (~c1_1(a1558)))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(1221,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 1.28/1.48 tff(1222,plain,
% 1.28/1.48 (~c0_1(a1542)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1221, 319, 132, 1215, 1214, 1203, 1212, 835, 1211])).
% 1.28/1.48 tff(1223,plain,
% 1.28/1.48 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_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) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.28/1.48 inference(bind,[status(th)],[])).
% 1.28/1.48 tff(1224,plain,
% 1.28/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_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) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.28/1.48 inference(quant_intro,[status(thm)],[1223])).
% 1.28/1.48 tff(1225,plain,
% 1.28/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_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) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1226,plain,
% 1.28/1.48 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_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) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_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) | (~c3_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) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | 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) | (~c3_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) | (~c3_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) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | 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) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.28/1.48 inference(bind,[status(th)],[])).
% 1.28/1.48 tff(1227,plain,
% 1.28/1.48 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | 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) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.28/1.48 inference(quant_intro,[status(thm)],[1226])).
% 1.28/1.48 tff(1228,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.28/1.48 tff(1229,plain,
% 1.28/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 1.28/1.48 tff(1230,plain,
% 1.28/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1229, 1225])).
% 1.28/1.48 tff(1231,plain,(
% 1.28/1.48 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.28/1.48 inference(skolemize,[status(sab)],[1230])).
% 1.28/1.48 tff(1232,plain,
% 1.28/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1231, 1224])).
% 1.28/1.48 tff(1233,plain,
% 1.28/1.48 (c2_1(a1542)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[538, 1213])).
% 1.28/1.48 tff(1234,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp23 | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1235,plain,
% 1.28/1.48 ((hskp23 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558))) <=> (hskp23 | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1236,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[1235])).
% 1.28/1.48 tff(1237,plain,
% 1.28/1.48 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp23 | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.28/1.48 inference(transitivity,[status(thm)],[1236, 1234])).
% 1.28/1.48 tff(1238,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(1239,plain,
% 1.28/1.48 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp23 | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.28/1.48 tff(1240,plain,
% 1.28/1.48 (hskp23),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1239, 319, 1215, 1233, 1214, 1204, 1203, 205, 1211])).
% 1.28/1.48 tff(1241,plain,
% 1.28/1.48 (~c2_1(a1593)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[293, 1240])).
% 1.28/1.48 tff(1242,plain,
% 1.28/1.48 (c3_1(a1593)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[254, 1240])).
% 1.28/1.48 tff(1243,plain,
% 1.28/1.48 (c0_1(a1593)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[262, 1240])).
% 1.28/1.48 tff(1244,plain,
% 1.28/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1593) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c3_1(a1535)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1593) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c3_1(a1535)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1245,plain,
% 1.28/1.48 (((~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c2_1(a1535) | c1_1(a1535) | (~c3_1(a1535)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542))) <=> (c2_1(a1593) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c3_1(a1535)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1246,plain,
% 1.28/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c2_1(a1535) | c1_1(a1535) | (~c3_1(a1535)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1593) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c3_1(a1535)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[1245])).
% 1.28/1.48 tff(1247,plain,
% 1.28/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c2_1(a1535) | c1_1(a1535) | (~c3_1(a1535)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1593) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c3_1(a1535)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.28/1.48 inference(transitivity,[status(thm)],[1246, 1244])).
% 1.28/1.48 tff(1248,plain,
% 1.28/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1593) | (~c3_1(a1593)) | (~c0_1(a1593)) | c2_1(a1535) | c1_1(a1535) | (~c3_1(a1535)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(1249,plain,
% 1.28/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1593) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c3_1(a1535)) | (~c3_1(a1593)) | (~c0_1(a1593)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 1.28/1.48 tff(1250,plain,
% 1.28/1.48 ($false),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1249, 319, 1233, 1214, 1243, 1242, 844, 1241, 859, 850, 1232, 1222])).
% 1.28/1.48 tff(1251,plain,((~hskp2) | hskp15 | c2_1(a1538) | c3_1(a1538) | hskp1 | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | c3_1(a1545) | hskp3 | (~c2_1(a1545))), inference(lemma,lemma(discharge,[]))).
% 1.28/1.48 tff(1252,plain,
% 1.28/1.48 (~hskp2),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1251, 238, 156, 627, 47, 825, 819, 813, 187, 181, 132, 195])).
% 1.28/1.48 tff(1253,plain,
% 1.28/1.48 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.28/1.48 inference(bind,[status(th)],[])).
% 1.28/1.48 tff(1254,plain,
% 1.28/1.48 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.48 inference(quant_intro,[status(thm)],[1253])).
% 1.28/1.48 tff(1255,plain,
% 1.28/1.48 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1256,plain,
% 1.28/1.48 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.28/1.48 inference(bind,[status(th)],[])).
% 1.28/1.48 tff(1257,plain,
% 1.28/1.48 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.48 inference(quant_intro,[status(thm)],[1256])).
% 1.28/1.48 tff(1258,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.28/1.48 tff(1259,plain,
% 1.28/1.48 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 1.28/1.48 tff(1260,plain,
% 1.28/1.48 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1259, 1255])).
% 1.28/1.48 tff(1261,plain,(
% 1.28/1.48 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.48 inference(skolemize,[status(sab)],[1260])).
% 1.28/1.48 tff(1262,plain,
% 1.28/1.48 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1261, 1254])).
% 1.28/1.48 tff(1263,plain,
% 1.28/1.48 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | c1_1(a1624))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | c1_1(a1624))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1264,plain,
% 1.28/1.48 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a1624) | c1_1(a1624) | c0_1(a1624)) <=> (hskp2 | hskp1 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | c1_1(a1624))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1265,plain,
% 1.28/1.48 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1624) | c1_1(a1624) | c0_1(a1624))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | c1_1(a1624)))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[1264])).
% 1.28/1.48 tff(1266,plain,
% 1.28/1.48 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1624) | c1_1(a1624) | c0_1(a1624))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | c1_1(a1624))),
% 1.28/1.48 inference(transitivity,[status(thm)],[1265, 1263])).
% 1.28/1.48 tff(1267,plain,
% 1.28/1.48 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1624) | c1_1(a1624) | c0_1(a1624))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(1268,plain,
% 1.28/1.48 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | c1_1(a1624)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 1.28/1.48 tff(1269,plain,
% 1.28/1.48 (hskp2 | hskp1 | c1_1(a1624)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1268, 319, 825, 819, 1262])).
% 1.28/1.48 tff(1270,plain,
% 1.28/1.48 (c1_1(a1624)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1269, 1252, 47])).
% 1.28/1.48 tff(1271,assumption,(~hskp2), introduced(assumption)).
% 1.28/1.48 tff(1272,plain,
% 1.28/1.48 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1273,plain,
% 1.28/1.48 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a1538) | c1_1(a1538) | c0_1(a1538)) <=> (hskp2 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1274,plain,
% 1.28/1.48 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1538) | c1_1(a1538) | c0_1(a1538))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538)))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[1273])).
% 1.28/1.48 tff(1275,plain,
% 1.28/1.48 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1538) | c1_1(a1538) | c0_1(a1538))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538))),
% 1.28/1.48 inference(transitivity,[status(thm)],[1274, 1272])).
% 1.28/1.48 tff(1276,plain,
% 1.28/1.48 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a1538) | c1_1(a1538) | c0_1(a1538))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(1277,plain,
% 1.28/1.48 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538)),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 1.28/1.48 tff(1278,plain,
% 1.28/1.48 (hskp2 | c1_1(a1538) | c0_1(a1538)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1277, 319, 47, 156, 1262])).
% 1.28/1.48 tff(1279,plain,
% 1.28/1.48 (c0_1(a1538)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1278, 629, 1271])).
% 1.28/1.48 tff(1280,plain,
% 1.28/1.48 ($false),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[866, 1279, 629])).
% 1.28/1.48 tff(1281,plain,(c1_1(a1538) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c2_1(a1538) | c3_1(a1538) | hskp2 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.28/1.48 tff(1282,plain,
% 1.28/1.48 (c1_1(a1538)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1281, 1252, 819, 813, 156, 627, 825, 47])).
% 1.28/1.48 tff(1283,plain,
% 1.28/1.48 (~hskp4),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[161, 1282])).
% 1.28/1.48 tff(1284,plain,
% 1.28/1.48 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | (~c1_1(a1624)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | (~c1_1(a1624)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1285,plain,
% 1.28/1.48 ((hskp10 | hskp4 | (~ndr1_0) | c2_1(a1624) | c0_1(a1624) | (~c1_1(a1624))) <=> (hskp10 | hskp4 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | (~c1_1(a1624)))),
% 1.28/1.48 inference(rewrite,[status(thm)],[])).
% 1.28/1.48 tff(1286,plain,
% 1.28/1.48 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1624) | c0_1(a1624) | (~c1_1(a1624)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | (~c1_1(a1624))))),
% 1.28/1.48 inference(monotonicity,[status(thm)],[1285])).
% 1.28/1.48 tff(1287,plain,
% 1.28/1.48 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1624) | c0_1(a1624) | (~c1_1(a1624)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | (~c1_1(a1624)))),
% 1.28/1.48 inference(transitivity,[status(thm)],[1286, 1284])).
% 1.28/1.48 tff(1288,plain,
% 1.28/1.48 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1624) | c0_1(a1624) | (~c1_1(a1624)))),
% 1.28/1.48 inference(quant_inst,[status(thm)],[])).
% 1.28/1.48 tff(1289,plain,
% 1.28/1.48 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c0_1(a1624) | c2_1(a1624) | (~ndr1_0) | (~c1_1(a1624))),
% 1.28/1.48 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 1.28/1.48 tff(1290,plain,
% 1.28/1.48 (hskp10 | hskp4 | (~c1_1(a1624))),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1289, 319, 825, 819, 121])).
% 1.28/1.48 tff(1291,plain,
% 1.28/1.48 (hskp10),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[1290, 1283, 1270])).
% 1.28/1.48 tff(1292,plain,
% 1.28/1.48 (~c1_1(a1549)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[409, 1291])).
% 1.28/1.48 tff(1293,plain,
% 1.28/1.48 (hskp14),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[58, 1283, 47])).
% 1.28/1.48 tff(1294,plain,
% 1.28/1.48 (~c2_1(a1558)),
% 1.28/1.48 inference(unit_resolution,[status(thm)],[64, 1293])).
% 1.31/1.48 tff(1295,plain,
% 1.31/1.48 (c3_1(a1549)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[417, 1291])).
% 1.31/1.48 tff(1296,plain,
% 1.31/1.48 (c0_1(a1549)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[425, 1291])).
% 1.31/1.48 tff(1297,plain,
% 1.31/1.48 (c1_1(a1558)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[72, 1293])).
% 1.31/1.48 tff(1298,plain,
% 1.31/1.48 (c0_1(a1558)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[80, 1293])).
% 1.31/1.48 tff(1299,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a1558) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c0_1(a1558)) | (~c1_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a1558) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(1300,plain,
% 1.31/1.48 ((hskp22 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549))) <=> (hskp22 | c2_1(a1558) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(1301,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a1558) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c0_1(a1558)) | (~c1_1(a1558))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[1300])).
% 1.31/1.48 tff(1302,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a1558) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[1301, 1299])).
% 1.31/1.48 tff(1303,plain,
% 1.31/1.48 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(1304,plain,
% 1.31/1.48 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a1558) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c0_1(a1558)) | (~c1_1(a1558))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 1.31/1.48 tff(1305,plain,
% 1.31/1.48 (hskp22),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[1304, 319, 1298, 1297, 1296, 1295, 1294, 1292, 111])).
% 1.31/1.48 tff(1306,plain,
% 1.31/1.48 (((~hskp22) | (~c3_1(a1581))) <=> ((~hskp22) | (~c3_1(a1581)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(1307,plain,
% 1.31/1.48 (((~c3_1(a1581)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a1581)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(1308,axiom,((~c3_1(a1581)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.31/1.48 tff(1309,plain,
% 1.31/1.48 ((~hskp22) | (~c3_1(a1581))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 1.31/1.48 tff(1310,plain,
% 1.31/1.48 ((~hskp22) | (~c3_1(a1581))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[1309, 1306])).
% 1.31/1.48 tff(1311,plain,
% 1.31/1.48 (~c3_1(a1581)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[1310, 1305])).
% 1.31/1.48 tff(1312,plain,
% 1.31/1.48 (((~hskp22) | (~c1_1(a1581))) <=> ((~hskp22) | (~c1_1(a1581)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(1313,plain,
% 1.31/1.48 (((~c1_1(a1581)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a1581)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(1314,axiom,((~c1_1(a1581)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.31/1.49 tff(1315,plain,
% 1.31/1.49 ((~hskp22) | (~c1_1(a1581))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.31/1.49 tff(1316,plain,
% 1.31/1.49 ((~hskp22) | (~c1_1(a1581))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1315, 1312])).
% 1.31/1.49 tff(1317,plain,
% 1.31/1.49 (~c1_1(a1581)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1316, 1305])).
% 1.31/1.49 tff(1318,plain,
% 1.31/1.49 (((~hskp22) | c2_1(a1581)) <=> ((~hskp22) | c2_1(a1581))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1319,axiom,((~hskp22) | c2_1(a1581)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.31/1.49 tff(1320,plain,
% 1.31/1.49 ((~hskp22) | c2_1(a1581)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 1.31/1.49 tff(1321,plain,
% 1.31/1.49 ((~hskp22) | c2_1(a1581)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1320, 1318])).
% 1.31/1.49 tff(1322,plain,
% 1.31/1.49 ((~hskp22) | c2_1(a1581)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1321, 1318])).
% 1.31/1.49 tff(1323,plain,
% 1.31/1.49 ((~hskp22) | c2_1(a1581)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1322, 1318])).
% 1.31/1.49 tff(1324,plain,
% 1.31/1.49 ((~hskp22) | c2_1(a1581)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1323, 1318])).
% 1.31/1.49 tff(1325,plain,
% 1.31/1.49 (c2_1(a1581)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1324, 1305])).
% 1.31/1.49 tff(1326,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1624)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1327,plain,
% 1.31/1.49 ((hskp15 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c3_1(a1624) | c2_1(a1624) | (~c1_1(a1624))) <=> (hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1624)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1328,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c3_1(a1624) | c2_1(a1624) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1624))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[1327])).
% 1.31/1.49 tff(1329,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c3_1(a1624) | c2_1(a1624) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1624)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[1328, 1326])).
% 1.31/1.49 tff(1330,plain,
% 1.31/1.49 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c3_1(a1624) | c2_1(a1624) | (~c1_1(a1624)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(1331,plain,
% 1.31/1.49 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1624))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 1.31/1.49 tff(1332,plain,
% 1.31/1.49 (~c3_1(a1558)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1331, 319, 132, 1298, 1297, 819, 813, 835, 1270])).
% 1.31/1.49 tff(1333,plain,
% 1.31/1.49 (hskp28),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1105, 319, 132, 1298, 1294, 788, 1332])).
% 1.31/1.49 tff(1334,plain,
% 1.31/1.49 (c3_1(a1542)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[530, 1333])).
% 1.31/1.49 tff(1335,plain,
% 1.31/1.49 (c2_1(a1542)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[538, 1333])).
% 1.31/1.49 tff(1336,plain,
% 1.31/1.49 (c1_1(a1542)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[546, 1333])).
% 1.31/1.49 tff(1337,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | (~c0_1(a1581)) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | (~c0_1(a1581)) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1338,plain,
% 1.31/1.49 (((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)) | c1_1(a1581) | (~c2_1(a1581)) | (~c0_1(a1581))) <=> (c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | (~c0_1(a1581)) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1339,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)) | c1_1(a1581) | (~c2_1(a1581)) | (~c0_1(a1581)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | (~c0_1(a1581)) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[1338])).
% 1.31/1.49 tff(1340,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)) | c1_1(a1581) | (~c2_1(a1581)) | (~c0_1(a1581)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | (~c0_1(a1581)) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[1339, 1337])).
% 1.31/1.49 tff(1341,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)) | c1_1(a1581) | (~c2_1(a1581)) | (~c0_1(a1581)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(1342,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | (~c0_1(a1581)) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 1.31/1.49 tff(1343,plain,
% 1.31/1.49 (~c0_1(a1581)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1342, 319, 1336, 1335, 1334, 1325, 1317, 1311, 101])).
% 1.31/1.49 tff(1344,plain,
% 1.31/1.49 (((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549)))) <=> ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp31 | hskp3 | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1345,plain,
% 1.31/1.49 ((hskp31 | hskp3 | (~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c2_1(a1549))) <=> (hskp31 | hskp3 | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1346,plain,
% 1.31/1.49 (((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | (~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c2_1(a1549)))) <=> ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[1345])).
% 1.31/1.49 tff(1347,plain,
% 1.31/1.49 (((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | (~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c2_1(a1549)))) <=> ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp31 | hskp3 | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[1346, 1344])).
% 1.31/1.49 tff(1348,plain,
% 1.31/1.49 ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp31 | hskp3 | (~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c2_1(a1549)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(1349,plain,
% 1.31/1.49 ((~![U: $i] : (hskp31 | hskp3 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp31 | hskp3 | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 1.31/1.49 tff(1350,plain,
% 1.31/1.49 (~c2_1(a1549)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1349, 163, 319, 238, 1295, 1292, 573])).
% 1.31/1.49 tff(1351,plain,
% 1.31/1.49 (hskp11),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1012, 319, 47, 1296, 1292, 1006, 1350])).
% 1.31/1.49 tff(1352,plain,
% 1.31/1.49 (~c1_1(a1553)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[942, 1351])).
% 1.31/1.49 tff(1353,plain,
% 1.31/1.49 (c0_1(a1553)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[966, 1351])).
% 1.31/1.49 tff(1354,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c3_1(a1581) | c1_1(a1553) | (~ndr1_0) | c3_1(a1553) | (~c0_1(a1553)) | c0_1(a1581) | (~c2_1(a1581)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c3_1(a1581) | c1_1(a1553) | (~ndr1_0) | c3_1(a1553) | (~c0_1(a1553)) | c0_1(a1581) | (~c2_1(a1581)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1355,plain,
% 1.31/1.49 (((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624)) <=> (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c3_1(a1581) | c1_1(a1553) | (~ndr1_0) | c3_1(a1553) | (~c0_1(a1553)) | c0_1(a1581) | (~c2_1(a1581)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1356,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c3_1(a1581) | c1_1(a1553) | (~ndr1_0) | c3_1(a1553) | (~c0_1(a1553)) | c0_1(a1581) | (~c2_1(a1581))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[1355])).
% 1.31/1.49 tff(1357,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c3_1(a1581) | c1_1(a1553) | (~ndr1_0) | c3_1(a1553) | (~c0_1(a1553)) | c0_1(a1581) | (~c2_1(a1581)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[1356, 1354])).
% 1.31/1.49 tff(1358,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1553) | c3_1(a1553) | (~c0_1(a1553)) | c3_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(1359,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c3_1(a1581) | c1_1(a1553) | (~ndr1_0) | c3_1(a1553) | (~c0_1(a1553)) | c0_1(a1581) | (~c2_1(a1581))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 1.31/1.49 tff(1360,plain,
% 1.31/1.49 (c3_1(a1553)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1359, 319, 1325, 1353, 825, 819, 813, 1311, 1352, 714, 1343])).
% 1.31/1.49 tff(1361,plain,
% 1.31/1.49 (c2_1(a1553)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[958, 1351])).
% 1.31/1.49 tff(1362,plain,
% 1.31/1.49 ($false),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1022, 319, 132, 1361, 1296, 1295, 1352, 996, 1350, 1360])).
% 1.31/1.49 tff(1363,plain,(hskp3 | hskp15 | hskp1 | hskp31 | c2_1(a1538) | c3_1(a1538)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.49 tff(1364,plain,
% 1.31/1.49 (hskp3),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1363, 627, 47, 163, 156, 132])).
% 1.31/1.49 tff(1365,plain,
% 1.31/1.49 (c1_1(a1536)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[684, 1364])).
% 1.31/1.49 tff(1366,plain,
% 1.31/1.49 (~c2_1(a1536)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[668, 1364])).
% 1.31/1.49 tff(1367,plain,
% 1.31/1.49 (~c0_1(a1536)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[674, 1364])).
% 1.31/1.49 tff(1368,plain,
% 1.31/1.49 (hskp2),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1281, 629, 852, 851, 156, 627, 853, 47])).
% 1.31/1.49 tff(1369,plain,
% 1.31/1.49 (~c1_1(a1535)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[858, 1368])).
% 1.31/1.49 tff(1370,plain,
% 1.31/1.49 (~c2_1(a1535)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[849, 1368])).
% 1.31/1.49 tff(1371,plain,
% 1.31/1.49 (c3_1(a1535)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[843, 1368])).
% 1.31/1.49 tff(1372,assumption,(c1_1(a1536)), introduced(assumption)).
% 1.31/1.49 tff(1373,plain,
% 1.31/1.49 (~hskp28),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[975, 1369, 629, 1370, 853, 852, 851, 611, 23, 24, 1371, 156, 867])).
% 1.31/1.49 tff(1374,plain,
% 1.31/1.49 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1375,plain,
% 1.31/1.49 ((hskp28 | hskp1 | (~ndr1_0) | c0_1(a1536) | (~c1_1(a1536)) | (~c3_1(a1536))) <=> (hskp28 | hskp1 | c0_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1376,plain,
% 1.31/1.49 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c0_1(a1536) | (~c1_1(a1536)) | (~c3_1(a1536)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[1375])).
% 1.31/1.49 tff(1377,plain,
% 1.31/1.49 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c0_1(a1536) | (~c1_1(a1536)) | (~c3_1(a1536)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[1376, 1374])).
% 1.31/1.49 tff(1378,plain,
% 1.31/1.49 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c0_1(a1536) | (~c1_1(a1536)) | (~c3_1(a1536)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(1379,plain,
% 1.31/1.49 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 1.31/1.49 tff(1380,plain,
% 1.31/1.49 (hskp28 | (~c3_1(a1536))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1379, 319, 47, 1372, 696, 1150])).
% 1.31/1.49 tff(1381,plain,
% 1.31/1.49 (~c3_1(a1536)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1380, 1373])).
% 1.31/1.49 tff(1382,assumption,(~c3_1(a1536)), introduced(assumption)).
% 1.31/1.49 tff(1383,plain,
% 1.31/1.49 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(1384,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[1383])).
% 1.31/1.49 tff(1385,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1386,plain,
% 1.31/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(1387,plain,
% 1.31/1.49 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[1386])).
% 1.31/1.49 tff(1388,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.31/1.49 tff(1389,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 1.31/1.49 tff(1390,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1389, 1385])).
% 1.31/1.49 tff(1391,plain,(
% 1.31/1.49 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(skolemize,[status(sab)],[1390])).
% 1.31/1.49 tff(1392,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1391, 1384])).
% 1.31/1.49 tff(1393,assumption,(~hskp16), introduced(assumption)).
% 1.31/1.49 tff(1394,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c2_1(a1536) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | c3_1(a1536) | (~c1_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a1536) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | c3_1(a1536) | (~c1_1(a1536)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1395,plain,
% 1.31/1.49 ((hskp16 | (~ndr1_0) | c2_1(a1536) | c3_1(a1536) | (~c1_1(a1536)) | c2_1(a1535) | c1_1(a1535) | (~c0_1(a1535))) <=> (hskp16 | c2_1(a1536) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | c3_1(a1536) | (~c1_1(a1536)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1396,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1536) | c3_1(a1536) | (~c1_1(a1536)) | c2_1(a1535) | c1_1(a1535) | (~c0_1(a1535)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c2_1(a1536) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | c3_1(a1536) | (~c1_1(a1536))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[1395])).
% 1.31/1.49 tff(1397,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1536) | c3_1(a1536) | (~c1_1(a1536)) | c2_1(a1535) | c1_1(a1535) | (~c0_1(a1535)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a1536) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | c3_1(a1536) | (~c1_1(a1536)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[1396, 1394])).
% 1.31/1.49 tff(1398,plain,
% 1.31/1.49 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1536) | c3_1(a1536) | (~c1_1(a1536)) | c2_1(a1535) | c1_1(a1535) | (~c0_1(a1535)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(1399,plain,
% 1.31/1.49 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a1536) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | c3_1(a1536) | (~c1_1(a1536))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 1.31/1.49 tff(1400,plain,
% 1.31/1.49 (hskp16 | (~c0_1(a1535))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1399, 319, 1372, 715, 870, 869, 1392, 1382])).
% 1.31/1.49 tff(1401,plain,
% 1.31/1.49 (~c0_1(a1535)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1400, 1393])).
% 1.31/1.49 tff(1402,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a1536) | c2_1(a1536) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a1536) | c2_1(a1536) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1403,plain,
% 1.31/1.49 ((hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536)) <=> (hskp6 | c0_1(a1536) | c2_1(a1536) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1404,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a1536) | c2_1(a1536) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536)))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[1403])).
% 1.31/1.49 tff(1405,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a1536) | c2_1(a1536) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536))),
% 1.31/1.49 inference(transitivity,[status(thm)],[1404, 1402])).
% 1.31/1.49 tff(1406,plain,
% 1.31/1.49 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(1407,plain,
% 1.31/1.49 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a1536) | c2_1(a1536) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1536)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 1.31/1.49 tff(1408,plain,
% 1.31/1.49 (hskp6 | c0_1(a1535)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1407, 319, 868, 696, 715, 869, 899, 1382])).
% 1.31/1.49 tff(1409,plain,
% 1.31/1.49 (hskp6),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1408, 1401])).
% 1.31/1.49 tff(1410,plain,
% 1.31/1.49 (~c2_1(a1543)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[912, 1409])).
% 1.31/1.49 tff(1411,plain,
% 1.31/1.49 (~c1_1(a1543)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[918, 1409])).
% 1.31/1.49 tff(1412,plain,
% 1.31/1.49 (c0_1(a1543)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[950, 1409])).
% 1.31/1.49 tff(1413,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a1543) | c2_1(a1543) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c1_1(a1536)) | (~c0_1(a1543)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a1543) | c2_1(a1543) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c1_1(a1536)) | (~c0_1(a1543)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1414,plain,
% 1.31/1.49 ((hskp16 | (~ndr1_0) | c2_1(a1536) | c3_1(a1536) | (~c1_1(a1536)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543))) <=> (hskp16 | c1_1(a1543) | c2_1(a1543) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c1_1(a1536)) | (~c0_1(a1543)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(1415,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1536) | c3_1(a1536) | (~c1_1(a1536)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a1543) | c2_1(a1543) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c1_1(a1536)) | (~c0_1(a1543))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[1414])).
% 1.31/1.49 tff(1416,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1536) | c3_1(a1536) | (~c1_1(a1536)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a1543) | c2_1(a1543) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c1_1(a1536)) | (~c0_1(a1543)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[1415, 1413])).
% 1.31/1.50 tff(1417,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1536) | c3_1(a1536) | (~c1_1(a1536)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(1418,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a1543) | c2_1(a1543) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c1_1(a1536)) | (~c0_1(a1543))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 1.31/1.50 tff(1419,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1418, 319, 1393, 1412, 1372, 1411, 1410, 715, 1392, 1382])).
% 1.31/1.50 tff(1420,plain,(hskp16 | (~c1_1(a1536)) | c2_1(a1536) | c3_1(a1536) | (~c3_1(a1535)) | c0_1(a1536) | c2_1(a1535) | c1_1(a1535)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(1421,plain,
% 1.31/1.50 (hskp16),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1420, 1381, 715, 1372, 1371, 696, 1370, 1369])).
% 1.31/1.50 tff(1422,plain,
% 1.31/1.50 (((~hskp16) | c3_1(a1566)) <=> ((~hskp16) | c3_1(a1566))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1423,axiom,((~hskp16) | c3_1(a1566)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.31/1.50 tff(1424,plain,
% 1.31/1.50 ((~hskp16) | c3_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 1.31/1.50 tff(1425,plain,
% 1.31/1.50 ((~hskp16) | c3_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1424, 1422])).
% 1.31/1.50 tff(1426,plain,
% 1.31/1.50 ((~hskp16) | c3_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1425, 1422])).
% 1.31/1.50 tff(1427,plain,
% 1.31/1.50 ((~hskp16) | c3_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1426, 1422])).
% 1.31/1.50 tff(1428,plain,
% 1.31/1.50 ((~hskp16) | c3_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1427, 1422])).
% 1.31/1.50 tff(1429,plain,
% 1.31/1.50 (c3_1(a1566)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1428, 1421])).
% 1.31/1.50 tff(1430,plain,
% 1.31/1.50 (((~hskp16) | c2_1(a1566)) <=> ((~hskp16) | c2_1(a1566))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1431,axiom,((~hskp16) | c2_1(a1566)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.31/1.50 tff(1432,plain,
% 1.31/1.50 ((~hskp16) | c2_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 1.31/1.50 tff(1433,plain,
% 1.31/1.50 ((~hskp16) | c2_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1432, 1430])).
% 1.31/1.50 tff(1434,plain,
% 1.31/1.50 ((~hskp16) | c2_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1433, 1430])).
% 1.31/1.50 tff(1435,plain,
% 1.31/1.50 ((~hskp16) | c2_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1434, 1430])).
% 1.31/1.50 tff(1436,plain,
% 1.31/1.50 ((~hskp16) | c2_1(a1566)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1435, 1430])).
% 1.31/1.50 tff(1437,plain,
% 1.31/1.50 (c2_1(a1566)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1436, 1421])).
% 1.31/1.50 tff(1438,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1439,plain,
% 1.31/1.50 ((hskp15 | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538)) <=> (hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1440,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[1439])).
% 1.31/1.50 tff(1441,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[1440, 1438])).
% 1.31/1.50 tff(1442,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(1443,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | (~c0_1(a1566)) | (~c2_1(a1566))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 1.31/1.50 tff(1444,plain,
% 1.31/1.50 (~c0_1(a1566)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1443, 319, 132, 1437, 1429, 629, 156, 627, 149])).
% 1.31/1.50 tff(1445,plain,
% 1.31/1.50 (((~hskp16) | (~c1_1(a1566))) <=> ((~hskp16) | (~c1_1(a1566)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1446,plain,
% 1.31/1.50 (((~c1_1(a1566)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a1566)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1447,axiom,((~c1_1(a1566)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.31/1.50 tff(1448,plain,
% 1.31/1.50 ((~hskp16) | (~c1_1(a1566))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 1.31/1.50 tff(1449,plain,
% 1.31/1.50 ((~hskp16) | (~c1_1(a1566))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1448, 1445])).
% 1.31/1.50 tff(1450,plain,
% 1.31/1.50 (~c1_1(a1566)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1449, 1421])).
% 1.31/1.50 tff(1451,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a1566) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a1566) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | (~c2_1(a1566)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1452,plain,
% 1.31/1.50 ((hskp15 | (~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c1_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566))) <=> (hskp15 | c1_1(a1566) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | (~c2_1(a1566)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1453,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c1_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a1566) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | (~c2_1(a1566))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[1452])).
% 1.31/1.50 tff(1454,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c1_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a1566) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | (~c2_1(a1566)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[1453, 1451])).
% 1.31/1.50 tff(1455,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c1_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(1456,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a1566) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | (~c2_1(a1566))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 1.31/1.50 tff(1457,plain,
% 1.31/1.50 (~c0_1(a1535)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1456, 319, 132, 1437, 1429, 1371, 1450, 1370, 996])).
% 1.31/1.50 tff(1458,plain,
% 1.31/1.50 (hskp6 | c0_1(a1535)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1407, 319, 1371, 696, 715, 1370, 899, 1381])).
% 1.31/1.50 tff(1459,plain,
% 1.31/1.50 (hskp6),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1458, 1457])).
% 1.31/1.50 tff(1460,plain,
% 1.31/1.50 (~c2_1(a1543)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[912, 1459])).
% 1.31/1.50 tff(1461,plain,
% 1.31/1.50 (~c1_1(a1543)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[918, 1459])).
% 1.31/1.50 tff(1462,plain,
% 1.31/1.50 (c0_1(a1543)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[950, 1459])).
% 1.31/1.50 tff(1463,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1464,plain,
% 1.31/1.50 (((~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c2_1(a1543) | c1_1(a1543) | (~c3_1(a1543)) | c0_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566))) <=> (c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1465,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c2_1(a1543) | c1_1(a1543) | (~c3_1(a1543)) | c0_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[1464])).
% 1.31/1.50 tff(1466,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c2_1(a1543) | c1_1(a1543) | (~c3_1(a1543)) | c0_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.31/1.50 tff(1467,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c2_1(a1543) | c1_1(a1543) | (~c3_1(a1543)) | c0_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(1468,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.31/1.50 tff(1469,plain,
% 1.31/1.50 (~c3_1(a1543)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1468, 319, 1437, 1429, 1462, 1461, 1460, 1232, 1444])).
% 1.31/1.50 tff(1470,plain,
% 1.31/1.50 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1471,plain,
% 1.31/1.50 ((hskp28 | hskp15 | (~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543))) <=> (hskp28 | hskp15 | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1472,plain,
% 1.31/1.50 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[1471])).
% 1.31/1.50 tff(1473,plain,
% 1.31/1.50 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[1472, 1470])).
% 1.31/1.50 tff(1474,plain,
% 1.31/1.50 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(1475,plain,
% 1.31/1.50 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 1.31/1.50 tff(1476,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1475, 319, 1373, 132, 1462, 1460, 788, 1469])).
% 1.31/1.50 tff(1477,plain,(c1_1(a1538) | hskp15 | c0_1(a1536) | c2_1(a1536) | c2_1(a1538) | c3_1(a1538) | (~c1_1(a1536)) | hskp1 | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | (~c2_1(a1545)) | c0_1(a1545) | c3_1(a1545)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(1478,plain,
% 1.31/1.50 (c1_1(a1538)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1477, 1367, 132, 1366, 156, 627, 1365, 47, 825, 819, 813, 195, 187, 181])).
% 1.31/1.50 tff(1479,plain,
% 1.31/1.50 (~hskp4),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[161, 1478])).
% 1.31/1.50 tff(1480,plain,
% 1.31/1.50 (hskp14),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[58, 1479, 47])).
% 1.31/1.50 tff(1481,plain,
% 1.31/1.50 (c1_1(a1558)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[72, 1480])).
% 1.31/1.50 tff(1482,plain,
% 1.31/1.50 (c0_1(a1558)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[80, 1480])).
% 1.31/1.50 tff(1483,plain,
% 1.31/1.50 (~c3_1(a1558)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1210, 319, 132, 1482, 1481, 1478, 156, 627, 835])).
% 1.31/1.50 tff(1484,plain,
% 1.31/1.50 (~c2_1(a1558)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[64, 1480])).
% 1.31/1.50 tff(1485,plain,
% 1.31/1.50 (hskp28),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1105, 319, 132, 1482, 1484, 788, 1483])).
% 1.31/1.50 tff(1486,plain,
% 1.31/1.50 (c3_1(a1542)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[530, 1485])).
% 1.31/1.50 tff(1487,plain,
% 1.31/1.50 (c1_1(a1542)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[546, 1485])).
% 1.31/1.50 tff(1488,plain,
% 1.31/1.50 (~c0_1(a1542)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1221, 319, 132, 1487, 1486, 1481, 1484, 835, 1483])).
% 1.31/1.50 tff(1489,plain,
% 1.31/1.50 (hskp10 | hskp4),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[732, 319, 1365, 1367, 1366, 121])).
% 1.31/1.50 tff(1490,plain,
% 1.31/1.50 (hskp10),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1489, 1479])).
% 1.31/1.50 tff(1491,plain,
% 1.31/1.50 (~c1_1(a1549)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[409, 1490])).
% 1.31/1.50 tff(1492,plain,
% 1.31/1.50 (c3_1(a1549)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[417, 1490])).
% 1.31/1.50 tff(1493,plain,
% 1.31/1.50 (c0_1(a1549)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[425, 1490])).
% 1.31/1.50 tff(1494,plain,
% 1.31/1.50 (c2_1(a1542)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[538, 1485])).
% 1.31/1.50 tff(1495,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1496,plain,
% 1.31/1.50 (((~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542))) <=> (c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1497,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[1496])).
% 1.31/1.50 tff(1498,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.31/1.50 inference(transitivity,[status(thm)],[1497, 1495])).
% 1.31/1.50 tff(1499,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(1500,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 1.31/1.50 tff(1501,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1500, 319, 1487, 1494, 1486, 1493, 1492, 1491, 382, 1488])).
% 1.31/1.50 tff(1502,plain,(c3_1(a1538) | hskp15 | c2_1(a1538) | hskp1 | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(1503,plain,
% 1.31/1.50 (c3_1(a1538)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1502, 156, 132, 47, 163])).
% 1.31/1.50 tff(1504,plain,
% 1.31/1.50 (~hskp4),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[154, 1503])).
% 1.31/1.50 tff(1505,plain,
% 1.31/1.50 (hskp14),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[58, 1504, 47])).
% 1.31/1.50 tff(1506,plain,
% 1.31/1.50 (~c2_1(a1558)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[64, 1505])).
% 1.31/1.50 tff(1507,plain,
% 1.31/1.50 (c1_1(a1558)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[72, 1505])).
% 1.31/1.50 tff(1508,plain,
% 1.31/1.50 (c0_1(a1558)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[80, 1505])).
% 1.31/1.50 tff(1509,assumption,(~c2_1(a1558)), introduced(assumption)).
% 1.31/1.50 tff(1510,assumption,(c0_1(a1558)), introduced(assumption)).
% 1.31/1.50 tff(1511,plain,
% 1.31/1.50 (hskp28 | c3_1(a1558)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1105, 319, 132, 1510, 1509, 788])).
% 1.31/1.50 tff(1512,plain,
% 1.31/1.50 (c3_1(a1558)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1511, 12])).
% 1.31/1.50 tff(1513,assumption,(c1_1(a1558)), introduced(assumption)).
% 1.31/1.50 tff(1514,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp5 | c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp5 | c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1515,plain,
% 1.31/1.50 ((hskp5 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c2_1(a1558) | (~c1_1(a1558)) | (~c3_1(a1558))) <=> (hskp5 | c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1516,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c2_1(a1558) | (~c1_1(a1558)) | (~c3_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp5 | c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[1515])).
% 1.31/1.50 tff(1517,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c2_1(a1558) | (~c1_1(a1558)) | (~c3_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp5 | c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[1516, 1514])).
% 1.31/1.50 tff(1518,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c2_1(a1558) | (~c1_1(a1558)) | (~c3_1(a1558)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(1519,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp5 | c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 1.31/1.50 tff(1520,plain,
% 1.31/1.50 (hskp5 | (~c3_1(a1558))),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1519, 319, 1510, 1513, 1509, 46])).
% 1.31/1.50 tff(1521,plain,
% 1.31/1.50 (hskp5),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1520, 1512])).
% 1.31/1.50 tff(1522,plain,
% 1.31/1.50 (~c0_1(a1539)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[474, 1521])).
% 1.31/1.50 tff(1523,plain,
% 1.31/1.50 (c3_1(a1539)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[482, 1521])).
% 1.31/1.50 tff(1524,plain,
% 1.31/1.50 (c1_1(a1539)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[490, 1521])).
% 1.31/1.50 tff(1525,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1156, 319, 12, 47, 1524, 1523, 1522, 1150])).
% 1.31/1.50 tff(1526,plain,(hskp28 | hskp1 | (~c0_1(a1558)) | (~c1_1(a1558)) | c2_1(a1558) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(1527,plain,
% 1.31/1.50 (hskp28),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1526, 1508, 47, 1507, 1506, 132])).
% 1.31/1.50 tff(1528,plain,
% 1.31/1.50 (c3_1(a1542)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[530, 1527])).
% 1.31/1.50 tff(1529,plain,
% 1.31/1.50 (c2_1(a1542)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[538, 1527])).
% 1.31/1.50 tff(1530,plain,
% 1.31/1.50 (c1_1(a1542)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[546, 1527])).
% 1.31/1.50 tff(1531,plain,
% 1.31/1.50 (hskp22),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1304, 319, 1510, 1513, 426, 418, 1509, 410, 111])).
% 1.31/1.50 tff(1532,plain,
% 1.31/1.50 (~c3_1(a1581)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1310, 1531])).
% 1.31/1.50 tff(1533,plain,
% 1.31/1.50 (~c1_1(a1581)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1316, 1531])).
% 1.31/1.50 tff(1534,plain,
% 1.31/1.50 (c2_1(a1581)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1324, 1531])).
% 1.31/1.50 tff(1535,assumption,(c3_1(a1542)), introduced(assumption)).
% 1.31/1.50 tff(1536,assumption,(c2_1(a1542)), introduced(assumption)).
% 1.31/1.50 tff(1537,assumption,(c1_1(a1542)), introduced(assumption)).
% 1.31/1.50 tff(1538,plain,
% 1.31/1.50 (~c0_1(a1581)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1342, 319, 1537, 1536, 1535, 1534, 1533, 1532, 101])).
% 1.31/1.50 tff(1539,plain,
% 1.31/1.50 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(1540,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[1539])).
% 1.31/1.50 tff(1541,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1542,plain,
% 1.31/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(1543,plain,
% 1.31/1.50 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[1542])).
% 1.31/1.50 tff(1544,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.31/1.50 tff(1545,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 1.31/1.50 tff(1546,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1545, 1541])).
% 1.31/1.50 tff(1547,plain,(
% 1.31/1.50 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.31/1.50 inference(skolemize,[status(sab)],[1546])).
% 1.31/1.50 tff(1548,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1547, 1540])).
% 1.31/1.50 tff(1549,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | c2_1(a1624) | c3_1(a1624) | c1_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c2_1(a1581)) | c1_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp4 | c2_1(a1624) | c3_1(a1624) | c1_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c2_1(a1581)) | c1_1(a1624))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1550,plain,
% 1.31/1.50 ((hskp4 | (~ndr1_0) | c1_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624)) <=> (hskp4 | c2_1(a1624) | c3_1(a1624) | c1_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c2_1(a1581)) | c1_1(a1624))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1551,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | c2_1(a1624) | c3_1(a1624) | c1_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c2_1(a1581)) | c1_1(a1624)))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[1550])).
% 1.31/1.50 tff(1552,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp4 | c2_1(a1624) | c3_1(a1624) | c1_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c2_1(a1581)) | c1_1(a1624))),
% 1.31/1.50 inference(transitivity,[status(thm)],[1551, 1549])).
% 1.31/1.50 tff(1553,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(1554,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp4 | c2_1(a1624) | c3_1(a1624) | c1_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c2_1(a1581)) | c1_1(a1624)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 1.31/1.50 tff(1555,plain,
% 1.31/1.50 (c1_1(a1624)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1554, 319, 36, 1534, 852, 851, 1533, 1548, 1538])).
% 1.31/1.50 tff(1556,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | (~c1_1(a1624)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1557,plain,
% 1.31/1.50 ((hskp15 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1624) | c2_1(a1624) | (~c1_1(a1624))) <=> (hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | (~c1_1(a1624)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(1558,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1624) | c2_1(a1624) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | (~c1_1(a1624))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[1557])).
% 1.31/1.51 tff(1559,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1624) | c2_1(a1624) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | (~c1_1(a1624)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[1558, 1556])).
% 1.31/1.51 tff(1560,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1624) | c2_1(a1624) | (~c1_1(a1624)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(1561,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | (~c1_1(a1624))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 1.31/1.51 tff(1562,plain,
% 1.31/1.51 ((~c0_1(a1542)) | (~c1_1(a1624))),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1561, 319, 132, 1537, 1535, 852, 851, 835])).
% 1.31/1.51 tff(1563,plain,
% 1.31/1.51 (~c0_1(a1542)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1562, 1555])).
% 1.31/1.51 tff(1564,plain,
% 1.31/1.51 ($false),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1500, 319, 1537, 1536, 1535, 426, 418, 410, 382, 1563])).
% 1.31/1.51 tff(1565,plain,((~hskp10) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c3_1(a1542)) | hskp15 | c2_1(a1624) | c3_1(a1624) | hskp4 | (~c0_1(a1558)) | (~c1_1(a1558)) | c2_1(a1558)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.51 tff(1566,plain,
% 1.31/1.51 (~hskp10),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1565, 1530, 1529, 1528, 132, 819, 813, 1504, 1508, 1507, 1506])).
% 1.31/1.51 tff(1567,plain,
% 1.31/1.51 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1568,plain,
% 1.31/1.51 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(1569,plain,
% 1.31/1.51 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 1.31/1.51 tff(1570,plain,
% 1.31/1.51 (hskp10 | (~c0_1(a1542))),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1569, 319, 874, 882, 10])).
% 1.31/1.51 tff(1571,plain,
% 1.31/1.51 (~c0_1(a1542)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1570, 11])).
% 1.31/1.51 tff(1572,assumption,(c3_1(a1538)), introduced(assumption)).
% 1.31/1.51 tff(1573,plain,
% 1.31/1.51 (~hskp4),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[154, 1572])).
% 1.31/1.51 tff(1574,plain,
% 1.31/1.51 (hskp10 | hskp4 | (~c1_1(a1624))),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1289, 319, 853, 852, 121])).
% 1.31/1.51 tff(1575,plain,
% 1.31/1.51 (~c1_1(a1624)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1574, 11, 1573])).
% 1.31/1.51 tff(1576,plain,
% 1.31/1.51 (hskp2 | hskp1 | c1_1(a1624)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1268, 319, 853, 852, 1262])).
% 1.31/1.51 tff(1577,plain,
% 1.31/1.51 (hskp2),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1576, 1575, 47])).
% 1.31/1.51 tff(1578,plain,
% 1.31/1.51 (~c1_1(a1535)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[858, 1577])).
% 1.31/1.51 tff(1579,plain,
% 1.31/1.51 (c3_1(a1535)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[843, 1577])).
% 1.31/1.51 tff(1580,plain,
% 1.31/1.51 (~c2_1(a1535)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[849, 1577])).
% 1.31/1.51 tff(1581,plain,
% 1.31/1.51 (c0_1(a1538)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[975, 1580, 872, 629, 853, 852, 851, 611, 23, 24, 1579, 156, 1578])).
% 1.31/1.51 tff(1582,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1583,plain,
% 1.31/1.51 (((~ndr1_0) | c1_1(a1538) | (~c3_1(a1538)) | (~c0_1(a1538)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542))) <=> (c1_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1584,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1538) | (~c3_1(a1538)) | (~c0_1(a1538)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[1583])).
% 1.31/1.51 tff(1585,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1538) | (~c3_1(a1538)) | (~c0_1(a1538)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.31/1.51 inference(transitivity,[status(thm)],[1584, 1582])).
% 1.31/1.51 tff(1586,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1538) | (~c3_1(a1538)) | (~c0_1(a1538)) | c0_1(a1542) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(1587,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 1.31/1.51 tff(1588,plain,
% 1.31/1.51 ($false),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1587, 319, 874, 873, 882, 629, 1572, 382, 1581, 1571])).
% 1.31/1.51 tff(1589,plain,(hskp10 | c1_1(a1538) | (~c3_1(a1538)) | (~hskp28) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | (~c2_1(a1545)) | c0_1(a1545) | c3_1(a1545) | c2_1(a1538) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.31/1.51 tff(1590,plain,
% 1.31/1.51 (c1_1(a1538)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1589, 1566, 1503, 1527, 825, 819, 813, 195, 187, 181, 156, 47])).
% 1.31/1.51 tff(1591,plain,
% 1.31/1.51 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~c1_1(a1538)) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~c1_1(a1538)) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1592,plain,
% 1.31/1.51 ((hskp10 | (~ndr1_0) | (~c1_1(a1538)) | (~c3_1(a1538)) | (~c0_1(a1538))) <=> (hskp10 | (~c1_1(a1538)) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1593,plain,
% 1.31/1.51 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1538)) | (~c3_1(a1538)) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~c1_1(a1538)) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[1592])).
% 1.31/1.51 tff(1594,plain,
% 1.31/1.51 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1538)) | (~c3_1(a1538)) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~c1_1(a1538)) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[1593, 1591])).
% 1.31/1.51 tff(1595,plain,
% 1.31/1.51 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1538)) | (~c3_1(a1538)) | (~c0_1(a1538)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(1596,plain,
% 1.31/1.51 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~c1_1(a1538)) | (~c3_1(a1538)) | (~ndr1_0) | (~c0_1(a1538))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.31/1.51 tff(1597,plain,
% 1.31/1.51 (hskp10 | (~c1_1(a1538)) | (~c0_1(a1538))),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1596, 319, 1503, 10])).
% 1.31/1.51 tff(1598,plain,
% 1.31/1.51 (~c0_1(a1538)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1597, 1590, 1566])).
% 1.31/1.51 tff(1599,plain,
% 1.31/1.51 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.31/1.51 inference(bind,[status(th)],[])).
% 1.31/1.51 tff(1600,plain,
% 1.31/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.31/1.51 inference(quant_intro,[status(thm)],[1599])).
% 1.31/1.51 tff(1601,plain,
% 1.31/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1602,plain,
% 1.31/1.51 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.31/1.51 inference(bind,[status(th)],[])).
% 1.31/1.51 tff(1603,plain,
% 1.31/1.51 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.31/1.51 inference(quant_intro,[status(thm)],[1602])).
% 1.31/1.51 tff(1604,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.31/1.51 tff(1605,plain,
% 1.31/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.31/1.51 tff(1606,plain,
% 1.31/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1605, 1601])).
% 1.31/1.51 tff(1607,plain,(
% 1.31/1.51 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.31/1.51 inference(skolemize,[status(sab)],[1606])).
% 1.31/1.51 tff(1608,plain,
% 1.31/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1607, 1600])).
% 1.31/1.51 tff(1609,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a1538)) | c2_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | c0_1(a1538) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a1538)) | c2_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | c0_1(a1538) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1610,plain,
% 1.31/1.51 (((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c2_1(a1538) | c0_1(a1538) | (~c3_1(a1538)) | c2_1(a1538) | c0_1(a1538) | (~c1_1(a1538))) <=> ((~c1_1(a1538)) | c2_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | c0_1(a1538) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1611,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c2_1(a1538) | c0_1(a1538) | (~c3_1(a1538)) | c2_1(a1538) | c0_1(a1538) | (~c1_1(a1538)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a1538)) | c2_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | c0_1(a1538) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[1610])).
% 1.31/1.51 tff(1612,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c2_1(a1538) | c0_1(a1538) | (~c3_1(a1538)) | c2_1(a1538) | c0_1(a1538) | (~c1_1(a1538)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a1538)) | c2_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | c0_1(a1538) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[1611, 1609])).
% 1.31/1.51 tff(1613,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c2_1(a1538) | c0_1(a1538) | (~c3_1(a1538)) | c2_1(a1538) | c0_1(a1538) | (~c1_1(a1538)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(1614,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a1538)) | c2_1(a1538) | (~c3_1(a1538)) | (~ndr1_0) | c0_1(a1538) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 1.31/1.51 tff(1615,plain,
% 1.31/1.51 ((~c1_1(a1538)) | c0_1(a1538)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1614, 319, 1530, 1529, 1528, 156, 1503, 1608])).
% 1.31/1.51 tff(1616,plain,
% 1.31/1.51 ($false),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1615, 1598, 1590])).
% 1.31/1.51 tff(1617,plain,(c2_1(a1538) | hskp1 | hskp15 | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.31/1.51 tff(1618,plain,
% 1.31/1.51 (c2_1(a1538)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1617, 47, 132, 163])).
% 1.31/1.51 tff(1619,plain,
% 1.31/1.51 (~hskp4),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[138, 1618])).
% 1.31/1.51 tff(1620,plain,
% 1.31/1.51 (hskp14),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[58, 1619, 47])).
% 1.31/1.51 tff(1621,plain,
% 1.31/1.51 (~c2_1(a1558)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[64, 1620])).
% 1.31/1.51 tff(1622,plain,
% 1.31/1.51 (c1_1(a1558)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[72, 1620])).
% 1.31/1.51 tff(1623,plain,
% 1.31/1.51 (c0_1(a1558)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[80, 1620])).
% 1.31/1.51 tff(1624,plain,
% 1.31/1.51 (hskp28),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1526, 1623, 47, 1622, 1621, 132])).
% 1.31/1.51 tff(1625,plain,
% 1.31/1.51 (c3_1(a1542)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[530, 1624])).
% 1.31/1.51 tff(1626,plain,
% 1.31/1.51 (c2_1(a1542)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[538, 1624])).
% 1.31/1.51 tff(1627,plain,
% 1.31/1.51 (c1_1(a1542)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[546, 1624])).
% 1.31/1.51 tff(1628,plain,
% 1.31/1.51 (~hskp10),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1565, 1627, 1626, 1625, 132, 819, 813, 1619, 1623, 1622, 1621])).
% 1.31/1.51 tff(1629,plain,
% 1.31/1.51 (~c1_1(a1624)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1290, 1628, 1619])).
% 1.31/1.51 tff(1630,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1558) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1558)) | (~c1_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1558) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1631,plain,
% 1.31/1.51 ((hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545))) <=> (hskp10 | c2_1(a1558) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1632,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1558) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1558)) | (~c1_1(a1558))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[1631])).
% 1.31/1.51 tff(1633,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1558) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[1632, 1630])).
% 1.31/1.51 tff(1634,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(1635,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1558) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1558)) | (~c1_1(a1558))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 1.31/1.51 tff(1636,plain,
% 1.31/1.51 (~c1_1(a1545)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1635, 319, 1628, 1623, 1622, 195, 1621, 187, 1121])).
% 1.31/1.51 tff(1637,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c1_1(a1545) | c1_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp4 | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c1_1(a1545) | c1_1(a1624))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1638,plain,
% 1.31/1.51 ((hskp4 | (~ndr1_0) | c1_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624)) <=> (hskp4 | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c1_1(a1545) | c1_1(a1624))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1639,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c1_1(a1545) | c1_1(a1624)))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[1638])).
% 1.31/1.51 tff(1640,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp4 | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c1_1(a1545) | c1_1(a1624))),
% 1.31/1.51 inference(transitivity,[status(thm)],[1639, 1637])).
% 1.31/1.51 tff(1641,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(1642,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp4 | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | c1_1(a1545) | c1_1(a1624)),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 1.31/1.51 tff(1643,plain,
% 1.31/1.51 ($false),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1642, 319, 1619, 195, 819, 813, 187, 1548, 1636, 1629])).
% 1.31/1.51 tff(1644,plain,(hskp1 | hskp15 | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.31/1.51 tff(1645,plain,
% 1.31/1.51 (hskp1),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1644, 163, 132])).
% 1.31/1.51 tff(1646,plain,
% 1.31/1.51 (~c3_1(a1534)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[228, 1645])).
% 1.31/1.51 tff(1647,plain,
% 1.31/1.51 (c2_1(a1534)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[222, 1645])).
% 1.31/1.51 tff(1648,plain,
% 1.31/1.51 (c0_1(a1534)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[236, 1645])).
% 1.31/1.51 tff(1649,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1650,plain,
% 1.31/1.51 (((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624)) <=> (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(1651,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[1650])).
% 1.31/1.51 tff(1652,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[1651, 1649])).
% 1.31/1.52 tff(1653,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1624) | c2_1(a1624) | c0_1(a1624))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(1654,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 1.31/1.52 tff(1655,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1654, 319, 611, 265, 853, 852, 851, 23, 24, 264, 714, 267])).
% 1.31/1.52 tff(1656,plain,(c1_1(a1534) | (~c2_1(a1545)) | (~c0_1(a1534)) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(1657,plain,
% 1.31/1.52 (c1_1(a1534)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1656, 195, 1648, 825, 819, 813, 187, 181, 1646])).
% 1.31/1.52 tff(1658,plain,
% 1.31/1.52 (~hskp10),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[555, 1657, 1646, 1647, 1648])).
% 1.31/1.52 tff(1659,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c0_1(a1624) | c2_1(a1624) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | c1_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1624) | c2_1(a1624) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | c1_1(a1624))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1660,plain,
% 1.31/1.52 (((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1624) | c0_1(a1624) | c1_1(a1624)) <=> (c0_1(a1624) | c2_1(a1624) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | c1_1(a1624))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1661,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1624) | c0_1(a1624) | c1_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c0_1(a1624) | c2_1(a1624) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | c1_1(a1624)))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[1660])).
% 1.31/1.52 tff(1662,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1624) | c0_1(a1624) | c1_1(a1624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1624) | c2_1(a1624) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | c1_1(a1624))),
% 1.31/1.52 inference(transitivity,[status(thm)],[1661, 1659])).
% 1.31/1.52 tff(1663,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1624) | c0_1(a1624) | c1_1(a1624))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(1664,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1624) | c2_1(a1624) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | c1_1(a1624)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1663, 1662])).
% 1.31/1.52 tff(1665,plain,
% 1.31/1.52 (c1_1(a1624)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1664, 319, 195, 1648, 1647, 825, 819, 187, 181, 650, 1657])).
% 1.31/1.52 tff(1666,plain,
% 1.31/1.52 (hskp4),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1290, 1665, 1658])).
% 1.31/1.52 tff(1667,plain,
% 1.31/1.52 (~c2_1(a1538)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[138, 1666])).
% 1.31/1.52 tff(1668,plain,
% 1.31/1.52 (~c3_1(a1538)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[154, 1666])).
% 1.31/1.52 tff(1669,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1545) | c3_1(a1545) | c2_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c0_1(a1538) | (~c2_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1545) | c3_1(a1545) | c2_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c0_1(a1538) | (~c2_1(a1545)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1670,plain,
% 1.31/1.52 (((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1538) | c2_1(a1538) | c0_1(a1538)) <=> (c0_1(a1545) | c3_1(a1545) | c2_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c0_1(a1538) | (~c2_1(a1545)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1671,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1538) | c2_1(a1538) | c0_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1545) | c3_1(a1545) | c2_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c0_1(a1538) | (~c2_1(a1545))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[1670])).
% 1.31/1.52 tff(1672,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1538) | c2_1(a1538) | c0_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1545) | c3_1(a1545) | c2_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c0_1(a1538) | (~c2_1(a1545)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[1671, 1669])).
% 1.31/1.52 tff(1673,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1538) | c2_1(a1538) | c0_1(a1538))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(1674,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1545) | c3_1(a1545) | c2_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c0_1(a1538) | (~c2_1(a1545))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 1.31/1.52 tff(1675,plain,
% 1.31/1.52 (c0_1(a1538)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1674, 319, 611, 265, 23, 24, 156, 627, 264, 714, 267])).
% 1.31/1.52 tff(1676,plain,
% 1.31/1.52 (hskp28 | c2_1(a1538) | (~c0_1(a1538))),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[794, 319, 132, 627, 788])).
% 1.31/1.52 tff(1677,plain,
% 1.31/1.52 (hskp28),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1676, 1675, 156])).
% 1.31/1.52 tff(1678,plain,
% 1.31/1.52 (c3_1(a1542)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[530, 1677])).
% 1.31/1.52 tff(1679,plain,
% 1.31/1.52 (c2_1(a1542)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[538, 1677])).
% 1.31/1.52 tff(1680,plain,
% 1.31/1.52 (c1_1(a1542)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[546, 1677])).
% 1.31/1.52 tff(1681,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1682,plain,
% 1.31/1.52 (((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1534) | (~c2_1(a1534)) | (~c0_1(a1534))) <=> (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1683,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1534) | (~c2_1(a1534)) | (~c0_1(a1534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[1682])).
% 1.31/1.52 tff(1684,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1534) | (~c2_1(a1534)) | (~c0_1(a1534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[1683, 1681])).
% 1.31/1.52 tff(1685,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1534) | (~c2_1(a1534)) | (~c0_1(a1534)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(1686,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 1.31/1.52 tff(1687,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1686, 319, 1680, 1679, 1678, 265, 266, 264, 101, 267])).
% 1.31/1.52 tff(1688,plain,(c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c2_1(a1538) | hskp15 | c3_1(a1538) | (~c2_1(a1545)) | c0_1(a1545) | c3_1(a1545)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(1689,plain,
% 1.31/1.52 (c1_1(a1534)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1688, 627, 266, 264, 156, 132, 265, 611, 23, 24])).
% 1.31/1.52 tff(1690,plain,
% 1.31/1.52 (~hskp10),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[555, 1689, 264, 266, 265])).
% 1.31/1.52 tff(1691,plain,
% 1.31/1.52 (c1_1(a1624)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1664, 319, 611, 265, 266, 853, 852, 23, 24, 650, 1689])).
% 1.31/1.52 tff(1692,plain,
% 1.31/1.52 (hskp4),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1574, 1691, 1690])).
% 1.31/1.52 tff(1693,plain,
% 1.31/1.52 (~c1_1(a1538)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[161, 1692])).
% 1.31/1.52 tff(1694,plain,
% 1.31/1.52 (c1_1(a1538) | c0_1(a1538)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[656, 319, 611, 265, 266, 23, 24, 156, 650, 1689])).
% 1.31/1.52 tff(1695,plain,
% 1.31/1.52 (c0_1(a1538)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1694, 1693])).
% 1.31/1.52 tff(1696,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[866, 1695, 1693])).
% 1.31/1.52 tff(1697,plain,(c3_1(a1538) | c0_1(a1624) | c2_1(a1624) | c3_1(a1624) | c2_1(a1538) | (~c2_1(a1545)) | (~c0_1(a1534)) | (~c2_1(a1534)) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(1698,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1697, 1668, 1667, 819, 813, 825, 195, 1648, 1647, 187, 181, 1646, 132])).
% 1.31/1.52 tff(1699,plain,(hskp31 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(1700,plain,
% 1.31/1.52 (hskp31),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1699, 132])).
% 1.31/1.52 tff(1701,plain,
% 1.31/1.52 (((~hskp31) | c3_1(a1562)) <=> ((~hskp31) | c3_1(a1562))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1702,axiom,((~hskp31) | c3_1(a1562)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.31/1.52 tff(1703,plain,
% 1.31/1.52 ((~hskp31) | c3_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 1.31/1.52 tff(1704,plain,
% 1.31/1.52 ((~hskp31) | c3_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1703, 1701])).
% 1.31/1.52 tff(1705,plain,
% 1.31/1.52 ((~hskp31) | c3_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1704, 1701])).
% 1.31/1.52 tff(1706,plain,
% 1.31/1.52 ((~hskp31) | c3_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1705, 1701])).
% 1.31/1.52 tff(1707,plain,
% 1.31/1.52 ((~hskp31) | c3_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1706, 1701])).
% 1.31/1.52 tff(1708,plain,
% 1.31/1.52 (c3_1(a1562)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1707, 1700])).
% 1.31/1.52 tff(1709,plain,
% 1.31/1.52 (((~hskp31) | c2_1(a1562)) <=> ((~hskp31) | c2_1(a1562))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1710,axiom,((~hskp31) | c2_1(a1562)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.31/1.52 tff(1711,plain,
% 1.31/1.52 ((~hskp31) | c2_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1710, 1709])).
% 1.31/1.52 tff(1712,plain,
% 1.31/1.52 ((~hskp31) | c2_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1711, 1709])).
% 1.31/1.52 tff(1713,plain,
% 1.31/1.52 ((~hskp31) | c2_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1712, 1709])).
% 1.31/1.52 tff(1714,plain,
% 1.31/1.52 ((~hskp31) | c2_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1713, 1709])).
% 1.31/1.52 tff(1715,plain,
% 1.31/1.52 ((~hskp31) | c2_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1714, 1709])).
% 1.31/1.52 tff(1716,plain,
% 1.31/1.52 (c2_1(a1562)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1715, 1700])).
% 1.31/1.52 tff(1717,plain,
% 1.31/1.52 (((~hskp31) | c0_1(a1562)) <=> ((~hskp31) | c0_1(a1562))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1718,axiom,((~hskp31) | c0_1(a1562)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.31/1.52 tff(1719,plain,
% 1.31/1.52 ((~hskp31) | c0_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 1.31/1.52 tff(1720,plain,
% 1.31/1.52 ((~hskp31) | c0_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1719, 1717])).
% 1.31/1.52 tff(1721,plain,
% 1.31/1.52 ((~hskp31) | c0_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1720, 1717])).
% 1.31/1.52 tff(1722,plain,
% 1.31/1.52 ((~hskp31) | c0_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1721, 1717])).
% 1.31/1.52 tff(1723,plain,
% 1.31/1.52 ((~hskp31) | c0_1(a1562)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1722, 1717])).
% 1.31/1.52 tff(1724,plain,
% 1.31/1.52 (c0_1(a1562)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1723, 1700])).
% 1.31/1.52 tff(1725,plain,
% 1.31/1.52 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1726,plain,
% 1.31/1.52 ((hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538)) <=> (hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1727,plain,
% 1.31/1.52 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[1726])).
% 1.31/1.52 tff(1728,plain,
% 1.31/1.52 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[1727, 1725])).
% 1.31/1.52 tff(1729,plain,
% 1.31/1.52 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(1730,plain,
% 1.31/1.52 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 1.31/1.52 tff(1731,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1730, 319, 132, 1724, 1716, 1708, 162, 156, 155, 149])).
% 1.31/1.52 tff(1732,plain,((~hskp4) | hskp15 | c2_1(a1538)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(1733,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1732, 139, 133, 132])).
% 1.31/1.52 tff(1734,plain,((~hskp4) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(1735,plain,
% 1.31/1.52 (~hskp4),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1734, 132])).
% 1.31/1.52 tff(1736,assumption,(hskp20), introduced(assumption)).
% 1.31/1.52 tff(1737,plain,
% 1.31/1.52 (((~hskp20) | c3_1(a1574)) <=> ((~hskp20) | c3_1(a1574))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1738,axiom,((~hskp20) | c3_1(a1574)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.31/1.52 tff(1739,plain,
% 1.31/1.52 ((~hskp20) | c3_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 1.31/1.52 tff(1740,plain,
% 1.31/1.52 ((~hskp20) | c3_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1739, 1737])).
% 1.31/1.52 tff(1741,plain,
% 1.31/1.52 ((~hskp20) | c3_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1740, 1737])).
% 1.31/1.52 tff(1742,plain,
% 1.31/1.52 ((~hskp20) | c3_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1741, 1737])).
% 1.31/1.52 tff(1743,plain,
% 1.31/1.52 ((~hskp20) | c3_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1742, 1737])).
% 1.31/1.52 tff(1744,plain,
% 1.31/1.52 (c3_1(a1574)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1743, 1736])).
% 1.31/1.52 tff(1745,plain,
% 1.31/1.52 (((~hskp20) | c1_1(a1574)) <=> ((~hskp20) | c1_1(a1574))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1746,axiom,((~hskp20) | c1_1(a1574)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.31/1.52 tff(1747,plain,
% 1.31/1.52 ((~hskp20) | c1_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 1.31/1.52 tff(1748,plain,
% 1.31/1.52 ((~hskp20) | c1_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1747, 1745])).
% 1.31/1.52 tff(1749,plain,
% 1.31/1.52 ((~hskp20) | c1_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1748, 1745])).
% 1.31/1.52 tff(1750,plain,
% 1.31/1.52 ((~hskp20) | c1_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1749, 1745])).
% 1.31/1.52 tff(1751,plain,
% 1.31/1.52 ((~hskp20) | c1_1(a1574)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1750, 1745])).
% 1.31/1.52 tff(1752,plain,
% 1.31/1.52 (c1_1(a1574)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1751, 1736])).
% 1.31/1.52 tff(1753,plain,
% 1.31/1.52 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1754,plain,
% 1.31/1.52 ((hskp10 | (~ndr1_0) | (~c1_1(a1574)) | (~c3_1(a1574)) | (~c0_1(a1574))) <=> (hskp10 | (~ndr1_0) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1755,plain,
% 1.31/1.52 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1574)) | (~c3_1(a1574)) | (~c0_1(a1574)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[1754])).
% 1.31/1.52 tff(1756,plain,
% 1.31/1.52 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1574)) | (~c3_1(a1574)) | (~c0_1(a1574)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[1755, 1753])).
% 1.31/1.52 tff(1757,plain,
% 1.31/1.52 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1574)) | (~c3_1(a1574)) | (~c0_1(a1574)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(1758,plain,
% 1.31/1.52 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 1.31/1.52 tff(1759,plain,
% 1.31/1.52 (~c0_1(a1574)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1758, 319, 11, 1752, 1744, 10])).
% 1.31/1.52 tff(1760,plain,
% 1.31/1.52 (((~hskp20) | (~c2_1(a1574))) <=> ((~hskp20) | (~c2_1(a1574)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1761,plain,
% 1.31/1.52 (((~c2_1(a1574)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a1574)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1762,axiom,((~c2_1(a1574)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.31/1.52 tff(1763,plain,
% 1.31/1.52 ((~hskp20) | (~c2_1(a1574))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.31/1.52 tff(1764,plain,
% 1.31/1.52 ((~hskp20) | (~c2_1(a1574))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1763, 1760])).
% 1.31/1.52 tff(1765,plain,
% 1.31/1.52 (~c2_1(a1574)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1764, 1736])).
% 1.31/1.52 tff(1766,plain,
% 1.31/1.52 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c2_1(a1574) | (~ndr1_0) | c0_1(a1574) | (~c1_1(a1574)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c2_1(a1574) | (~ndr1_0) | c0_1(a1574) | (~c1_1(a1574)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1767,plain,
% 1.31/1.52 ((hskp10 | hskp4 | (~ndr1_0) | c2_1(a1574) | c0_1(a1574) | (~c1_1(a1574))) <=> (hskp10 | hskp4 | c2_1(a1574) | (~ndr1_0) | c0_1(a1574) | (~c1_1(a1574)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1768,plain,
% 1.31/1.52 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1574) | c0_1(a1574) | (~c1_1(a1574)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c2_1(a1574) | (~ndr1_0) | c0_1(a1574) | (~c1_1(a1574))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[1767])).
% 1.31/1.52 tff(1769,plain,
% 1.31/1.52 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1574) | c0_1(a1574) | (~c1_1(a1574)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c2_1(a1574) | (~ndr1_0) | c0_1(a1574) | (~c1_1(a1574)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[1768, 1766])).
% 1.31/1.52 tff(1770,plain,
% 1.31/1.52 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1574) | c0_1(a1574) | (~c1_1(a1574)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(1771,plain,
% 1.31/1.52 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c2_1(a1574) | (~ndr1_0) | c0_1(a1574) | (~c1_1(a1574))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 1.31/1.52 tff(1772,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1771, 319, 11, 36, 1752, 1765, 121, 1759])).
% 1.31/1.52 tff(1773,plain,((~hskp20) | hskp10 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(1774,plain,
% 1.31/1.52 (~hskp20),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1773, 11, 1735])).
% 1.31/1.52 tff(1775,plain,
% 1.31/1.52 ((hskp20 | hskp15 | hskp14) <=> (hskp20 | hskp15 | hskp14)),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1776,plain,
% 1.31/1.52 (((hskp14 | hskp20) | hskp15) <=> (hskp20 | hskp15 | hskp14)),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1777,axiom,((hskp14 | hskp20) | hskp15), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 1.31/1.52 tff(1778,plain,
% 1.31/1.52 (hskp20 | hskp15 | hskp14),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.31/1.52 tff(1779,plain,
% 1.31/1.52 (hskp20 | hskp15 | hskp14),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1778, 1775])).
% 1.31/1.52 tff(1780,plain,
% 1.31/1.52 (hskp20 | hskp15 | hskp14),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1779, 1775])).
% 1.31/1.52 tff(1781,plain,
% 1.31/1.52 (hskp20 | hskp15 | hskp14),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1780, 1775])).
% 1.31/1.52 tff(1782,plain,
% 1.31/1.52 (hskp20 | hskp15 | hskp14),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1781, 1775])).
% 1.31/1.52 tff(1783,plain,
% 1.31/1.52 (hskp14),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1782, 1774, 132])).
% 1.31/1.52 tff(1784,plain,
% 1.31/1.52 (c1_1(a1558)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[72, 1783])).
% 1.31/1.52 tff(1785,plain,
% 1.31/1.52 (c0_1(a1558)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[80, 1783])).
% 1.31/1.52 tff(1786,plain,
% 1.31/1.52 (~c3_1(a1558)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1097, 319, 11, 1785, 1784, 10])).
% 1.31/1.52 tff(1787,plain,
% 1.31/1.52 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1562)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1562)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1788,plain,
% 1.31/1.52 ((hskp10 | (~ndr1_0) | (~c1_1(a1562)) | (~c3_1(a1562)) | (~c0_1(a1562))) <=> (hskp10 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1562)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1789,plain,
% 1.31/1.52 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1562)) | (~c3_1(a1562)) | (~c0_1(a1562)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1562))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[1788])).
% 1.31/1.52 tff(1790,plain,
% 1.31/1.52 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1562)) | (~c3_1(a1562)) | (~c0_1(a1562)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1562)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[1789, 1787])).
% 1.31/1.52 tff(1791,plain,
% 1.31/1.52 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1562)) | (~c3_1(a1562)) | (~c0_1(a1562)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(1792,plain,
% 1.31/1.52 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1562))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 1.31/1.52 tff(1793,plain,
% 1.31/1.52 (hskp10 | (~c1_1(a1562))),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1792, 319, 1724, 1708, 10])).
% 1.31/1.52 tff(1794,plain,
% 1.31/1.52 (~c1_1(a1562)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1793, 11])).
% 1.31/1.52 tff(1795,plain,
% 1.31/1.52 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.31/1.52 inference(bind,[status(th)],[])).
% 1.31/1.52 tff(1796,plain,
% 1.31/1.52 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.52 inference(quant_intro,[status(thm)],[1795])).
% 1.31/1.52 tff(1797,plain,
% 1.31/1.52 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(1798,plain,
% 1.31/1.52 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.31/1.53 inference(bind,[status(th)],[])).
% 1.31/1.53 tff(1799,plain,
% 1.31/1.53 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.53 inference(quant_intro,[status(thm)],[1798])).
% 1.31/1.53 tff(1800,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.31/1.53 tff(1801,plain,
% 1.31/1.53 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.31/1.53 tff(1802,plain,
% 1.31/1.53 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1801, 1797])).
% 1.31/1.53 tff(1803,plain,(
% 1.31/1.53 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.53 inference(skolemize,[status(sab)],[1802])).
% 1.31/1.53 tff(1804,plain,
% 1.31/1.53 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1803, 1796])).
% 1.31/1.53 tff(1805,plain,
% 1.31/1.53 (~c2_1(a1558)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[64, 1783])).
% 1.31/1.53 tff(1806,plain,
% 1.31/1.53 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c2_1(a1558) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1558) | (~c1_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1558) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1558) | (~c1_1(a1558)))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1807,plain,
% 1.31/1.53 ((hskp20 | (~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c1_1(a1558)) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562))) <=> (hskp20 | c2_1(a1558) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1558) | (~c1_1(a1558)))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1808,plain,
% 1.31/1.53 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c1_1(a1558)) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c2_1(a1558) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1558) | (~c1_1(a1558))))),
% 1.31/1.53 inference(monotonicity,[status(thm)],[1807])).
% 1.31/1.53 tff(1809,plain,
% 1.31/1.53 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c1_1(a1558)) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1558) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1558) | (~c1_1(a1558)))),
% 1.31/1.53 inference(transitivity,[status(thm)],[1808, 1806])).
% 1.31/1.53 tff(1810,plain,
% 1.31/1.53 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c1_1(a1558)) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)))),
% 1.31/1.53 inference(quant_inst,[status(thm)],[])).
% 1.31/1.53 tff(1811,plain,
% 1.31/1.53 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1558) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1558) | (~c1_1(a1558))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 1.31/1.53 tff(1812,plain,
% 1.31/1.53 ($false),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1811, 319, 1774, 1724, 1716, 1784, 1805, 1804, 1794, 1786])).
% 1.31/1.53 tff(1813,plain,(hskp10 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.31/1.53 tff(1814,plain,
% 1.31/1.53 (hskp10),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1813, 132])).
% 1.31/1.53 tff(1815,assumption,(hskp1), introduced(assumption)).
% 1.31/1.53 tff(1816,plain,
% 1.31/1.53 (c0_1(a1534)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[236, 1815])).
% 1.31/1.53 tff(1817,plain,
% 1.31/1.53 (c2_1(a1534)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[222, 1815])).
% 1.31/1.53 tff(1818,plain,
% 1.31/1.53 (~c3_1(a1534)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[228, 1815])).
% 1.31/1.53 tff(1819,plain,
% 1.31/1.53 (~c1_1(a1534)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[555, 1818, 404, 1817, 1816])).
% 1.31/1.53 tff(1820,plain,
% 1.31/1.53 ($false),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1686, 319, 1537, 1536, 1535, 1816, 1817, 1818, 101, 1819])).
% 1.31/1.53 tff(1821,plain,((~hskp1) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c3_1(a1542)) | (~hskp10)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.53 tff(1822,plain,
% 1.31/1.53 (~hskp1),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1821, 874, 873, 882, 1814])).
% 1.31/1.53 tff(1823,plain,
% 1.31/1.53 (hskp26),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[214, 1822, 132])).
% 1.31/1.53 tff(1824,plain,
% 1.31/1.53 (hskp14),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[58, 47, 1735])).
% 1.31/1.53 tff(1825,plain,
% 1.31/1.53 (~c2_1(a1558)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[64, 1824])).
% 1.31/1.53 tff(1826,plain,
% 1.31/1.53 (c1_1(a1558)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[72, 1824])).
% 1.31/1.53 tff(1827,plain,
% 1.31/1.53 (hskp26),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[214, 47, 132])).
% 1.31/1.53 tff(1828,plain,
% 1.31/1.53 (~c3_1(a1624)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[812, 1827])).
% 1.31/1.53 tff(1829,plain,
% 1.31/1.53 (c0_1(a1558)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[80, 1824])).
% 1.31/1.53 tff(1830,plain,
% 1.31/1.53 ($false),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1565, 1829, 1828, 1814, 1537, 132, 1535, 1536, 1735, 852, 1826, 1825])).
% 1.31/1.53 tff(1831,plain,(hskp1 | (~c1_1(a1542)) | hskp15 | (~c3_1(a1542)) | (~c2_1(a1542)) | c2_1(a1624)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.53 tff(1832,plain,
% 1.31/1.53 (c2_1(a1624)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1831, 1822, 132, 882, 873, 874])).
% 1.31/1.53 tff(1833,plain,
% 1.31/1.53 ($false),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[818, 1832, 1823])).
% 1.31/1.53 tff(1834,plain,((~hskp28) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.31/1.53 tff(1835,plain,
% 1.31/1.53 (~hskp28),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1834, 132])).
% 1.31/1.53 tff(1836,plain,
% 1.31/1.53 ($false),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1526, 73, 81, 12, 47, 65, 132])).
% 1.31/1.53 tff(1837,plain,(hskp1 | hskp28 | hskp15 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.31/1.53 tff(1838,plain,
% 1.31/1.53 (hskp1),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1837, 1835, 132, 1735])).
% 1.31/1.53 tff(1839,plain,
% 1.31/1.53 (c0_1(a1534)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[236, 1838])).
% 1.31/1.53 tff(1840,plain,
% 1.31/1.53 (~c3_1(a1534)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[228, 1838])).
% 1.31/1.53 tff(1841,plain,
% 1.31/1.53 (c2_1(a1534)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[222, 1838])).
% 1.31/1.53 tff(1842,plain,
% 1.31/1.53 (~c1_1(a1534)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[555, 1840, 1814, 1841, 1839])).
% 1.31/1.53 tff(1843,plain,
% 1.31/1.53 (~hskp23),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[371, 1842, 1841, 1840, 1839])).
% 1.31/1.53 tff(1844,plain,
% 1.31/1.53 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~c0_1(a1624)) | c2_1(a1624) | c3_1(a1624) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | (~c0_1(a1624)) | c2_1(a1624) | c3_1(a1624) | (~ndr1_0))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1845,plain,
% 1.31/1.53 ((hskp28 | hskp15 | (~ndr1_0) | c2_1(a1624) | c3_1(a1624) | (~c0_1(a1624))) <=> (hskp28 | hskp15 | (~c0_1(a1624)) | c2_1(a1624) | c3_1(a1624) | (~ndr1_0))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1846,plain,
% 1.31/1.53 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1624) | c3_1(a1624) | (~c0_1(a1624)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~c0_1(a1624)) | c2_1(a1624) | c3_1(a1624) | (~ndr1_0)))),
% 1.31/1.53 inference(monotonicity,[status(thm)],[1845])).
% 1.31/1.53 tff(1847,plain,
% 1.31/1.53 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1624) | c3_1(a1624) | (~c0_1(a1624)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | (~c0_1(a1624)) | c2_1(a1624) | c3_1(a1624) | (~ndr1_0))),
% 1.31/1.53 inference(transitivity,[status(thm)],[1846, 1844])).
% 1.31/1.53 tff(1848,plain,
% 1.31/1.53 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c2_1(a1624) | c3_1(a1624) | (~c0_1(a1624)))),
% 1.31/1.53 inference(quant_inst,[status(thm)],[])).
% 1.31/1.53 tff(1849,plain,
% 1.31/1.53 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp15 | (~c0_1(a1624)) | c2_1(a1624) | c3_1(a1624) | (~ndr1_0)),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 1.31/1.53 tff(1850,plain,
% 1.31/1.53 ((~c0_1(a1624)) | c3_1(a1624)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1849, 319, 1835, 132, 852, 788])).
% 1.31/1.53 tff(1851,plain,
% 1.31/1.53 (~c0_1(a1624)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1850, 851])).
% 1.31/1.53 tff(1852,plain,
% 1.31/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c1_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c1_1(a1624))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1853,plain,
% 1.31/1.53 ((hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624)) <=> (hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c1_1(a1624))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1854,plain,
% 1.31/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c1_1(a1624)))),
% 1.31/1.53 inference(monotonicity,[status(thm)],[1853])).
% 1.31/1.53 tff(1855,plain,
% 1.31/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c1_1(a1624))),
% 1.31/1.53 inference(transitivity,[status(thm)],[1854, 1852])).
% 1.31/1.53 tff(1856,plain,
% 1.31/1.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1624) | c2_1(a1624) | c1_1(a1624))),
% 1.31/1.53 inference(quant_inst,[status(thm)],[])).
% 1.31/1.53 tff(1857,plain,
% 1.31/1.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c1_1(a1624)),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1856, 1855])).
% 1.31/1.53 tff(1858,plain,
% 1.31/1.53 (c1_1(a1624)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1857, 319, 132, 1724, 1716, 1708, 852, 851, 149])).
% 1.31/1.53 tff(1859,plain,
% 1.31/1.53 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.31/1.53 inference(bind,[status(th)],[])).
% 1.31/1.53 tff(1860,plain,
% 1.31/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.53 inference(quant_intro,[status(thm)],[1859])).
% 1.31/1.53 tff(1861,plain,
% 1.31/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1862,plain,
% 1.31/1.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.31/1.53 inference(bind,[status(th)],[])).
% 1.31/1.53 tff(1863,plain,
% 1.31/1.53 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.53 inference(quant_intro,[status(thm)],[1862])).
% 1.31/1.53 tff(1864,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.31/1.53 tff(1865,plain,
% 1.31/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 1.31/1.53 tff(1866,plain,
% 1.31/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1865, 1861])).
% 1.31/1.53 tff(1867,plain,(
% 1.31/1.53 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.53 inference(skolemize,[status(sab)],[1866])).
% 1.31/1.53 tff(1868,plain,
% 1.31/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1867, 1860])).
% 1.31/1.53 tff(1869,plain,
% 1.31/1.53 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1624) | c2_1(a1624) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1624) | c2_1(a1624) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1624)))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1870,plain,
% 1.31/1.53 ((hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1624) | c0_1(a1624) | (~c1_1(a1624))) <=> (hskp9 | c0_1(a1624) | c2_1(a1624) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1624)))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1871,plain,
% 1.31/1.53 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1624) | c0_1(a1624) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1624) | c2_1(a1624) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1624))))),
% 1.31/1.53 inference(monotonicity,[status(thm)],[1870])).
% 1.31/1.53 tff(1872,plain,
% 1.31/1.53 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1624) | c0_1(a1624) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1624) | c2_1(a1624) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1624)))),
% 1.31/1.53 inference(transitivity,[status(thm)],[1871, 1869])).
% 1.31/1.53 tff(1873,plain,
% 1.31/1.53 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1624) | c0_1(a1624) | (~c1_1(a1624)))),
% 1.31/1.53 inference(quant_inst,[status(thm)],[])).
% 1.31/1.53 tff(1874,plain,
% 1.31/1.53 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1624) | c2_1(a1624) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1624))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 1.31/1.53 tff(1875,plain,
% 1.31/1.53 (hskp9 | c0_1(a1624) | (~c1_1(a1624))),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1874, 319, 1841, 852, 1840, 1868, 1842])).
% 1.31/1.53 tff(1876,plain,
% 1.31/1.53 (hskp9),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1875, 1858, 1851])).
% 1.31/1.53 tff(1877,plain,
% 1.31/1.53 (((~hskp9) | (~c1_1(a1548))) <=> ((~hskp9) | (~c1_1(a1548)))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1878,plain,
% 1.31/1.53 (((~c1_1(a1548)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1548)))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1879,axiom,((~c1_1(a1548)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.31/1.53 tff(1880,plain,
% 1.31/1.53 ((~hskp9) | (~c1_1(a1548))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 1.31/1.53 tff(1881,plain,
% 1.31/1.53 ((~hskp9) | (~c1_1(a1548))),
% 1.31/1.53 inference(modus_ponens,[status(thm)],[1880, 1877])).
% 1.31/1.53 tff(1882,plain,
% 1.31/1.53 (~c1_1(a1548)),
% 1.31/1.53 inference(unit_resolution,[status(thm)],[1881, 1876])).
% 1.31/1.53 tff(1883,plain,
% 1.31/1.53 (((~hskp9) | (~c0_1(a1548))) <=> ((~hskp9) | (~c0_1(a1548)))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1884,plain,
% 1.31/1.53 (((~c0_1(a1548)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a1548)))),
% 1.31/1.53 inference(rewrite,[status(thm)],[])).
% 1.31/1.53 tff(1885,axiom,((~c0_1(a1548)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.36/1.53 tff(1886,plain,
% 1.36/1.53 ((~hskp9) | (~c0_1(a1548))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 1.36/1.53 tff(1887,plain,
% 1.36/1.53 ((~hskp9) | (~c0_1(a1548))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1886, 1883])).
% 1.36/1.53 tff(1888,plain,
% 1.36/1.53 (~c0_1(a1548)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1887, 1876])).
% 1.36/1.53 tff(1889,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1624)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1890,plain,
% 1.36/1.53 ((hskp20 | (~ndr1_0) | c2_1(a1624) | c3_1(a1624) | (~c1_1(a1624)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534))) <=> (hskp20 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1624)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1891,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1624) | c3_1(a1624) | (~c1_1(a1624)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1624))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1890])).
% 1.36/1.53 tff(1892,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1624) | c3_1(a1624) | (~c1_1(a1624)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1624)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1891, 1889])).
% 1.36/1.53 tff(1893,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1624) | c3_1(a1624) | (~c1_1(a1624)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1894,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1624) | c3_1(a1624) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1624))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 1.36/1.53 tff(1895,plain,
% 1.36/1.53 (hskp20 | c3_1(a1624) | (~c1_1(a1624))),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1894, 319, 1839, 1841, 852, 1804, 1842])).
% 1.36/1.53 tff(1896,plain,
% 1.36/1.53 (hskp20),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1895, 1858, 851])).
% 1.36/1.53 tff(1897,plain,
% 1.36/1.53 (~c2_1(a1574)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1764, 1896])).
% 1.36/1.53 tff(1898,plain,
% 1.36/1.53 (c3_1(a1574)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1743, 1896])).
% 1.36/1.53 tff(1899,plain,
% 1.36/1.53 (c1_1(a1574)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1751, 1896])).
% 1.36/1.53 tff(1900,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a1574) | c0_1(a1548) | c1_1(a1548) | (~ndr1_0) | (~c2_1(a1548)) | (~c3_1(a1574)) | (~c1_1(a1574)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a1574) | c0_1(a1548) | c1_1(a1548) | (~ndr1_0) | (~c2_1(a1548)) | (~c3_1(a1574)) | (~c1_1(a1574)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1901,plain,
% 1.36/1.53 ((hskp28 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1548) | c0_1(a1548) | (~c2_1(a1548))) <=> (hskp28 | c2_1(a1574) | c0_1(a1548) | c1_1(a1548) | (~ndr1_0) | (~c2_1(a1548)) | (~c3_1(a1574)) | (~c1_1(a1574)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1902,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1548) | c0_1(a1548) | (~c2_1(a1548)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a1574) | c0_1(a1548) | c1_1(a1548) | (~ndr1_0) | (~c2_1(a1548)) | (~c3_1(a1574)) | (~c1_1(a1574))))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1901])).
% 1.36/1.53 tff(1903,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1548) | c0_1(a1548) | (~c2_1(a1548)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a1574) | c0_1(a1548) | c1_1(a1548) | (~ndr1_0) | (~c2_1(a1548)) | (~c3_1(a1574)) | (~c1_1(a1574)))),
% 1.36/1.53 inference(transitivity,[status(thm)],[1902, 1900])).
% 1.36/1.53 tff(1904,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1548) | c0_1(a1548) | (~c2_1(a1548)))),
% 1.36/1.53 inference(quant_inst,[status(thm)],[])).
% 1.36/1.53 tff(1905,plain,
% 1.36/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a1574) | c0_1(a1548) | c1_1(a1548) | (~ndr1_0) | (~c2_1(a1548)) | (~c3_1(a1574)) | (~c1_1(a1574))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1904, 1903])).
% 1.36/1.53 tff(1906,plain,
% 1.36/1.53 (~c2_1(a1548)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1905, 319, 1835, 1899, 1898, 1897, 1888, 1882, 22])).
% 1.36/1.53 tff(1907,plain,
% 1.36/1.53 (((~hskp9) | (~c3_1(a1548))) <=> ((~hskp9) | (~c3_1(a1548)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1908,plain,
% 1.36/1.53 (((~c3_1(a1548)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a1548)))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1909,axiom,((~c3_1(a1548)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.36/1.53 tff(1910,plain,
% 1.36/1.53 ((~hskp9) | (~c3_1(a1548))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 1.36/1.53 tff(1911,plain,
% 1.36/1.53 ((~hskp9) | (~c3_1(a1548))),
% 1.36/1.53 inference(modus_ponens,[status(thm)],[1910, 1907])).
% 1.36/1.53 tff(1912,plain,
% 1.36/1.53 (~c3_1(a1548)),
% 1.36/1.53 inference(unit_resolution,[status(thm)],[1911, 1876])).
% 1.36/1.53 tff(1913,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c1_1(a1548) | c3_1(a1548) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1548))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1548) | c3_1(a1548) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1548))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1914,plain,
% 1.36/1.53 ((hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1548) | c2_1(a1548) | c1_1(a1548)) <=> (hskp15 | c1_1(a1548) | c3_1(a1548) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1548))),
% 1.36/1.53 inference(rewrite,[status(thm)],[])).
% 1.36/1.53 tff(1915,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1548) | c2_1(a1548) | c1_1(a1548))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | c1_1(a1548) | c3_1(a1548) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1548)))),
% 1.36/1.53 inference(monotonicity,[status(thm)],[1914])).
% 1.36/1.53 tff(1916,plain,
% 1.36/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1548) | c2_1(a1548) | c1_1(a1548))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1548) | c3_1(a1548) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1548))),
% 1.36/1.54 inference(transitivity,[status(thm)],[1915, 1913])).
% 1.36/1.54 tff(1917,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp15 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c3_1(a1548) | c2_1(a1548) | c1_1(a1548))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(1918,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp15 | c1_1(a1548) | c3_1(a1548) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1548)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 1.36/1.54 tff(1919,plain,
% 1.36/1.54 ($false),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1918, 319, 132, 1724, 1716, 1708, 1882, 1912, 149, 1906])).
% 1.36/1.54 tff(1920,plain,(c3_1(a1624) | hskp15 | c2_1(a1624)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.54 tff(1921,plain,
% 1.36/1.54 (c3_1(a1624)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1920, 852, 132])).
% 1.36/1.54 tff(1922,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a1624) | c2_1(a1624) | (~c3_1(a1624)) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a1624) | c2_1(a1624) | (~c3_1(a1624)) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1923,plain,
% 1.36/1.54 ((hskp4 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1624) | c0_1(a1624) | (~c3_1(a1624))) <=> (hskp4 | c0_1(a1624) | c2_1(a1624) | (~c3_1(a1624)) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1924,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1624) | c0_1(a1624) | (~c3_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a1624) | c2_1(a1624) | (~c3_1(a1624)) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[1923])).
% 1.36/1.54 tff(1925,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1624) | c0_1(a1624) | (~c3_1(a1624)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a1624) | c2_1(a1624) | (~c3_1(a1624)) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[1924, 1922])).
% 1.36/1.54 tff(1926,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1624) | c0_1(a1624) | (~c3_1(a1624)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(1927,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a1624) | c2_1(a1624) | (~c3_1(a1624)) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 1.36/1.54 tff(1928,plain,
% 1.36/1.54 (c0_1(a1624) | (~c3_1(a1624))),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1927, 319, 1735, 1724, 1716, 1708, 852, 131])).
% 1.36/1.54 tff(1929,plain,
% 1.36/1.54 (c0_1(a1624)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1928, 1921])).
% 1.36/1.54 tff(1930,plain,
% 1.36/1.54 (~c1_1(a1549)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[409, 1814])).
% 1.36/1.54 tff(1931,plain,
% 1.36/1.54 (c3_1(a1549)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[417, 1814])).
% 1.36/1.54 tff(1932,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1933,plain,
% 1.36/1.54 ((hskp15 | (~ndr1_0) | c2_1(a1624) | (~c3_1(a1624)) | (~c0_1(a1624)) | c1_1(a1549) | (~c3_1(a1549)) | (~c2_1(a1549))) <=> (hskp15 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1934,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a1624) | (~c3_1(a1624)) | (~c0_1(a1624)) | c1_1(a1549) | (~c3_1(a1549)) | (~c2_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[1933])).
% 1.36/1.54 tff(1935,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a1624) | (~c3_1(a1624)) | (~c0_1(a1624)) | c1_1(a1549) | (~c3_1(a1549)) | (~c2_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[1934, 1932])).
% 1.36/1.54 tff(1936,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a1624) | (~c3_1(a1624)) | (~c0_1(a1624)) | c1_1(a1549) | (~c3_1(a1549)) | (~c2_1(a1549)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(1937,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c2_1(a1549))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 1.36/1.54 tff(1938,plain,
% 1.36/1.54 ((~c0_1(a1624)) | (~c3_1(a1624)) | (~c2_1(a1549))),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1937, 319, 132, 1931, 852, 1930, 996])).
% 1.36/1.54 tff(1939,plain,
% 1.36/1.54 (~c2_1(a1549)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1938, 1929, 1921])).
% 1.36/1.54 tff(1940,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1941,plain,
% 1.36/1.54 ((hskp17 | (~ndr1_0) | c2_1(a1624) | (~c3_1(a1624)) | (~c0_1(a1624)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534))) <=> (hskp17 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1942,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1624) | (~c3_1(a1624)) | (~c0_1(a1624)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[1941])).
% 1.36/1.54 tff(1943,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1624) | (~c3_1(a1624)) | (~c0_1(a1624)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[1942, 1940])).
% 1.36/1.54 tff(1944,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a1624) | (~c3_1(a1624)) | (~c0_1(a1624)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(1945,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | (~c0_1(a1624)) | c2_1(a1624) | (~c3_1(a1624)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 1.36/1.54 tff(1946,plain,
% 1.36/1.54 (hskp17 | (~c0_1(a1624)) | (~c3_1(a1624))),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1945, 319, 1839, 852, 1840, 287, 1842])).
% 1.36/1.54 tff(1947,plain,
% 1.36/1.54 (hskp17),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1946, 1929, 1921])).
% 1.36/1.54 tff(1948,plain,
% 1.36/1.54 (~c1_1(a1570)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[331, 1947])).
% 1.36/1.54 tff(1949,plain,
% 1.36/1.54 (~c0_1(a1570)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[337, 1947])).
% 1.36/1.54 tff(1950,plain,
% 1.36/1.54 (c0_1(a1549)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[425, 1814])).
% 1.36/1.54 tff(1951,plain,
% 1.36/1.54 (c3_1(a1570)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[345, 1947])).
% 1.36/1.54 tff(1952,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1570) | c1_1(a1570) | c1_1(a1549) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1570)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1570) | c1_1(a1570) | c1_1(a1549) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1570)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1953,plain,
% 1.36/1.54 (((~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570))) <=> (c0_1(a1570) | c1_1(a1570) | c1_1(a1549) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1570)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1954,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1570) | c1_1(a1570) | c1_1(a1549) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1570))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[1953])).
% 1.36/1.54 tff(1955,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1570) | c1_1(a1570) | c1_1(a1549) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1570)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[1954, 1952])).
% 1.36/1.54 tff(1956,plain,
% 1.36/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c2_1(a1549) | c1_1(a1549) | (~c0_1(a1549)) | c0_1(a1570) | c1_1(a1570) | (~c3_1(a1570)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(1957,plain,
% 1.36/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1570) | c1_1(a1570) | c1_1(a1549) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1549)) | c2_1(a1549) | (~c3_1(a1570))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 1.36/1.54 tff(1958,plain,
% 1.36/1.54 ($false),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1957, 319, 1951, 1950, 1839, 1841, 1949, 1948, 1930, 277, 1842, 1939])).
% 1.36/1.54 tff(1959,plain,(c2_1(a1624) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.36/1.54 tff(1960,plain,
% 1.36/1.54 (c2_1(a1624)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1959, 132])).
% 1.36/1.54 tff(1961,plain,
% 1.36/1.54 (~hskp26),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[818, 1960])).
% 1.36/1.54 tff(1962,plain,
% 1.36/1.54 (hskp3),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[246, 1961, 1843])).
% 1.36/1.54 tff(1963,plain,
% 1.36/1.54 (~c2_1(a1536)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[668, 1962])).
% 1.36/1.54 tff(1964,plain,
% 1.36/1.54 (~c0_1(a1536)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[674, 1962])).
% 1.36/1.54 tff(1965,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c3_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c3_1(a1536)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1966,plain,
% 1.36/1.54 ((hskp4 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1536) | c0_1(a1536) | (~c3_1(a1536))) <=> (hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c3_1(a1536)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1967,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1536) | c0_1(a1536) | (~c3_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c3_1(a1536))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[1966])).
% 1.36/1.54 tff(1968,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1536) | c0_1(a1536) | (~c3_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c3_1(a1536)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[1967, 1965])).
% 1.36/1.54 tff(1969,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | c2_1(a1536) | c0_1(a1536) | (~c3_1(a1536)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(1970,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c3_1(a1536))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 1.36/1.54 tff(1971,plain,
% 1.36/1.54 (~c3_1(a1536)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1970, 319, 1735, 1724, 1716, 1708, 1964, 1963, 131])).
% 1.36/1.54 tff(1972,plain,
% 1.36/1.54 (c1_1(a1536)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[684, 1962])).
% 1.36/1.54 tff(1973,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1536)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1974,plain,
% 1.36/1.54 ((hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536))) <=> (hskp9 | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1536)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1975,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1536))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[1974])).
% 1.36/1.54 tff(1976,plain,
% 1.36/1.54 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1536)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[1975, 1973])).
% 1.36/1.54 tff(1977,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536)))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(1978,plain,
% 1.36/1.54 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | (~c1_1(a1536))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 1.36/1.54 tff(1979,plain,
% 1.36/1.54 (hskp9),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1978, 319, 1972, 1841, 1964, 1963, 1840, 1868, 1842])).
% 1.36/1.54 tff(1980,plain,
% 1.36/1.54 (~c3_1(a1548)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1911, 1979])).
% 1.36/1.54 tff(1981,plain,
% 1.36/1.54 (~c0_1(a1548)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1887, 1979])).
% 1.36/1.54 tff(1982,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1548) | c3_1(a1548) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1548)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1548) | c3_1(a1548) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1548)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1983,plain,
% 1.36/1.54 (((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1548) | c0_1(a1548) | (~c2_1(a1548)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536)) <=> (c0_1(a1548) | c3_1(a1548) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1548)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1984,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1548) | c0_1(a1548) | (~c2_1(a1548)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1548) | c3_1(a1548) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1548))))),
% 1.36/1.54 inference(monotonicity,[status(thm)],[1983])).
% 1.36/1.54 tff(1985,plain,
% 1.36/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1548) | c0_1(a1548) | (~c2_1(a1548)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1548) | c3_1(a1548) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1548)))),
% 1.36/1.54 inference(transitivity,[status(thm)],[1984, 1982])).
% 1.36/1.54 tff(1986,plain,
% 1.36/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1548) | c0_1(a1548) | (~c2_1(a1548)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))),
% 1.36/1.54 inference(quant_inst,[status(thm)],[])).
% 1.36/1.54 tff(1987,plain,
% 1.36/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1548) | c3_1(a1548) | c0_1(a1536) | c2_1(a1536) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1536) | (~c2_1(a1548))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 1.36/1.54 tff(1988,plain,
% 1.36/1.54 (~c2_1(a1548)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1987, 319, 1839, 1981, 1980, 1964, 1963, 1840, 714, 1842, 1971])).
% 1.36/1.54 tff(1989,plain,
% 1.36/1.54 (~c1_1(a1548)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1881, 1979])).
% 1.36/1.54 tff(1990,plain,
% 1.36/1.54 ($false),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1918, 319, 132, 1724, 1716, 1708, 1989, 1980, 149, 1988])).
% 1.36/1.54 tff(1991,plain,(hskp15), inference(lemma,lemma(discharge,[]))).
% 1.36/1.54 tff(1992,plain,
% 1.36/1.54 (((~hskp15) | (~c2_1(a1565))) <=> ((~hskp15) | (~c2_1(a1565)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1993,plain,
% 1.36/1.54 (((~c2_1(a1565)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a1565)))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1994,axiom,((~c2_1(a1565)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.36/1.54 tff(1995,plain,
% 1.36/1.54 ((~hskp15) | (~c2_1(a1565))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 1.36/1.54 tff(1996,plain,
% 1.36/1.54 ((~hskp15) | (~c2_1(a1565))),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1995, 1992])).
% 1.36/1.54 tff(1997,plain,
% 1.36/1.54 (~c2_1(a1565)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[1996, 1991])).
% 1.36/1.54 tff(1998,plain,
% 1.36/1.54 (((~hskp15) | c1_1(a1565)) <=> ((~hskp15) | c1_1(a1565))),
% 1.36/1.54 inference(rewrite,[status(thm)],[])).
% 1.36/1.54 tff(1999,axiom,((~hskp15) | c1_1(a1565)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.36/1.54 tff(2000,plain,
% 1.36/1.54 ((~hskp15) | c1_1(a1565)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 1.36/1.54 tff(2001,plain,
% 1.36/1.54 ((~hskp15) | c1_1(a1565)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[2000, 1998])).
% 1.36/1.54 tff(2002,plain,
% 1.36/1.54 ((~hskp15) | c1_1(a1565)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[2001, 1998])).
% 1.36/1.54 tff(2003,plain,
% 1.36/1.54 ((~hskp15) | c1_1(a1565)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[2002, 1998])).
% 1.36/1.54 tff(2004,plain,
% 1.36/1.54 ((~hskp15) | c1_1(a1565)),
% 1.36/1.54 inference(modus_ponens,[status(thm)],[2003, 1998])).
% 1.36/1.54 tff(2005,plain,
% 1.36/1.54 (c1_1(a1565)),
% 1.36/1.54 inference(unit_resolution,[status(thm)],[2004, 1991])).
% 1.36/1.54 tff(2006,plain,
% 1.36/1.54 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c2_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1565)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c2_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1565)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(2007,plain,
% 1.37/1.54 ((hskp10 | hskp4 | (~ndr1_0) | c2_1(a1565) | c0_1(a1565) | (~c1_1(a1565))) <=> (hskp10 | hskp4 | c2_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1565)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(2008,plain,
% 1.37/1.54 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1565) | c0_1(a1565) | (~c1_1(a1565)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | c2_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1565))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[2007])).
% 1.37/1.54 tff(2009,plain,
% 1.37/1.54 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1565) | c0_1(a1565) | (~c1_1(a1565)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c2_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1565)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[2008, 2006])).
% 1.37/1.54 tff(2010,plain,
% 1.37/1.54 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c2_1(a1565) | c0_1(a1565) | (~c1_1(a1565)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(2011,plain,
% 1.37/1.54 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp10 | hskp4 | c2_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1565))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 1.37/1.54 tff(2012,plain,
% 1.37/1.54 (hskp10 | hskp4 | c0_1(a1565)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[2011, 319, 2005, 1997, 121])).
% 1.37/1.54 tff(2013,plain,
% 1.37/1.54 (c0_1(a1565)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[2012, 11, 36])).
% 1.37/1.54 tff(2014,assumption,(hskp3), introduced(assumption)).
% 1.37/1.54 tff(2015,plain,
% 1.37/1.54 (~c2_1(a1536)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[668, 2014])).
% 1.37/1.54 tff(2016,plain,
% 1.37/1.54 (~c0_1(a1536)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[674, 2014])).
% 1.37/1.54 tff(2017,plain,
% 1.37/1.54 (c1_1(a1536)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[684, 2014])).
% 1.37/1.54 tff(2018,plain,
% 1.37/1.54 ($false),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[732, 319, 11, 36, 2017, 2016, 2015, 121])).
% 1.37/1.54 tff(2019,plain,((~hskp3) | hskp10 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.37/1.54 tff(2020,plain,
% 1.37/1.54 (~hskp3),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[2019, 11, 36])).
% 1.37/1.54 tff(2021,plain,
% 1.37/1.54 (hskp12),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1058, 2020, 11])).
% 1.37/1.54 tff(2022,plain,
% 1.37/1.54 (~c0_1(a1554)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1064, 2021])).
% 1.37/1.54 tff(2023,plain,
% 1.37/1.54 (c2_1(a1554)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1072, 2021])).
% 1.37/1.54 tff(2024,plain,
% 1.37/1.54 (c1_1(a1554)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1080, 2021])).
% 1.37/1.54 tff(2025,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1565) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1565)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(2026,plain,
% 1.37/1.54 ((hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554))) <=> (hskp10 | c2_1(a1565) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(2027,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1565) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1565)) | (~c1_1(a1565))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[2026])).
% 1.37/1.55 tff(2028,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[2027, 2025])).
% 1.37/1.55 tff(2029,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(2030,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1565)) | (~c1_1(a1565))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2029, 2028])).
% 1.37/1.55 tff(2031,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2030, 319, 11, 2005, 2024, 2023, 1997, 2022, 1121, 2013])).
% 1.37/1.55 tff(2032,plain,(hskp10 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(2033,plain,
% 1.37/1.55 (hskp10),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2032, 36])).
% 1.37/1.55 tff(2034,plain,
% 1.37/1.55 (~c1_1(a1549)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[409, 2033])).
% 1.37/1.55 tff(2035,plain,
% 1.37/1.55 (~hskp1),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1821, 873, 874, 882, 2033])).
% 1.37/1.55 tff(2036,plain,
% 1.37/1.55 (hskp14),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[58, 2035, 36])).
% 1.37/1.55 tff(2037,plain,
% 1.37/1.55 (~c2_1(a1558)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[64, 2036])).
% 1.37/1.55 tff(2038,plain,
% 1.37/1.55 (c3_1(a1549)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[417, 2033])).
% 1.37/1.55 tff(2039,plain,
% 1.37/1.55 (c0_1(a1549)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[425, 2033])).
% 1.37/1.55 tff(2040,plain,
% 1.37/1.55 (c1_1(a1558)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[72, 2036])).
% 1.37/1.55 tff(2041,plain,
% 1.37/1.55 (c0_1(a1558)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[80, 2036])).
% 1.37/1.55 tff(2042,plain,
% 1.37/1.55 (hskp22),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1304, 319, 2041, 2040, 2039, 2038, 2037, 2034, 111])).
% 1.37/1.55 tff(2043,plain,
% 1.37/1.55 (~c3_1(a1581)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1310, 2042])).
% 1.37/1.55 tff(2044,plain,
% 1.37/1.55 (~c1_1(a1581)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1316, 2042])).
% 1.37/1.55 tff(2045,plain,
% 1.37/1.55 (c2_1(a1581)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1324, 2042])).
% 1.37/1.55 tff(2046,plain,
% 1.37/1.55 (~c0_1(a1581)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1342, 319, 874, 873, 882, 2045, 2044, 2043, 101])).
% 1.37/1.55 tff(2047,assumption,(~c0_1(a1542)), introduced(assumption)).
% 1.37/1.55 tff(2048,assumption,(~c1_1(a1549)), introduced(assumption)).
% 1.37/1.55 tff(2049,assumption,(c3_1(a1549)), introduced(assumption)).
% 1.37/1.55 tff(2050,assumption,(c0_1(a1549)), introduced(assumption)).
% 1.37/1.55 tff(2051,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1500, 319, 1537, 1536, 1535, 2050, 2049, 2048, 382, 2047])).
% 1.37/1.55 tff(2052,plain,(c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1549)) | (~c3_1(a1549)) | c1_1(a1549)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(2053,plain,
% 1.37/1.55 (c0_1(a1542)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2052, 874, 873, 882, 2039, 2038, 2034])).
% 1.37/1.55 tff(2054,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2055,plain,
% 1.37/1.55 (((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c2_1(a1558) | (~c3_1(a1558)) | (~c1_1(a1558))) <=> (c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2056,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c2_1(a1558) | (~c3_1(a1558)) | (~c1_1(a1558)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[2055])).
% 1.37/1.55 tff(2057,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c2_1(a1558) | (~c3_1(a1558)) | (~c1_1(a1558)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[2056, 2054])).
% 1.37/1.55 tff(2058,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c2_1(a1558) | (~c3_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(2059,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1558) | (~ndr1_0) | (~c3_1(a1558)) | (~c1_1(a1558)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2058, 2057])).
% 1.37/1.55 tff(2060,plain,
% 1.37/1.55 ((~c3_1(a1558)) | (~c0_1(a1542))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2059, 319, 874, 873, 882, 2040, 2037, 508])).
% 1.37/1.55 tff(2061,plain,
% 1.37/1.55 (~c3_1(a1558)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2060, 2053])).
% 1.37/1.55 tff(2062,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | c0_1(a1581))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | c0_1(a1581))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2063,plain,
% 1.37/1.55 ((hskp5 | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c3_1(a1581) | c1_1(a1581) | c0_1(a1581)) <=> (hskp5 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | c0_1(a1581))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2064,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c3_1(a1581) | c1_1(a1581) | c0_1(a1581))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | c0_1(a1581)))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[2063])).
% 1.37/1.55 tff(2065,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c3_1(a1581) | c1_1(a1581) | c0_1(a1581))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | c0_1(a1581))),
% 1.37/1.55 inference(transitivity,[status(thm)],[2064, 2062])).
% 1.37/1.55 tff(2066,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c3_1(a1581) | c1_1(a1581) | c0_1(a1581))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(2067,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)) | c0_1(a1581)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 1.37/1.55 tff(2068,plain,
% 1.37/1.55 (hskp5),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2067, 319, 2041, 2040, 2044, 2043, 462, 2061, 2046])).
% 1.37/1.55 tff(2069,plain,
% 1.37/1.55 (~c0_1(a1539)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[474, 2068])).
% 1.37/1.55 tff(2070,plain,
% 1.37/1.55 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(2071,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[2070])).
% 1.37/1.55 tff(2072,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2073,plain,
% 1.37/1.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp3))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(2074,plain,
% 1.37/1.55 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[2073])).
% 1.37/1.55 tff(2075,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.37/1.55 tff(2076,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 1.37/1.55 tff(2077,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2076, 2072])).
% 1.37/1.55 tff(2078,plain,(
% 1.37/1.55 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.55 inference(skolemize,[status(sab)],[2077])).
% 1.37/1.55 tff(2079,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2078, 2071])).
% 1.37/1.55 tff(2080,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2081,plain,
% 1.37/1.55 ((hskp3 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1581) | c1_1(a1581) | c0_1(a1581)) <=> (hskp3 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2082,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1581) | c1_1(a1581) | c0_1(a1581))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[2081])).
% 1.37/1.55 tff(2083,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1581) | c1_1(a1581) | c0_1(a1581))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[2082, 2080])).
% 1.37/1.55 tff(2084,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp3 | (~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c3_1(a1581) | c1_1(a1581) | c0_1(a1581))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(2085,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp3 | c1_1(a1581) | c3_1(a1581) | (~ndr1_0) | c0_1(a1581) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 1.37/1.55 tff(2086,plain,
% 1.37/1.55 (hskp3 | (~c0_1(a1542))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2085, 319, 874, 882, 2044, 2043, 2079, 2046])).
% 1.37/1.55 tff(2087,plain,
% 1.37/1.55 (hskp3),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2086, 2053])).
% 1.37/1.55 tff(2088,plain,
% 1.37/1.55 (~c2_1(a1536)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[668, 2087])).
% 1.37/1.55 tff(2089,plain,
% 1.37/1.55 (~c0_1(a1536)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[674, 2087])).
% 1.37/1.55 tff(2090,plain,
% 1.37/1.55 (c1_1(a1536)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[684, 2087])).
% 1.37/1.55 tff(2091,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c1_1(a1581) | c3_1(a1581) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c2_1(a1581)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c1_1(a1581) | c3_1(a1581) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c2_1(a1581)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2092,plain,
% 1.37/1.55 ((hskp9 | (~ndr1_0) | c1_1(a1581) | c3_1(a1581) | (~c2_1(a1581)) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536))) <=> (hskp9 | c1_1(a1581) | c3_1(a1581) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c2_1(a1581)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2093,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1581) | c3_1(a1581) | (~c2_1(a1581)) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c1_1(a1581) | c3_1(a1581) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c2_1(a1581))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[2092])).
% 1.37/1.55 tff(2094,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1581) | c3_1(a1581) | (~c2_1(a1581)) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c1_1(a1581) | c3_1(a1581) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c2_1(a1581)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[2093, 2091])).
% 1.37/1.55 tff(2095,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1581) | c3_1(a1581) | (~c2_1(a1581)) | c2_1(a1536) | c0_1(a1536) | (~c1_1(a1536)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(2096,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c1_1(a1581) | c3_1(a1581) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c2_1(a1581))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 1.37/1.55 tff(2097,plain,
% 1.37/1.55 (hskp9),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2096, 319, 2045, 2090, 2044, 2043, 2089, 2088, 1868])).
% 1.37/1.55 tff(2098,plain,
% 1.37/1.55 (~c3_1(a1548)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1911, 2097])).
% 1.37/1.55 tff(2099,plain,
% 1.37/1.55 (~c1_1(a1548)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1881, 2097])).
% 1.37/1.55 tff(2100,plain,
% 1.37/1.55 (~c0_1(a1548)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1887, 2097])).
% 1.37/1.55 tff(2101,plain,
% 1.37/1.55 (c3_1(a1539)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[482, 2068])).
% 1.37/1.55 tff(2102,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a1548) | c1_1(a1548) | c3_1(a1548) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a1548) | c1_1(a1548) | c3_1(a1548) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2103,plain,
% 1.37/1.55 ((hskp4 | (~ndr1_0) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c3_1(a1548) | c1_1(a1548) | c0_1(a1548)) <=> (hskp4 | c0_1(a1548) | c1_1(a1548) | c3_1(a1548) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2104,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c3_1(a1548) | c1_1(a1548) | c0_1(a1548))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a1548) | c1_1(a1548) | c3_1(a1548) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[2103])).
% 1.37/1.55 tff(2105,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c3_1(a1548) | c1_1(a1548) | c0_1(a1548))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a1548) | c1_1(a1548) | c3_1(a1548) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[2104, 2102])).
% 1.37/1.55 tff(2106,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a1539) | (~c3_1(a1539)) | (~c2_1(a1539)) | c3_1(a1548) | c1_1(a1548) | c0_1(a1548))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(2107,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a1548) | c1_1(a1548) | c3_1(a1548) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c2_1(a1539))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 1.37/1.55 tff(2108,plain,
% 1.37/1.55 (~c2_1(a1539)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2107, 319, 36, 2101, 2100, 2099, 2098, 2069, 91])).
% 1.37/1.55 tff(2109,plain,
% 1.37/1.55 (c1_1(a1539)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[490, 2068])).
% 1.37/1.55 tff(2110,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2111,plain,
% 1.37/1.55 (((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c2_1(a1536) | (~c3_1(a1536)) | (~c1_1(a1536))) <=> (c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2112,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c2_1(a1536) | (~c3_1(a1536)) | (~c1_1(a1536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[2111])).
% 1.37/1.55 tff(2113,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c2_1(a1536) | (~c3_1(a1536)) | (~c1_1(a1536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[2112, 2110])).
% 1.37/1.55 tff(2114,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c2_1(a1536) | (~c3_1(a1536)) | (~c1_1(a1536)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(2115,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1536) | (~ndr1_0) | (~c1_1(a1536)) | (~c3_1(a1536)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[2114, 2113])).
% 1.37/1.55 tff(2116,plain,
% 1.37/1.55 (~c3_1(a1536)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2115, 319, 874, 873, 882, 2090, 2088, 508, 2053])).
% 1.37/1.55 tff(2117,plain,
% 1.37/1.55 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(2118,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[2117])).
% 1.37/1.55 tff(2119,plain,
% 1.37/1.55 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(2120,plain,
% 1.37/1.55 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp29))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.37/1.56 inference(bind,[status(th)],[])).
% 1.37/1.56 tff(2121,plain,
% 1.37/1.56 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(quant_intro,[status(thm)],[2120])).
% 1.37/1.56 tff(2122,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.37/1.56 tff(2123,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.37/1.56 tff(2124,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2123, 2119])).
% 1.37/1.56 tff(2125,plain,(
% 1.37/1.56 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(skolemize,[status(sab)],[2124])).
% 1.37/1.56 tff(2126,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2125, 2118])).
% 1.37/1.56 tff(2127,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | c0_1(a1539) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c3_1(a1539)) | (~c1_1(a1539)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c0_1(a1539) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2128,plain,
% 1.37/1.56 ((hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536)) <=> (hskp29 | c0_1(a1539) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2129,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | c0_1(a1539) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c3_1(a1539)) | (~c1_1(a1539))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[2128])).
% 1.37/1.56 tff(2130,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c0_1(a1539) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[2129, 2127])).
% 1.37/1.56 tff(2131,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(2132,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c0_1(a1539) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c3_1(a1539)) | (~c1_1(a1539))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2131, 2130])).
% 1.37/1.56 tff(2133,plain,
% 1.37/1.56 (hskp29),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2132, 319, 2109, 2101, 2069, 2089, 2088, 2126, 2116])).
% 1.37/1.56 tff(2134,plain,
% 1.37/1.56 (((~hskp29) | c2_1(a1544)) <=> ((~hskp29) | c2_1(a1544))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2135,axiom,((~hskp29) | c2_1(a1544)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.37/1.56 tff(2136,plain,
% 1.37/1.56 ((~hskp29) | c2_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 1.37/1.56 tff(2137,plain,
% 1.37/1.56 ((~hskp29) | c2_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2136, 2134])).
% 1.37/1.56 tff(2138,plain,
% 1.37/1.56 ((~hskp29) | c2_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2137, 2134])).
% 1.37/1.56 tff(2139,plain,
% 1.37/1.56 ((~hskp29) | c2_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2138, 2134])).
% 1.37/1.56 tff(2140,plain,
% 1.37/1.56 ((~hskp29) | c2_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2139, 2134])).
% 1.37/1.56 tff(2141,plain,
% 1.37/1.56 (c2_1(a1544)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2140, 2133])).
% 1.37/1.56 tff(2142,plain,
% 1.37/1.56 (((~hskp29) | c1_1(a1544)) <=> ((~hskp29) | c1_1(a1544))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2143,axiom,((~hskp29) | c1_1(a1544)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.37/1.56 tff(2144,plain,
% 1.37/1.56 ((~hskp29) | c1_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2143, 2142])).
% 1.37/1.56 tff(2145,plain,
% 1.37/1.56 ((~hskp29) | c1_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2144, 2142])).
% 1.37/1.56 tff(2146,plain,
% 1.37/1.56 ((~hskp29) | c1_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2145, 2142])).
% 1.37/1.56 tff(2147,plain,
% 1.37/1.56 ((~hskp29) | c1_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2146, 2142])).
% 1.37/1.56 tff(2148,plain,
% 1.37/1.56 ((~hskp29) | c1_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2147, 2142])).
% 1.37/1.56 tff(2149,plain,
% 1.37/1.56 (c1_1(a1544)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2148, 2133])).
% 1.37/1.56 tff(2150,plain,
% 1.37/1.56 (((~hskp29) | c0_1(a1544)) <=> ((~hskp29) | c0_1(a1544))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2151,axiom,((~hskp29) | c0_1(a1544)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.37/1.56 tff(2152,plain,
% 1.37/1.56 ((~hskp29) | c0_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 1.37/1.56 tff(2153,plain,
% 1.37/1.56 ((~hskp29) | c0_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2152, 2150])).
% 1.37/1.56 tff(2154,plain,
% 1.37/1.56 ((~hskp29) | c0_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2153, 2150])).
% 1.37/1.56 tff(2155,plain,
% 1.37/1.56 ((~hskp29) | c0_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2154, 2150])).
% 1.37/1.56 tff(2156,plain,
% 1.37/1.56 ((~hskp29) | c0_1(a1544)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2155, 2150])).
% 1.37/1.56 tff(2157,plain,
% 1.37/1.56 (c0_1(a1544)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2156, 2133])).
% 1.37/1.56 tff(2158,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2159,plain,
% 1.37/1.56 (((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c2_1(a1539) | (~c3_1(a1539)) | (~c1_1(a1539))) <=> ((~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2160,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c2_1(a1539) | (~c3_1(a1539)) | (~c1_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[2159])).
% 1.37/1.56 tff(2161,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c2_1(a1539) | (~c3_1(a1539)) | (~c1_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[2160, 2158])).
% 1.37/1.56 tff(2162,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c2_1(a1539) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(2163,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c2_1(a1542)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 1.37/1.56 tff(2164,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2163, 319, 2157, 2149, 2141, 874, 873, 882, 2109, 2101, 508, 2108])).
% 1.37/1.56 tff(2165,plain,((~hskp28) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(2166,plain,
% 1.37/1.56 (~hskp28),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2165, 36])).
% 1.37/1.56 tff(2167,assumption,(hskp5), introduced(assumption)).
% 1.37/1.56 tff(2168,plain,
% 1.37/1.56 (~c0_1(a1539)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[474, 2167])).
% 1.37/1.56 tff(2169,plain,
% 1.37/1.56 (c3_1(a1539)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[482, 2167])).
% 1.37/1.56 tff(2170,plain,
% 1.37/1.56 (c1_1(a1539)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[490, 2167])).
% 1.37/1.56 tff(2171,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1156, 319, 12, 47, 2170, 2169, 2168, 1150])).
% 1.37/1.56 tff(2172,plain,((~hskp5) | hskp28 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(2173,plain,
% 1.37/1.56 (~hskp5),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2172, 47, 2166])).
% 1.37/1.56 tff(2174,plain,
% 1.37/1.56 (~c3_1(a1558)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1519, 319, 2173, 81, 73, 65, 46])).
% 1.37/1.56 tff(2175,plain,
% 1.37/1.56 (hskp22),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1304, 319, 81, 73, 2039, 2038, 65, 2034, 111])).
% 1.37/1.56 tff(2176,plain,
% 1.37/1.56 (~c3_1(a1581)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1310, 2175])).
% 1.37/1.56 tff(2177,plain,
% 1.37/1.56 (~c1_1(a1581)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1316, 2175])).
% 1.37/1.56 tff(2178,plain,
% 1.37/1.56 (c0_1(a1581)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2067, 319, 2173, 81, 73, 2177, 2176, 462, 2174])).
% 1.37/1.56 tff(2179,plain,
% 1.37/1.56 (((~hskp15) | (~c3_1(a1565))) <=> ((~hskp15) | (~c3_1(a1565)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2180,plain,
% 1.37/1.56 (((~c3_1(a1565)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a1565)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2181,axiom,((~c3_1(a1565)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.37/1.56 tff(2182,plain,
% 1.37/1.56 ((~hskp15) | (~c3_1(a1565))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 1.37/1.56 tff(2183,plain,
% 1.37/1.56 ((~hskp15) | (~c3_1(a1565))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2182, 2179])).
% 1.37/1.56 tff(2184,plain,
% 1.37/1.56 (~c3_1(a1565)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2183, 1991])).
% 1.37/1.56 tff(2185,plain,
% 1.37/1.56 (c2_1(a1581)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1324, 2175])).
% 1.37/1.56 tff(2186,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c1_1(a1581) | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c1_1(a1581) | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2187,plain,
% 1.37/1.56 ((hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581))) <=> (hskp20 | c1_1(a1581) | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2188,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c1_1(a1581) | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[2187])).
% 1.37/1.56 tff(2189,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c1_1(a1581) | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[2188, 2186])).
% 1.37/1.56 tff(2190,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(2191,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c1_1(a1581) | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 1.37/1.56 tff(2192,plain,
% 1.37/1.56 (hskp20),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2191, 319, 2185, 2005, 2177, 1997, 2184, 1804, 2178])).
% 1.37/1.56 tff(2193,plain,
% 1.37/1.56 (~c2_1(a1574)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1764, 2192])).
% 1.37/1.56 tff(2194,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1581) | c3_1(a1581) | c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565) | (~c0_1(a1581)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1581) | c3_1(a1581) | c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565) | (~c0_1(a1581)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2195,plain,
% 1.37/1.56 (((~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)) | c3_1(a1581) | c1_1(a1581) | (~c0_1(a1581)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (c1_1(a1581) | c3_1(a1581) | c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565) | (~c0_1(a1581)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2196,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)) | c3_1(a1581) | c1_1(a1581) | (~c0_1(a1581)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1581) | c3_1(a1581) | c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565) | (~c0_1(a1581))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[2195])).
% 1.37/1.56 tff(2197,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)) | c3_1(a1581) | c1_1(a1581) | (~c0_1(a1581)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1581) | c3_1(a1581) | c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565) | (~c0_1(a1581)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[2196, 2194])).
% 1.37/1.56 tff(2198,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)) | c3_1(a1581) | c1_1(a1581) | (~c0_1(a1581)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(2199,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1581) | c3_1(a1581) | c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | (~ndr1_0) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565) | (~c0_1(a1581))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 1.37/1.56 tff(2200,plain,
% 1.37/1.56 (c0_1(a1565)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2199, 319, 81, 2177, 2176, 1997, 2184, 65, 35, 2174, 2178])).
% 1.37/1.56 tff(2201,plain,
% 1.37/1.56 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.37/1.56 inference(bind,[status(th)],[])).
% 1.37/1.56 tff(2202,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.37/1.56 inference(quant_intro,[status(thm)],[2201])).
% 1.37/1.56 tff(2203,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2204,plain,
% 1.37/1.56 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(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)) | (~c0_1(V)) | (~c2_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))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~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)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.37/1.56 inference(bind,[status(th)],[])).
% 1.37/1.56 tff(2205,plain,
% 1.37/1.56 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.37/1.56 inference(quant_intro,[status(thm)],[2204])).
% 1.37/1.56 tff(2206,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.37/1.56 tff(2207,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 1.37/1.56 tff(2208,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2207, 2203])).
% 1.37/1.56 tff(2209,plain,(
% 1.37/1.56 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.37/1.56 inference(skolemize,[status(sab)],[2208])).
% 1.37/1.56 tff(2210,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2209, 2202])).
% 1.37/1.56 tff(2211,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | c1_1(a1581) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp21 | c1_1(a1581) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2212,plain,
% 1.37/1.56 ((hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581))) <=> (hskp21 | c1_1(a1581) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2213,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | c1_1(a1581) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[2212])).
% 1.37/1.56 tff(2214,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp21 | c1_1(a1581) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[2213, 2211])).
% 1.37/1.56 tff(2215,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1581) | (~c0_1(a1581)) | (~c2_1(a1581)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(2216,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp21 | c1_1(a1581) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1581)) | (~c2_1(a1581))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 1.37/1.56 tff(2217,plain,
% 1.37/1.56 (hskp21),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2216, 319, 2185, 2005, 2177, 1997, 2210, 2200, 2178])).
% 1.37/1.56 tff(2218,plain,
% 1.37/1.56 (~c1_1(a1575)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[438, 2217])).
% 1.37/1.56 tff(2219,plain,
% 1.37/1.56 (~c0_1(a1575)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[444, 2217])).
% 1.37/1.56 tff(2220,plain,
% 1.37/1.56 (c3_1(a1574)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1743, 2192])).
% 1.37/1.56 tff(2221,plain,
% 1.37/1.56 (c1_1(a1574)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1751, 2192])).
% 1.37/1.56 tff(2222,plain,
% 1.37/1.56 (c2_1(a1575)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[515, 2217])).
% 1.37/1.56 tff(2223,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c0_1(a1575) | c1_1(a1575) | c2_1(a1574) | (~ndr1_0) | (~c3_1(a1574)) | (~c1_1(a1574)) | (~c2_1(a1575)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c0_1(a1575) | c1_1(a1575) | c2_1(a1574) | (~ndr1_0) | (~c3_1(a1574)) | (~c1_1(a1574)) | (~c2_1(a1575)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2224,plain,
% 1.37/1.56 ((hskp28 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575))) <=> (hskp28 | c0_1(a1575) | c1_1(a1575) | c2_1(a1574) | (~ndr1_0) | (~c3_1(a1574)) | (~c1_1(a1574)) | (~c2_1(a1575)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2225,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c0_1(a1575) | c1_1(a1575) | c2_1(a1574) | (~ndr1_0) | (~c3_1(a1574)) | (~c1_1(a1574)) | (~c2_1(a1575))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[2224])).
% 1.37/1.56 tff(2226,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c0_1(a1575) | c1_1(a1575) | c2_1(a1574) | (~ndr1_0) | (~c3_1(a1574)) | (~c1_1(a1574)) | (~c2_1(a1575)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[2225, 2223])).
% 1.37/1.56 tff(2227,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(2228,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c0_1(a1575) | c1_1(a1575) | c2_1(a1574) | (~ndr1_0) | (~c3_1(a1574)) | (~c1_1(a1574)) | (~c2_1(a1575))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 1.37/1.56 tff(2229,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2228, 319, 2166, 2222, 2221, 2220, 2219, 2218, 2193, 22])).
% 1.37/1.56 tff(2230,plain,(hskp1 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(2231,plain,
% 1.37/1.56 (hskp1),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[2230, 36])).
% 1.37/1.56 tff(2232,plain,
% 1.37/1.56 (c0_1(a1534)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[236, 2231])).
% 1.37/1.56 tff(2233,plain,
% 1.37/1.56 (~c3_1(a1534)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[228, 2231])).
% 1.37/1.56 tff(2234,plain,
% 1.37/1.56 (c2_1(a1534)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[222, 2231])).
% 1.37/1.56 tff(2235,plain,
% 1.37/1.56 (~c1_1(a1534)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[555, 2234, 2033, 2233, 2232])).
% 1.37/1.56 tff(2236,plain,
% 1.37/1.56 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.37/1.56 inference(bind,[status(th)],[])).
% 1.37/1.56 tff(2237,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.56 inference(quant_intro,[status(thm)],[2236])).
% 1.37/1.56 tff(2238,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(2239,plain,
% 1.37/1.56 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_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)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_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)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(2240,plain,
% 1.37/1.57 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[2239])).
% 1.37/1.57 tff(2241,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.37/1.57 tff(2242,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.37/1.57 tff(2243,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2242, 2238])).
% 1.37/1.57 tff(2244,plain,(
% 1.37/1.57 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.57 inference(skolemize,[status(sab)],[2243])).
% 1.37/1.57 tff(2245,plain,
% 1.37/1.57 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2244, 2237])).
% 1.37/1.57 tff(2246,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1565)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2247,plain,
% 1.37/1.57 ((hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534))) <=> (hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1565)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2248,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1565))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[2247])).
% 1.37/1.57 tff(2249,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1565)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[2248, 2246])).
% 1.37/1.57 tff(2250,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(2251,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c1_1(a1565))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 1.37/1.57 tff(2252,plain,
% 1.37/1.57 (hskp20),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2251, 319, 2005, 2232, 2234, 1997, 2184, 1804, 2235])).
% 1.37/1.57 tff(2253,plain,
% 1.37/1.57 (~c2_1(a1574)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1764, 2252])).
% 1.37/1.57 tff(2254,plain,
% 1.37/1.57 (c3_1(a1574)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1743, 2252])).
% 1.37/1.57 tff(2255,plain,
% 1.37/1.57 (c1_1(a1574)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1751, 2252])).
% 1.37/1.57 tff(2256,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | c2_1(a1574) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c3_1(a1574)) | (~c1_1(a1574)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp14 | c2_1(a1574) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c3_1(a1574)) | (~c1_1(a1574)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2257,plain,
% 1.37/1.57 ((hskp14 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549))) <=> (hskp14 | c2_1(a1574) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c3_1(a1574)) | (~c1_1(a1574)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2258,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | c2_1(a1574) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c3_1(a1574)) | (~c1_1(a1574))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[2257])).
% 1.37/1.57 tff(2259,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp14 | c2_1(a1574) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c3_1(a1574)) | (~c1_1(a1574)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[2258, 2256])).
% 1.37/1.57 tff(2260,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1574) | (~c1_1(a1574)) | (~c3_1(a1574)) | c1_1(a1549) | (~c3_1(a1549)) | (~c0_1(a1549)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(2261,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp14 | c2_1(a1574) | c1_1(a1549) | (~ndr1_0) | (~c3_1(a1549)) | (~c0_1(a1549)) | (~c3_1(a1574)) | (~c1_1(a1574))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2260, 2259])).
% 1.37/1.57 tff(2262,plain,
% 1.37/1.57 (hskp14),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2261, 319, 2255, 2254, 2039, 2038, 2253, 2034, 2245])).
% 1.37/1.57 tff(2263,plain,
% 1.37/1.57 (c1_1(a1558)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[72, 2262])).
% 1.37/1.57 tff(2264,plain,
% 1.37/1.57 (c0_1(a1558)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[80, 2262])).
% 1.37/1.57 tff(2265,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2266,plain,
% 1.37/1.57 (((~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534))) <=> (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2267,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[2266])).
% 1.37/1.57 tff(2268,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[2267, 2265])).
% 1.37/1.57 tff(2269,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1558)) | (~c3_1(a1558)) | (~c0_1(a1558)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(2270,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1558)) | (~c0_1(a1558)) | (~c1_1(a1558))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2269, 2268])).
% 1.37/1.57 tff(2271,plain,
% 1.37/1.57 (~c3_1(a1558)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2270, 319, 2264, 2263, 2232, 2234, 2233, 363, 2235])).
% 1.37/1.57 tff(2272,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2273,plain,
% 1.37/1.57 (((~ndr1_0) | (~c1_1(a1574)) | (~c3_1(a1574)) | (~c0_1(a1574)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534))) <=> (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2274,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1574)) | (~c3_1(a1574)) | (~c0_1(a1574)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[2273])).
% 1.37/1.57 tff(2275,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1574)) | (~c3_1(a1574)) | (~c0_1(a1574)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[2274, 2272])).
% 1.37/1.57 tff(2276,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1574)) | (~c3_1(a1574)) | (~c0_1(a1574)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(2277,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1574)) | (~c0_1(a1574)) | (~c1_1(a1574))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2276, 2275])).
% 1.37/1.57 tff(2278,plain,
% 1.37/1.57 (~c0_1(a1574)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2277, 319, 2255, 2254, 2232, 2234, 2233, 363, 2235])).
% 1.37/1.57 tff(2279,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1574) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | c0_1(a1574) | (~c1_1(a1574)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1574) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | c0_1(a1574) | (~c1_1(a1574)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2280,plain,
% 1.37/1.57 ((hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1574) | c0_1(a1574) | (~c1_1(a1574))) <=> (hskp9 | c2_1(a1574) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | c0_1(a1574) | (~c1_1(a1574)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2281,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1574) | c0_1(a1574) | (~c1_1(a1574)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a1574) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | c0_1(a1574) | (~c1_1(a1574))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[2280])).
% 1.37/1.57 tff(2282,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1574) | c0_1(a1574) | (~c1_1(a1574)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1574) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | c0_1(a1574) | (~c1_1(a1574)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[2281, 2279])).
% 1.37/1.57 tff(2283,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c2_1(a1534)) | c2_1(a1574) | c0_1(a1574) | (~c1_1(a1574)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(2284,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a1574) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c2_1(a1534)) | c0_1(a1574) | (~c1_1(a1574))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2283, 2282])).
% 1.37/1.57 tff(2285,plain,
% 1.37/1.57 (hskp9),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2284, 319, 2255, 2234, 2253, 2233, 1868, 2235, 2278])).
% 1.37/1.57 tff(2286,plain,
% 1.37/1.57 (~c1_1(a1548)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1881, 2285])).
% 1.37/1.57 tff(2287,plain,
% 1.37/1.57 (~c0_1(a1548)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1887, 2285])).
% 1.37/1.57 tff(2288,plain,
% 1.37/1.57 (~c2_1(a1548)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1905, 319, 2166, 2255, 2254, 2253, 2287, 2286, 22])).
% 1.37/1.57 tff(2289,plain,
% 1.37/1.57 (~c3_1(a1548)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1911, 2285])).
% 1.37/1.57 tff(2290,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c0_1(a1548) | c3_1(a1548) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c2_1(a1548) | (~c0_1(a1565)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c0_1(a1548) | c3_1(a1548) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c2_1(a1548) | (~c0_1(a1565)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2291,plain,
% 1.37/1.57 (((~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c0_1(a1565)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1548) | c2_1(a1548) | c0_1(a1548)) <=> (c2_1(a1565) | c3_1(a1565) | c0_1(a1548) | c3_1(a1548) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c2_1(a1548) | (~c0_1(a1565)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2292,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c0_1(a1565)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1548) | c2_1(a1548) | c0_1(a1548))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c0_1(a1548) | c3_1(a1548) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c2_1(a1548) | (~c0_1(a1565))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[2291])).
% 1.37/1.57 tff(2293,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c0_1(a1565)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1548) | c2_1(a1548) | c0_1(a1548))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c0_1(a1548) | c3_1(a1548) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c2_1(a1548) | (~c0_1(a1565)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[2292, 2290])).
% 1.37/1.57 tff(2294,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c0_1(a1565)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1548) | c2_1(a1548) | c0_1(a1548))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(2295,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c0_1(a1548) | c3_1(a1548) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c2_1(a1548) | (~c0_1(a1565))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 1.37/1.57 tff(2296,plain,
% 1.37/1.57 (~c0_1(a1565)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2295, 319, 2232, 1997, 2184, 2287, 2289, 2233, 35, 2235, 2288])).
% 1.37/1.57 tff(2297,plain,
% 1.37/1.57 (~c2_1(a1558)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[64, 2262])).
% 1.37/1.57 tff(2298,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2299,plain,
% 1.37/1.57 (((~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2300,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565)))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[2299])).
% 1.37/1.57 tff(2301,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565))),
% 1.37/1.57 inference(transitivity,[status(thm)],[2300, 2298])).
% 1.37/1.57 tff(2302,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1558) | c3_1(a1558) | (~c0_1(a1558)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(2303,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c2_1(a1558) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1558) | (~c0_1(a1558)) | c0_1(a1565)),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 1.37/1.57 tff(2304,plain,
% 1.37/1.57 (c3_1(a1558) | c0_1(a1565)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2303, 319, 2264, 2232, 1997, 2184, 2297, 2233, 35, 2235])).
% 1.37/1.57 tff(2305,plain,
% 1.37/1.57 ($false),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2304, 2296, 2271])).
% 1.37/1.57 tff(2306,plain,(hskp4), inference(lemma,lemma(discharge,[]))).
% 1.37/1.57 tff(2307,plain,
% 1.37/1.57 (~c3_1(a1538)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[154, 2306])).
% 1.37/1.57 tff(2308,plain,
% 1.37/1.57 (~c2_1(a1538)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[138, 2306])).
% 1.37/1.57 tff(2309,plain,
% 1.37/1.57 (~c1_1(a1538)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[161, 2306])).
% 1.37/1.57 tff(2310,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c0_1(a1565))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2311,plain,
% 1.37/1.57 (((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c0_1(a1565))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2312,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c0_1(a1565)))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[2311])).
% 1.37/1.57 tff(2313,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c0_1(a1565))),
% 1.37/1.57 inference(transitivity,[status(thm)],[2312, 2310])).
% 1.37/1.57 tff(2314,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(2315,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c0_1(a1565)),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 1.37/1.57 tff(2316,plain,
% 1.37/1.57 ((~c0_1(a1538)) | c0_1(a1565)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2315, 319, 1997, 2184, 2309, 2308, 2307, 35])).
% 1.37/1.57 tff(2317,plain,
% 1.37/1.57 (~c0_1(a1538)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2316, 25])).
% 1.37/1.57 tff(2318,plain,
% 1.37/1.57 (~hskp5),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2172, 47, 12])).
% 1.37/1.57 tff(2319,assumption,(hskp12), introduced(assumption)).
% 1.37/1.57 tff(2320,plain,
% 1.37/1.57 (~c0_1(a1554)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1064, 2319])).
% 1.37/1.57 tff(2321,plain,
% 1.37/1.57 (c2_1(a1554)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1072, 2319])).
% 1.37/1.57 tff(2322,plain,
% 1.37/1.57 (c1_1(a1554)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1080, 2319])).
% 1.37/1.57 tff(2323,assumption,(~hskp14), introduced(assumption)).
% 1.37/1.57 tff(2324,plain,
% 1.37/1.57 ($false),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1088, 319, 2323, 1082, 2322, 2321, 2320, 1050])).
% 1.37/1.57 tff(2325,plain,((~hskp12) | hskp14 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.37/1.57 tff(2326,plain,
% 1.37/1.57 (hskp14),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[2325, 2319, 1082])).
% 1.37/1.57 tff(2327,plain,
% 1.37/1.57 (~c2_1(a1558)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[64, 2326])).
% 1.37/1.57 tff(2328,plain,
% 1.37/1.57 (c1_1(a1558)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[72, 2326])).
% 1.37/1.57 tff(2329,plain,
% 1.37/1.57 (c0_1(a1558)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[80, 2326])).
% 1.37/1.57 tff(2330,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1558) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1558)) | (~c1_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1558) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(2331,plain,
% 1.37/1.57 ((hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554))) <=> (hskp10 | c2_1(a1558) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2332,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1558) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1558)) | (~c1_1(a1558))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[2331])).
% 1.37/1.58 tff(2333,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1558) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[2332, 2330])).
% 1.37/1.58 tff(2334,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c0_1(a1554) | (~c1_1(a1554)) | (~c2_1(a1554)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(2335,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1558) | c0_1(a1554) | (~ndr1_0) | (~c2_1(a1554)) | (~c1_1(a1554)) | (~c0_1(a1558)) | (~c1_1(a1558))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 1.37/1.58 tff(2336,plain,
% 1.37/1.58 ($false),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2335, 319, 11, 2329, 2328, 2322, 2321, 2327, 2320, 1121])).
% 1.37/1.58 tff(2337,plain,((~hskp12) | hskp10 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.37/1.58 tff(2338,plain,
% 1.37/1.58 (~hskp12),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2337, 11, 2318])).
% 1.37/1.58 tff(2339,plain,
% 1.37/1.58 (hskp3),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1058, 2338, 11])).
% 1.37/1.58 tff(2340,plain,
% 1.37/1.58 (~c0_1(a1536)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[674, 2339])).
% 1.37/1.58 tff(2341,plain,
% 1.37/1.58 (c1_1(a1536)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[684, 2339])).
% 1.37/1.58 tff(2342,plain,
% 1.37/1.58 (~c3_1(a1536)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1379, 319, 12, 47, 2341, 2340, 1150])).
% 1.37/1.58 tff(2343,plain,
% 1.37/1.58 (~c2_1(a1536)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[668, 2339])).
% 1.37/1.58 tff(2344,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c0_1(a1538)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c0_1(a1538)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2345,plain,
% 1.37/1.58 (((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536)) <=> (c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c0_1(a1538)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2346,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c0_1(a1538))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[2345])).
% 1.37/1.58 tff(2347,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c0_1(a1538)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[2346, 2344])).
% 1.37/1.58 tff(2348,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1536) | c2_1(a1536) | c0_1(a1536))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(2349,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c0_1(a1536) | c2_1(a1536) | (~ndr1_0) | c3_1(a1536) | (~c0_1(a1538))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.37/1.58 tff(2350,plain,
% 1.37/1.58 (~c0_1(a1538)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2349, 319, 2309, 2308, 2307, 2340, 2343, 35, 2342])).
% 1.37/1.58 tff(2351,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c3_1(a1565) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c0_1(a1565)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c3_1(a1565) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2352,plain,
% 1.37/1.58 ((hskp5 | (~ndr1_0) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c3_1(a1538) | c1_1(a1538) | c0_1(a1538)) <=> (hskp5 | c3_1(a1565) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2353,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c3_1(a1538) | c1_1(a1538) | c0_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c3_1(a1565) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c0_1(a1565)) | (~c1_1(a1565))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[2352])).
% 1.37/1.58 tff(2354,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c3_1(a1538) | c1_1(a1538) | c0_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c3_1(a1565) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[2353, 2351])).
% 1.37/1.58 tff(2355,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c3_1(a1538) | c1_1(a1538) | c0_1(a1538))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(2356,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c3_1(a1565) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c0_1(a1565)) | (~c1_1(a1565))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2355, 2354])).
% 1.37/1.58 tff(2357,plain,
% 1.37/1.58 (hskp5 | c0_1(a1538) | (~c0_1(a1565))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2356, 319, 2005, 2184, 2309, 2307, 462])).
% 1.37/1.58 tff(2358,plain,
% 1.37/1.58 (~c0_1(a1565)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2357, 2350, 2318])).
% 1.37/1.58 tff(2359,plain,
% 1.37/1.58 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(2360,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[2359])).
% 1.37/1.58 tff(2361,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2362,plain,
% 1.37/1.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | 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)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | 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)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | 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)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(2363,plain,
% 1.37/1.58 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[2362])).
% 1.37/1.58 tff(2364,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.37/1.58 tff(2365,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 1.37/1.58 tff(2366,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2365, 2361])).
% 1.37/1.58 tff(2367,plain,(
% 1.37/1.58 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.58 inference(skolemize,[status(sab)],[2366])).
% 1.37/1.58 tff(2368,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2367, 2360])).
% 1.37/1.58 tff(2369,plain,
% 1.37/1.58 (hskp2 | hskp1 | c0_1(a1538)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1277, 319, 2309, 2308, 1262])).
% 1.37/1.58 tff(2370,plain,
% 1.37/1.58 (hskp2),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2369, 2350, 47])).
% 1.37/1.58 tff(2371,plain,
% 1.37/1.58 (~c2_1(a1535)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[849, 2370])).
% 1.37/1.58 tff(2372,plain,
% 1.37/1.58 (c3_1(a1535)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[843, 2370])).
% 1.37/1.58 tff(2373,plain,
% 1.37/1.58 (^[U: $i] : refl((hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(2374,plain,
% 1.37/1.58 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[2373])).
% 1.37/1.58 tff(2375,plain,
% 1.37/1.58 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2376,plain,
% 1.37/1.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp1) <=> ((hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp1))), rewrite(((hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp1) <=> (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp1) <=> (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(2377,plain,
% 1.37/1.58 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp1) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[2376])).
% 1.37/1.58 tff(2378,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.37/1.58 tff(2379,plain,
% 1.37/1.58 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2378, 2377])).
% 1.37/1.58 tff(2380,plain,
% 1.37/1.58 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2379, 2375])).
% 1.37/1.58 tff(2381,plain,(
% 1.37/1.58 ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.58 inference(skolemize,[status(sab)],[2380])).
% 1.37/1.58 tff(2382,plain,
% 1.37/1.58 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2381, 2374])).
% 1.37/1.58 tff(2383,plain,
% 1.37/1.58 (~hskp12),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2325, 2323, 2318])).
% 1.37/1.58 tff(2384,plain,
% 1.37/1.58 (hskp3),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1058, 2383, 11])).
% 1.37/1.58 tff(2385,plain,
% 1.37/1.58 (c1_1(a1536)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[684, 2384])).
% 1.37/1.58 tff(2386,assumption,(~c2_1(a1545)), introduced(assumption)).
% 1.37/1.58 tff(2387,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2388,plain,
% 1.37/1.58 (((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545)) <=> (c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2389,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[2388])).
% 1.37/1.58 tff(2390,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[2389, 2387])).
% 1.37/1.58 tff(2391,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1538) | c3_1(a1538) | (~c0_1(a1538)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(2392,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 1.37/1.58 tff(2393,plain,
% 1.37/1.58 (c2_1(a1545) | (~c0_1(a1538))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2392, 319, 23, 24, 2309, 2308, 2307, 35])).
% 1.37/1.58 tff(2394,plain,
% 1.37/1.58 (~c0_1(a1538)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2393, 2386])).
% 1.37/1.58 tff(2395,plain,
% 1.37/1.58 (~c0_1(a1565)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2357, 2394, 1082])).
% 1.37/1.58 tff(2396,plain,
% 1.37/1.58 (hskp2),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2369, 2394, 47])).
% 1.37/1.58 tff(2397,plain,
% 1.37/1.58 (~c2_1(a1535)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[849, 2396])).
% 1.37/1.58 tff(2398,plain,
% 1.37/1.58 (c3_1(a1535)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[843, 2396])).
% 1.37/1.58 tff(2399,plain,
% 1.37/1.58 (~hskp7),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[194, 2386])).
% 1.37/1.58 tff(2400,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | c0_1(a1565))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2401,plain,
% 1.37/1.58 ((hskp7 | (~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | c0_1(a1565))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2402,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | c0_1(a1565)))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[2401])).
% 1.37/1.58 tff(2403,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | c0_1(a1565))),
% 1.37/1.58 inference(transitivity,[status(thm)],[2402, 2400])).
% 1.37/1.58 tff(2404,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(2405,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | c0_1(a1565)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 1.37/1.58 tff(2406,plain,
% 1.37/1.58 (~c0_1(a1535)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2405, 319, 2399, 2398, 1997, 2184, 2397, 2368, 2395])).
% 1.37/1.58 tff(2407,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c0_1(a1565))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2408,plain,
% 1.37/1.58 ((hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (hskp6 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c0_1(a1565))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2409,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c0_1(a1565)))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[2408])).
% 1.37/1.58 tff(2410,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c0_1(a1565))),
% 1.37/1.58 inference(transitivity,[status(thm)],[2409, 2407])).
% 1.37/1.58 tff(2411,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(2412,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a1565) | c3_1(a1565) | c2_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | c0_1(a1565)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 1.37/1.58 tff(2413,plain,
% 1.37/1.58 (hskp6),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2412, 319, 2398, 1997, 2184, 2397, 899, 2395, 2406])).
% 1.37/1.58 tff(2414,plain,
% 1.37/1.58 (~c2_1(a1543)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[912, 2413])).
% 1.37/1.58 tff(2415,plain,
% 1.37/1.58 (c0_1(a1543)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[950, 2413])).
% 1.37/1.58 tff(2416,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | c0_1(a1565))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2417,plain,
% 1.37/1.58 ((hskp7 | (~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | c0_1(a1565))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(2418,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | c0_1(a1565)))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[2417])).
% 1.37/1.58 tff(2419,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | c0_1(a1565))),
% 1.37/1.58 inference(transitivity,[status(thm)],[2418, 2416])).
% 1.37/1.58 tff(2420,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(2421,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)) | c0_1(a1565)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[2420, 2419])).
% 1.37/1.58 tff(2422,plain,
% 1.37/1.58 (~c3_1(a1543)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[2421, 319, 2399, 2415, 1997, 2184, 2414, 2368, 2395])).
% 1.37/1.58 tff(2423,plain,
% 1.37/1.58 (~c1_1(a1543)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[918, 2413])).
% 1.37/1.58 tff(2424,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2425,plain,
% 1.37/1.59 (((~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (c2_1(a1565) | c3_1(a1565) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2426,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565)))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[2425])).
% 1.37/1.59 tff(2427,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565))),
% 1.37/1.59 inference(transitivity,[status(thm)],[2426, 2424])).
% 1.37/1.59 tff(2428,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(2429,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 1.37/1.59 tff(2430,plain,
% 1.37/1.59 ($false),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2429, 319, 2415, 1997, 2184, 2423, 2414, 35, 2395, 2422])).
% 1.37/1.59 tff(2431,plain,(c2_1(a1545) | hskp1 | hskp5 | c0_1(a1545) | c3_1(a1545)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.59 tff(2432,plain,
% 1.37/1.59 (c2_1(a1545)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2431, 24, 2318, 23, 47])).
% 1.37/1.59 tff(2433,plain,
% 1.37/1.59 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(2434,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[2433])).
% 1.37/1.59 tff(2435,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2436,plain,
% 1.37/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(2437,plain,
% 1.37/1.59 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[2436])).
% 1.37/1.59 tff(2438,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.37/1.59 tff(2439,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 1.37/1.59 tff(2440,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2439, 2435])).
% 1.37/1.59 tff(2441,plain,(
% 1.37/1.59 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.37/1.59 inference(skolemize,[status(sab)],[2440])).
% 1.37/1.59 tff(2442,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2441, 2434])).
% 1.37/1.59 tff(2443,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c1_1(a1565)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2444,plain,
% 1.37/1.59 ((hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545))) <=> (hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c1_1(a1565)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2445,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c1_1(a1565))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[2444])).
% 1.37/1.59 tff(2446,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c1_1(a1565)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[2445, 2443])).
% 1.37/1.59 tff(2447,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(2448,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c1_1(a1565))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 1.37/1.59 tff(2449,plain,
% 1.37/1.59 (hskp14 | (~c2_1(a1545)) | (~c1_1(a1545))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2448, 319, 2005, 1997, 2184, 23, 2442])).
% 1.37/1.59 tff(2450,plain,
% 1.37/1.59 (~c1_1(a1545)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2449, 2323, 2432])).
% 1.37/1.59 tff(2451,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2452,plain,
% 1.37/1.59 ((hskp5 | (~ndr1_0) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545)) <=> (hskp5 | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2453,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[2452])).
% 1.37/1.59 tff(2454,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[2453, 2451])).
% 1.37/1.59 tff(2455,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(2456,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 1.37/1.59 tff(2457,plain,
% 1.37/1.59 (c1_1(a1545) | (~c0_1(a1565))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2456, 319, 2318, 2005, 2184, 23, 24, 462])).
% 1.37/1.59 tff(2458,plain,
% 1.37/1.59 (~c0_1(a1565)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2457, 2450])).
% 1.37/1.59 tff(2459,plain,
% 1.37/1.59 (~c0_1(a1538)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2316, 2458])).
% 1.37/1.59 tff(2460,plain,
% 1.37/1.59 (hskp2),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2369, 2459, 47])).
% 1.37/1.59 tff(2461,plain,
% 1.37/1.59 (~c2_1(a1535)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[849, 2460])).
% 1.37/1.59 tff(2462,plain,
% 1.37/1.59 (~c0_1(a1536)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[674, 2384])).
% 1.37/1.59 tff(2463,plain,
% 1.37/1.59 (c3_1(a1535)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[843, 2460])).
% 1.37/1.59 tff(2464,plain,
% 1.37/1.59 (~c2_1(a1536)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[668, 2384])).
% 1.37/1.59 tff(2465,plain,
% 1.37/1.59 (~c1_1(a1535)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[858, 2460])).
% 1.37/1.59 tff(2466,plain,
% 1.37/1.59 (~c3_1(a1536)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1379, 319, 12, 47, 2385, 2462, 1150])).
% 1.37/1.59 tff(2467,plain,
% 1.37/1.59 (hskp16),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1420, 2466, 2465, 2464, 2463, 2462, 2461, 2385])).
% 1.37/1.59 tff(2468,plain,
% 1.37/1.59 (~c1_1(a1566)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1449, 2467])).
% 1.37/1.59 tff(2469,plain,
% 1.37/1.59 (c2_1(a1566)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1436, 2467])).
% 1.37/1.59 tff(2470,plain,
% 1.37/1.59 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | c1_1(a1566) | (~ndr1_0) | (~c0_1(a1566)) | (~c2_1(a1566)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp1 | c1_1(a1566) | (~ndr1_0) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2471,plain,
% 1.37/1.59 ((hskp14 | hskp1 | (~ndr1_0) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566))) <=> (hskp14 | hskp1 | c1_1(a1566) | (~ndr1_0) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2472,plain,
% 1.37/1.59 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | c1_1(a1566) | (~ndr1_0) | (~c0_1(a1566)) | (~c2_1(a1566))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[2471])).
% 1.37/1.59 tff(2473,plain,
% 1.37/1.59 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp1 | c1_1(a1566) | (~ndr1_0) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[2472, 2470])).
% 1.37/1.59 tff(2474,plain,
% 1.37/1.59 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(2475,plain,
% 1.37/1.59 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp1 | c1_1(a1566) | (~ndr1_0) | (~c0_1(a1566)) | (~c2_1(a1566))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2474, 2473])).
% 1.37/1.59 tff(2476,plain,
% 1.37/1.59 (~c0_1(a1566)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2475, 319, 2323, 47, 2469, 2468, 2382])).
% 1.37/1.59 tff(2477,plain,
% 1.37/1.59 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(2478,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[2477])).
% 1.37/1.59 tff(2479,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2480,plain,
% 1.37/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(2481,plain,
% 1.37/1.59 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[2480])).
% 1.37/1.59 tff(2482,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.37/1.59 tff(2483,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2482, 2481])).
% 1.37/1.59 tff(2484,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2483, 2479])).
% 1.37/1.59 tff(2485,plain,(
% 1.37/1.59 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.59 inference(skolemize,[status(sab)],[2484])).
% 1.37/1.59 tff(2486,plain,
% 1.37/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2485, 2478])).
% 1.37/1.59 tff(2487,plain,
% 1.37/1.59 (c3_1(a1566)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1428, 2467])).
% 1.37/1.59 tff(2488,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1566)) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2489,plain,
% 1.37/1.59 ((hskp0 | (~ndr1_0) | c1_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)) | c2_1(a1538) | c1_1(a1538) | c0_1(a1538)) <=> (hskp0 | c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2490,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)) | c2_1(a1538) | c1_1(a1538) | c0_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1566)) | (~c2_1(a1566))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[2489])).
% 1.37/1.59 tff(2491,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)) | c2_1(a1538) | c1_1(a1538) | c0_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[2490, 2488])).
% 1.37/1.59 tff(2492,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)) | c2_1(a1538) | c1_1(a1538) | c0_1(a1538))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(2493,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1566)) | (~c2_1(a1566))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2492, 2491])).
% 1.37/1.59 tff(2494,plain,
% 1.37/1.59 (hskp0),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2493, 319, 2469, 2487, 2468, 2309, 2308, 2486, 2459])).
% 1.37/1.59 tff(2495,plain,
% 1.37/1.59 (((~hskp0) | (~c0_1(a1533))) <=> ((~hskp0) | (~c0_1(a1533)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2496,plain,
% 1.37/1.59 (((~c0_1(a1533)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1533)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2497,axiom,((~c0_1(a1533)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.37/1.59 tff(2498,plain,
% 1.37/1.59 ((~hskp0) | (~c0_1(a1533))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 1.37/1.59 tff(2499,plain,
% 1.37/1.59 ((~hskp0) | (~c0_1(a1533))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2498, 2495])).
% 1.37/1.59 tff(2500,plain,
% 1.37/1.59 (~c0_1(a1533)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2499, 2494])).
% 1.37/1.59 tff(2501,plain,
% 1.37/1.59 (((~hskp0) | c1_1(a1533)) <=> ((~hskp0) | c1_1(a1533))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2502,axiom,((~hskp0) | c1_1(a1533)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.37/1.59 tff(2503,plain,
% 1.37/1.59 ((~hskp0) | c1_1(a1533)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 1.37/1.59 tff(2504,plain,
% 1.37/1.59 ((~hskp0) | c1_1(a1533)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2503, 2501])).
% 1.37/1.59 tff(2505,plain,
% 1.37/1.59 ((~hskp0) | c1_1(a1533)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2504, 2501])).
% 1.37/1.59 tff(2506,plain,
% 1.37/1.59 ((~hskp0) | c1_1(a1533)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2505, 2501])).
% 1.37/1.59 tff(2507,plain,
% 1.37/1.59 ((~hskp0) | c1_1(a1533)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2506, 2501])).
% 1.37/1.59 tff(2508,plain,
% 1.37/1.59 (c1_1(a1533)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2507, 2494])).
% 1.37/1.59 tff(2509,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1533) | (~ndr1_0) | (~c1_1(a1533)) | (~c2_1(a1533)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1533) | (~ndr1_0) | (~c1_1(a1533)) | (~c2_1(a1533)) | (~c1_1(a1565)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2510,plain,
% 1.37/1.59 ((hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1533) | (~c1_1(a1533)) | (~c2_1(a1533))) <=> (hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1533) | (~ndr1_0) | (~c1_1(a1533)) | (~c2_1(a1533)) | (~c1_1(a1565)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2511,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1533) | (~c1_1(a1533)) | (~c2_1(a1533)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1533) | (~ndr1_0) | (~c1_1(a1533)) | (~c2_1(a1533)) | (~c1_1(a1565))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[2510])).
% 1.37/1.59 tff(2512,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1533) | (~c1_1(a1533)) | (~c2_1(a1533)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1533) | (~ndr1_0) | (~c1_1(a1533)) | (~c2_1(a1533)) | (~c1_1(a1565)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[2511, 2509])).
% 1.37/1.59 tff(2513,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1533) | (~c1_1(a1533)) | (~c2_1(a1533)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(2514,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp14 | c2_1(a1565) | c3_1(a1565) | c0_1(a1533) | (~ndr1_0) | (~c1_1(a1533)) | (~c2_1(a1533)) | (~c1_1(a1565))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 1.37/1.59 tff(2515,plain,
% 1.37/1.59 (~c2_1(a1533)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[2514, 319, 2323, 2005, 2508, 1997, 2184, 2500, 2442])).
% 1.37/1.59 tff(2516,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2517,plain,
% 1.37/1.59 (((~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c2_1(a1535) | c1_1(a1535) | (~c3_1(a1535)) | c0_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566))) <=> (c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(2518,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c2_1(a1535) | c1_1(a1535) | (~c3_1(a1535)) | c0_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[2517])).
% 1.37/1.60 tff(2519,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c2_1(a1535) | c1_1(a1535) | (~c3_1(a1535)) | c0_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[2518, 2516])).
% 1.37/1.60 tff(2520,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1535)) | c2_1(a1535) | c1_1(a1535) | (~c3_1(a1535)) | c0_1(a1566) | (~c3_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(2521,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1535) | c2_1(a1535) | (~ndr1_0) | (~c0_1(a1535)) | (~c3_1(a1535)) | (~c3_1(a1566)) | c0_1(a1566) | (~c2_1(a1566))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 1.37/1.60 tff(2522,plain,
% 1.37/1.60 (~c0_1(a1535)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2521, 319, 2469, 2487, 2463, 2465, 2461, 1232, 2476])).
% 1.37/1.60 tff(2523,plain,
% 1.37/1.60 (((~hskp0) | (~c3_1(a1533))) <=> ((~hskp0) | (~c3_1(a1533)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2524,plain,
% 1.37/1.60 (((~c3_1(a1533)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a1533)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2525,axiom,((~c3_1(a1533)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.37/1.60 tff(2526,plain,
% 1.37/1.60 ((~hskp0) | (~c3_1(a1533))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2525, 2524])).
% 1.37/1.60 tff(2527,plain,
% 1.37/1.60 ((~hskp0) | (~c3_1(a1533))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2526, 2523])).
% 1.37/1.60 tff(2528,plain,
% 1.37/1.60 (~c3_1(a1533)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2527, 2494])).
% 1.37/1.60 tff(2529,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a1535) | c0_1(a1533) | c3_1(a1533) | (~ndr1_0) | c2_1(a1533) | c0_1(a1535) | (~c3_1(a1535)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a1535) | c0_1(a1533) | c3_1(a1533) | (~ndr1_0) | c2_1(a1533) | c0_1(a1535) | (~c3_1(a1535)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2530,plain,
% 1.37/1.60 ((hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1533) | c2_1(a1533) | c0_1(a1533)) <=> (hskp6 | c2_1(a1535) | c0_1(a1533) | c3_1(a1533) | (~ndr1_0) | c2_1(a1533) | c0_1(a1535) | (~c3_1(a1535)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2531,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1533) | c2_1(a1533) | c0_1(a1533))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a1535) | c0_1(a1533) | c3_1(a1533) | (~ndr1_0) | c2_1(a1533) | c0_1(a1535) | (~c3_1(a1535))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[2530])).
% 1.37/1.60 tff(2532,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1533) | c2_1(a1533) | c0_1(a1533))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a1535) | c0_1(a1533) | c3_1(a1533) | (~ndr1_0) | c2_1(a1533) | c0_1(a1535) | (~c3_1(a1535)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[2531, 2529])).
% 1.37/1.60 tff(2533,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1533) | c2_1(a1533) | c0_1(a1533))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(2534,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a1535) | c0_1(a1533) | c3_1(a1533) | (~ndr1_0) | c2_1(a1533) | c0_1(a1535) | (~c3_1(a1535))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2533, 2532])).
% 1.37/1.60 tff(2535,plain,
% 1.37/1.60 (hskp6),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2534, 319, 2463, 2461, 2500, 2528, 899, 2522, 2515])).
% 1.37/1.60 tff(2536,plain,
% 1.37/1.60 (~c2_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[912, 2535])).
% 1.37/1.60 tff(2537,plain,
% 1.37/1.60 (~c1_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[918, 2535])).
% 1.37/1.60 tff(2538,plain,
% 1.37/1.60 (c0_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[950, 2535])).
% 1.37/1.60 tff(2539,plain,
% 1.37/1.60 (~c3_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1468, 319, 2469, 2487, 2538, 2537, 2536, 1232, 2476])).
% 1.37/1.60 tff(2540,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c2_1(a1545)) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c2_1(a1545)) | c0_1(a1565))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2541,plain,
% 1.37/1.60 (((~ndr1_0) | c1_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c2_1(a1545)) | c0_1(a1565))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2542,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c2_1(a1545)) | c0_1(a1565)))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[2541])).
% 1.37/1.60 tff(2543,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c2_1(a1545)) | c0_1(a1565))),
% 1.37/1.60 inference(transitivity,[status(thm)],[2542, 2540])).
% 1.37/1.60 tff(2544,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(2545,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c2_1(a1545)) | c0_1(a1565)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2544, 2543])).
% 1.37/1.60 tff(2546,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2545, 319, 2432, 2538, 1997, 2184, 23, 24, 2537, 714, 2458, 2539])).
% 1.37/1.60 tff(2547,plain,(hskp14 | c0_1(a1545) | c3_1(a1545) | hskp1 | hskp28 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(2548,plain,
% 1.37/1.60 (hskp14),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2547, 24, 23, 47, 12, 11])).
% 1.37/1.60 tff(2549,plain,
% 1.37/1.60 (c1_1(a1558)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[72, 2548])).
% 1.37/1.60 tff(2550,plain,
% 1.37/1.60 (c0_1(a1558)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[80, 2548])).
% 1.37/1.60 tff(2551,plain,
% 1.37/1.60 (~c3_1(a1558)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1097, 319, 11, 2550, 2549, 10])).
% 1.37/1.60 tff(2552,plain,
% 1.37/1.60 (~c2_1(a1558)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[64, 2548])).
% 1.37/1.60 tff(2553,plain,
% 1.37/1.60 (~c1_1(a1545)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1635, 319, 11, 2550, 2549, 2432, 2552, 23, 1121])).
% 1.37/1.60 tff(2554,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2555,plain,
% 1.37/1.60 ((hskp5 | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545)) <=> (hskp5 | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2556,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[2555])).
% 1.37/1.60 tff(2557,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[2556, 2554])).
% 1.37/1.60 tff(2558,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1558) | (~c1_1(a1558)) | (~c0_1(a1558)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(2559,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a1545) | c3_1(a1545) | (~ndr1_0) | c1_1(a1545) | c3_1(a1558) | (~c0_1(a1558)) | (~c1_1(a1558))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 1.37/1.60 tff(2560,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2559, 319, 2318, 2550, 2549, 23, 24, 462, 2553, 2551])).
% 1.37/1.60 tff(2561,plain,(c3_1(a1545) | c0_1(a1545) | hskp10 | hskp1 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(2562,plain,
% 1.37/1.60 (c3_1(a1545)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2561, 23, 11, 47, 12])).
% 1.37/1.60 tff(2563,plain,
% 1.37/1.60 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1545) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1545) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2564,plain,
% 1.37/1.60 ((hskp28 | hskp1 | (~ndr1_0) | c0_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545))) <=> (hskp28 | hskp1 | c0_1(a1545) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2565,plain,
% 1.37/1.60 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c0_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | c0_1(a1545) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[2564])).
% 1.37/1.60 tff(2566,plain,
% 1.37/1.60 (((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c0_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)))) <=> ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1545) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[2565, 2563])).
% 1.37/1.60 tff(2567,plain,
% 1.37/1.60 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp1 | (~ndr1_0) | c0_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(2568,plain,
% 1.37/1.60 ((~![U: $i] : (hskp28 | hskp1 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp1 | c0_1(a1545) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 1.37/1.60 tff(2569,plain,
% 1.37/1.60 ((~c3_1(a1545)) | (~c1_1(a1545))),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2568, 319, 12, 47, 23, 1150])).
% 1.37/1.60 tff(2570,plain,
% 1.37/1.60 (~c1_1(a1545)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2569, 2562])).
% 1.37/1.60 tff(2571,assumption,(~c1_1(a1545)), introduced(assumption)).
% 1.37/1.60 tff(2572,assumption,(c0_1(a1538)), introduced(assumption)).
% 1.37/1.60 tff(2573,assumption,(c3_1(a1545)), introduced(assumption)).
% 1.37/1.60 tff(2574,plain,
% 1.37/1.60 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2575,plain,
% 1.37/1.60 ((hskp11 | hskp1 | (~ndr1_0) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538))) <=> (hskp11 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2576,plain,
% 1.37/1.60 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[2575])).
% 1.37/1.60 tff(2577,plain,
% 1.37/1.60 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[2576, 2574])).
% 1.37/1.60 tff(2578,plain,
% 1.37/1.60 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(2579,plain,
% 1.37/1.60 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp1 | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.37/1.60 tff(2580,plain,
% 1.37/1.60 (hskp11 | hskp1 | (~c0_1(a1538))),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2579, 319, 2309, 2308, 1006])).
% 1.37/1.60 tff(2581,plain,
% 1.37/1.60 (hskp11),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2580, 2572, 47])).
% 1.37/1.60 tff(2582,plain,
% 1.37/1.60 (~c1_1(a1553)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[942, 2581])).
% 1.37/1.60 tff(2583,plain,
% 1.37/1.60 (c2_1(a1553)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[958, 2581])).
% 1.37/1.60 tff(2584,plain,
% 1.37/1.60 (c0_1(a1553)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[966, 2581])).
% 1.37/1.60 tff(2585,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1553) | c0_1(a1545) | (~c3_1(a1545)) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c1_1(a1545) | (~c0_1(a1553)) | (~c2_1(a1553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1553) | c0_1(a1545) | (~c3_1(a1545)) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c1_1(a1545) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2586,plain,
% 1.37/1.60 (((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545))) <=> (c1_1(a1553) | c0_1(a1545) | (~c3_1(a1545)) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c1_1(a1545) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2587,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1553) | c0_1(a1545) | (~c3_1(a1545)) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c1_1(a1545) | (~c0_1(a1553)) | (~c2_1(a1553))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[2586])).
% 1.37/1.60 tff(2588,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1553) | c0_1(a1545) | (~c3_1(a1545)) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c1_1(a1545) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[2587, 2585])).
% 1.37/1.60 tff(2589,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(2590,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1553) | c0_1(a1545) | (~c3_1(a1545)) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | c1_1(a1545) | (~c0_1(a1553)) | (~c2_1(a1553))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2589, 2588])).
% 1.37/1.60 tff(2591,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2590, 319, 2584, 2583, 2582, 23, 2573, 2309, 2308, 277, 2572, 2571])).
% 1.37/1.60 tff(2592,plain,((~c0_1(a1538)) | c0_1(a1545) | (~c3_1(a1545)) | c1_1(a1545) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(2593,plain,
% 1.37/1.60 (~c0_1(a1538)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2592, 23, 2562, 2570, 47])).
% 1.37/1.60 tff(2594,plain,
% 1.37/1.60 (~c0_1(a1565)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2357, 2593, 2318])).
% 1.37/1.60 tff(2595,plain,
% 1.37/1.60 (hskp2),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2369, 2593, 47])).
% 1.37/1.60 tff(2596,plain,
% 1.37/1.60 (~c2_1(a1535)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[849, 2595])).
% 1.37/1.60 tff(2597,plain,
% 1.37/1.60 (c3_1(a1535)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[843, 2595])).
% 1.37/1.60 tff(2598,plain,
% 1.37/1.60 (~hskp7),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[180, 2562])).
% 1.37/1.60 tff(2599,plain,
% 1.37/1.60 (~c0_1(a1535)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2405, 319, 2598, 2597, 1997, 2184, 2596, 2368, 2594])).
% 1.37/1.60 tff(2600,plain,
% 1.37/1.60 (hskp6),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2412, 319, 2597, 1997, 2184, 2596, 899, 2594, 2599])).
% 1.37/1.60 tff(2601,plain,
% 1.37/1.60 (~c2_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[912, 2600])).
% 1.37/1.60 tff(2602,plain,
% 1.37/1.60 (c0_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[950, 2600])).
% 1.37/1.60 tff(2603,plain,
% 1.37/1.60 (~c3_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2421, 319, 2598, 2602, 1997, 2184, 2601, 2368, 2594])).
% 1.37/1.60 tff(2604,plain,
% 1.37/1.60 (~c1_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[918, 2600])).
% 1.37/1.60 tff(2605,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2429, 319, 2602, 1997, 2184, 2604, 2601, 35, 2594, 2603])).
% 1.37/1.60 tff(2606,plain,(c0_1(a1545) | hskp1 | hskp28 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(2607,plain,
% 1.37/1.60 (c0_1(a1545)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2606, 11, 12, 47])).
% 1.37/1.60 tff(2608,plain,
% 1.37/1.60 (~hskp7),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[186, 2607])).
% 1.37/1.60 tff(2609,plain,
% 1.37/1.60 (~c0_1(a1535)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2405, 319, 2608, 2372, 1997, 2184, 2371, 2368, 2358])).
% 1.37/1.60 tff(2610,plain,
% 1.37/1.60 (~c1_1(a1535)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[858, 2370])).
% 1.37/1.60 tff(2611,plain,
% 1.37/1.60 (hskp6),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2412, 319, 2372, 1997, 2184, 2371, 899, 2358, 2609])).
% 1.37/1.60 tff(2612,plain,
% 1.37/1.60 (~c2_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[912, 2611])).
% 1.37/1.60 tff(2613,plain,
% 1.37/1.60 (~c1_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[918, 2611])).
% 1.37/1.60 tff(2614,plain,
% 1.37/1.60 (hskp16),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1420, 2610, 2342, 2343, 2372, 2340, 2371, 2341])).
% 1.37/1.60 tff(2615,plain,
% 1.37/1.60 (~c1_1(a1566)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1449, 2614])).
% 1.37/1.60 tff(2616,plain,
% 1.37/1.60 (c0_1(a1543)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[950, 2611])).
% 1.37/1.60 tff(2617,plain,
% 1.37/1.60 (c2_1(a1566)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1436, 2614])).
% 1.37/1.60 tff(2618,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1566) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1566)) | (~c2_1(a1566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1566) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2619,plain,
% 1.37/1.60 (((~ndr1_0) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1535) | c1_1(a1535) | (~c3_1(a1535))) <=> (c1_1(a1566) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2620,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1535) | c1_1(a1535) | (~c3_1(a1535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1566) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1566)) | (~c2_1(a1566))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[2619])).
% 1.37/1.60 tff(2621,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1535) | c1_1(a1535) | (~c3_1(a1535)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1566) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[2620, 2618])).
% 1.37/1.60 tff(2622,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1535) | c1_1(a1535) | (~c3_1(a1535)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(2623,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1566) | c1_1(a1543) | c2_1(a1543) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c0_1(a1543)) | (~c0_1(a1566)) | (~c2_1(a1566))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 1.37/1.60 tff(2624,plain,
% 1.37/1.60 (~c0_1(a1566)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2623, 319, 2617, 2616, 2372, 2615, 2613, 2612, 2610, 277, 2609])).
% 1.37/1.60 tff(2625,plain,
% 1.37/1.60 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp1 | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2626,plain,
% 1.37/1.60 ((hskp11 | hskp1 | (~ndr1_0) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543))) <=> (hskp11 | hskp1 | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(2627,plain,
% 1.37/1.60 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[2626])).
% 1.37/1.60 tff(2628,plain,
% 1.37/1.60 (((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)))) <=> ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp1 | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[2627, 2625])).
% 1.37/1.60 tff(2629,plain,
% 1.37/1.60 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp1 | (~ndr1_0) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(2630,plain,
% 1.37/1.60 ((~![U: $i] : (hskp11 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp1 | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 1.37/1.60 tff(2631,plain,
% 1.37/1.60 (hskp11),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[2630, 319, 47, 2616, 2613, 2612, 1006])).
% 1.37/1.60 tff(2632,plain,
% 1.37/1.60 (~c1_1(a1553)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[942, 2631])).
% 1.37/1.60 tff(2633,plain,
% 1.37/1.60 (c2_1(a1553)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[958, 2631])).
% 1.37/1.60 tff(2634,plain,
% 1.37/1.60 (c0_1(a1553)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[966, 2631])).
% 1.37/1.60 tff(2635,plain,
% 1.37/1.60 (c3_1(a1566)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1428, 2614])).
% 1.37/1.60 tff(2636,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1566) | c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)) | (~c3_1(a1566)) | c0_1(a1566))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1566) | c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)) | (~c3_1(a1566)) | c0_1(a1566))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2637,plain,
% 1.37/1.61 (((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1566) | c1_1(a1566) | (~c3_1(a1566))) <=> (c1_1(a1566) | c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)) | (~c3_1(a1566)) | c0_1(a1566))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2638,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1566) | c1_1(a1566) | (~c3_1(a1566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1566) | c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)) | (~c3_1(a1566)) | c0_1(a1566)))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[2637])).
% 1.37/1.61 tff(2639,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1566) | c1_1(a1566) | (~c3_1(a1566)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1566) | c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)) | (~c3_1(a1566)) | c0_1(a1566))),
% 1.37/1.61 inference(transitivity,[status(thm)],[2638, 2636])).
% 1.37/1.61 tff(2640,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)) | c2_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c0_1(a1566) | c1_1(a1566) | (~c3_1(a1566)))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(2641,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1566) | c1_1(a1553) | c1_1(a1543) | c2_1(a1543) | (~ndr1_0) | (~c0_1(a1543)) | (~c0_1(a1553)) | (~c2_1(a1553)) | (~c3_1(a1566)) | c0_1(a1566)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2640, 2639])).
% 1.37/1.61 tff(2642,plain,
% 1.37/1.61 ($false),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2641, 319, 2635, 2634, 2633, 2616, 2615, 2632, 2613, 2612, 277, 2624])).
% 1.37/1.61 tff(2643,plain,(hskp10 | hskp1 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.37/1.61 tff(2644,plain,
% 1.37/1.61 (hskp10),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2643, 47, 12])).
% 1.37/1.61 tff(2645,plain,
% 1.37/1.61 (~c1_1(a1549)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[409, 2644])).
% 1.37/1.61 tff(2646,plain,
% 1.37/1.61 (c0_1(a1549)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[425, 2644])).
% 1.37/1.61 tff(2647,plain,
% 1.37/1.61 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | (~c2_1(a1549)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | (~c2_1(a1549)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2648,plain,
% 1.37/1.61 ((hskp14 | hskp1 | (~ndr1_0) | c1_1(a1549) | (~c0_1(a1549)) | (~c2_1(a1549))) <=> (hskp14 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | (~c2_1(a1549)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2649,plain,
% 1.37/1.61 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c1_1(a1549) | (~c0_1(a1549)) | (~c2_1(a1549)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | (~c2_1(a1549))))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[2648])).
% 1.37/1.61 tff(2650,plain,
% 1.37/1.61 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c1_1(a1549) | (~c0_1(a1549)) | (~c2_1(a1549)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | (~c2_1(a1549)))),
% 1.37/1.61 inference(transitivity,[status(thm)],[2649, 2647])).
% 1.37/1.61 tff(2651,plain,
% 1.37/1.61 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c1_1(a1549) | (~c0_1(a1549)) | (~c2_1(a1549)))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(2652,plain,
% 1.37/1.61 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp1 | c1_1(a1549) | (~ndr1_0) | (~c0_1(a1549)) | (~c2_1(a1549))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 1.37/1.61 tff(2653,plain,
% 1.37/1.61 (hskp14 | (~c2_1(a1549))),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2652, 319, 47, 2050, 2048, 2382])).
% 1.37/1.61 tff(2654,plain,
% 1.37/1.61 (~c2_1(a1549)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2653, 2323])).
% 1.37/1.61 tff(2655,plain,
% 1.37/1.61 (hskp11 | c2_1(a1549)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1012, 319, 47, 2050, 2048, 1006])).
% 1.37/1.61 tff(2656,plain,
% 1.37/1.61 (hskp11),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2655, 2654])).
% 1.37/1.61 tff(2657,plain,
% 1.37/1.61 (~c1_1(a1553)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[942, 2656])).
% 1.37/1.61 tff(2658,plain,
% 1.37/1.61 (c2_1(a1553)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[958, 2656])).
% 1.37/1.61 tff(2659,plain,
% 1.37/1.61 (c0_1(a1553)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[966, 2656])).
% 1.37/1.61 tff(2660,plain,
% 1.37/1.61 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | c1_1(a1553) | (~ndr1_0) | (~c0_1(a1553)) | (~c2_1(a1553)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp1 | c1_1(a1553) | (~ndr1_0) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2661,plain,
% 1.37/1.61 ((hskp14 | hskp1 | (~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553))) <=> (hskp14 | hskp1 | c1_1(a1553) | (~ndr1_0) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2662,plain,
% 1.37/1.61 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | c1_1(a1553) | (~ndr1_0) | (~c0_1(a1553)) | (~c2_1(a1553))))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[2661])).
% 1.37/1.61 tff(2663,plain,
% 1.37/1.61 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp1 | c1_1(a1553) | (~ndr1_0) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.37/1.61 inference(transitivity,[status(thm)],[2662, 2660])).
% 1.37/1.61 tff(2664,plain,
% 1.37/1.61 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp14 | hskp1 | (~ndr1_0) | c1_1(a1553) | (~c0_1(a1553)) | (~c2_1(a1553)))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(2665,plain,
% 1.37/1.61 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp14 | hskp1 | c1_1(a1553) | (~ndr1_0) | (~c0_1(a1553)) | (~c2_1(a1553))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 1.37/1.61 tff(2666,plain,
% 1.37/1.61 ($false),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2665, 319, 2323, 47, 2659, 2658, 2657, 2382])).
% 1.37/1.61 tff(2667,plain,(hskp14 | hskp1 | (~c0_1(a1549)) | c1_1(a1549)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.61 tff(2668,plain,
% 1.37/1.61 (hskp14),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2667, 47, 2646, 2645])).
% 1.37/1.61 tff(2669,plain,
% 1.37/1.61 (~c2_1(a1558)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[64, 2668])).
% 1.37/1.61 tff(2670,plain,
% 1.37/1.61 (c1_1(a1558)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[72, 2668])).
% 1.37/1.61 tff(2671,plain,
% 1.37/1.61 (c0_1(a1558)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[80, 2668])).
% 1.37/1.61 tff(2672,plain,
% 1.37/1.61 (~c3_1(a1558)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1519, 319, 2318, 2671, 2670, 2669, 46])).
% 1.37/1.61 tff(2673,plain,
% 1.37/1.61 (c3_1(a1549)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[417, 2644])).
% 1.37/1.61 tff(2674,plain,
% 1.37/1.61 (hskp22),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1304, 319, 2671, 2670, 2646, 2673, 2669, 2645, 111])).
% 1.37/1.61 tff(2675,plain,
% 1.37/1.61 (~c3_1(a1581)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1310, 2674])).
% 1.37/1.61 tff(2676,plain,
% 1.37/1.61 (~c1_1(a1581)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1316, 2674])).
% 1.37/1.61 tff(2677,plain,
% 1.37/1.61 (c0_1(a1581)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2067, 319, 2318, 2671, 2670, 2676, 2675, 462, 2672])).
% 1.37/1.61 tff(2678,plain,
% 1.37/1.61 (c2_1(a1581)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1324, 2674])).
% 1.37/1.61 tff(2679,plain,
% 1.37/1.61 (hskp20),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2191, 319, 2678, 2005, 2676, 1997, 2184, 1804, 2677])).
% 1.37/1.61 tff(2680,plain,
% 1.37/1.61 (~c2_1(a1574)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1764, 2679])).
% 1.37/1.61 tff(2681,plain,
% 1.37/1.61 (c0_1(a1565)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2199, 319, 2671, 2676, 2675, 1997, 2184, 2669, 35, 2672, 2677])).
% 1.37/1.61 tff(2682,plain,
% 1.37/1.61 (hskp21),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2216, 319, 2678, 2005, 2676, 1997, 2210, 2681, 2677])).
% 1.37/1.61 tff(2683,plain,
% 1.37/1.61 (~c1_1(a1575)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[438, 2682])).
% 1.37/1.61 tff(2684,plain,
% 1.37/1.61 (~c0_1(a1575)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[444, 2682])).
% 1.37/1.61 tff(2685,plain,
% 1.37/1.61 (c3_1(a1574)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1743, 2679])).
% 1.37/1.61 tff(2686,plain,
% 1.37/1.61 (c1_1(a1574)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1751, 2679])).
% 1.37/1.61 tff(2687,plain,
% 1.37/1.61 (c2_1(a1575)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[515, 2682])).
% 1.37/1.61 tff(2688,plain,
% 1.37/1.61 ($false),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2228, 319, 12, 2687, 2686, 2685, 2684, 2683, 2680, 22])).
% 1.37/1.61 tff(2689,plain,(hskp1 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.37/1.61 tff(2690,plain,
% 1.37/1.61 (hskp28),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2689, 47])).
% 1.37/1.61 tff(2691,plain,
% 1.37/1.61 (c1_1(a1542)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[546, 2690])).
% 1.37/1.61 tff(2692,plain,
% 1.37/1.61 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))),
% 1.37/1.61 inference(bind,[status(th)],[])).
% 1.37/1.61 tff(2693,plain,
% 1.37/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.37/1.61 inference(quant_intro,[status(thm)],[2692])).
% 1.37/1.61 tff(2694,plain,
% 1.37/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2695,plain,
% 1.37/1.61 (^[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))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c2_1(W) | c1_1(W))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c2_1(W) | c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))))),
% 1.37/1.61 inference(bind,[status(th)],[])).
% 1.37/1.61 tff(2696,plain,
% 1.37/1.61 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.37/1.61 inference(quant_intro,[status(thm)],[2695])).
% 1.37/1.61 tff(2697,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.37/1.61 tff(2698,plain,
% 1.37/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2697, 2696])).
% 1.37/1.61 tff(2699,plain,
% 1.37/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2698, 2694])).
% 1.37/1.61 tff(2700,plain,(
% 1.37/1.61 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.37/1.61 inference(skolemize,[status(sab)],[2699])).
% 1.37/1.61 tff(2701,plain,
% 1.37/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2700, 2693])).
% 1.37/1.61 tff(2702,plain,
% 1.37/1.61 (c3_1(a1542)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[530, 2690])).
% 1.37/1.61 tff(2703,plain,
% 1.37/1.61 (hskp10 | (~c0_1(a1542))),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1569, 319, 2691, 2702, 10])).
% 1.37/1.61 tff(2704,plain,
% 1.37/1.61 (~c0_1(a1542)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2703, 11])).
% 1.37/1.61 tff(2705,plain,
% 1.37/1.61 (c2_1(a1542)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[538, 2690])).
% 1.37/1.61 tff(2706,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2707,plain,
% 1.37/1.61 ((hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542))) <=> (hskp10 | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2708,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[2707])).
% 1.37/1.61 tff(2709,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.37/1.61 inference(transitivity,[status(thm)],[2708, 2706])).
% 1.37/1.61 tff(2710,plain,
% 1.37/1.61 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(2711,plain,
% 1.37/1.61 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2710, 2709])).
% 1.37/1.61 tff(2712,plain,
% 1.37/1.61 (~c0_1(a1565)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2711, 319, 11, 2691, 2705, 2005, 1997, 1121, 2704])).
% 1.37/1.61 tff(2713,plain,
% 1.37/1.61 (~c0_1(a1538)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2316, 2712])).
% 1.37/1.61 tff(2714,plain,
% 1.37/1.61 (hskp2),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2369, 2713, 47])).
% 1.37/1.61 tff(2715,plain,
% 1.37/1.61 (~c1_1(a1535)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[858, 2714])).
% 1.37/1.61 tff(2716,plain,
% 1.37/1.61 (c3_1(a1535)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[843, 2714])).
% 1.37/1.61 tff(2717,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1542)) | (~c3_1(a1542)) | c0_1(a1542))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1542)) | (~c3_1(a1542)) | c0_1(a1542))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2718,plain,
% 1.37/1.61 ((hskp29 | (~ndr1_0) | c0_1(a1542) | (~c1_1(a1542)) | (~c3_1(a1542)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (hskp29 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1542)) | (~c3_1(a1542)) | c0_1(a1542))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2719,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1542) | (~c1_1(a1542)) | (~c3_1(a1542)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1542)) | (~c3_1(a1542)) | c0_1(a1542)))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[2718])).
% 1.37/1.61 tff(2720,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1542) | (~c1_1(a1542)) | (~c3_1(a1542)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1542)) | (~c3_1(a1542)) | c0_1(a1542))),
% 1.37/1.61 inference(transitivity,[status(thm)],[2719, 2717])).
% 1.37/1.61 tff(2721,plain,
% 1.37/1.61 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1542) | (~c1_1(a1542)) | (~c3_1(a1542)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(2722,plain,
% 1.37/1.61 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c0_1(a1565) | (~c1_1(a1542)) | (~c3_1(a1542)) | c0_1(a1542)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2721, 2720])).
% 1.37/1.61 tff(2723,plain,
% 1.37/1.61 (hskp29),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2722, 319, 2691, 2702, 1997, 2184, 2126, 2712, 2704])).
% 1.37/1.61 tff(2724,plain,
% 1.37/1.61 (c2_1(a1544)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2140, 2723])).
% 1.37/1.61 tff(2725,plain,
% 1.37/1.61 (c1_1(a1544)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2148, 2723])).
% 1.37/1.61 tff(2726,plain,
% 1.37/1.61 (c0_1(a1544)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2156, 2723])).
% 1.37/1.61 tff(2727,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2728,plain,
% 1.37/1.61 (((~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c1_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538)) <=> (c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2729,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c1_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[2728])).
% 1.37/1.61 tff(2730,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c1_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.37/1.61 inference(transitivity,[status(thm)],[2729, 2727])).
% 1.37/1.61 tff(2731,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c1_1(a1535) | c0_1(a1535) | (~c3_1(a1535)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(2732,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | c1_1(a1535) | (~ndr1_0) | c0_1(a1535) | (~c3_1(a1535)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.37/1.61 tff(2733,plain,
% 1.37/1.61 (c0_1(a1535)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2732, 319, 2726, 2725, 2724, 2716, 2309, 2308, 2307, 2715, 2701])).
% 1.37/1.61 tff(2734,plain,
% 1.37/1.61 ($false),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[888, 319, 2691, 2705, 2702, 2716, 2715, 382, 2704, 2733])).
% 1.37/1.61 tff(2735,plain,(hskp10 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.37/1.61 tff(2736,plain,
% 1.37/1.61 (hskp10),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2735, 47])).
% 1.37/1.61 tff(2737,plain,
% 1.37/1.61 (c3_1(a1549)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[417, 2736])).
% 1.37/1.61 tff(2738,plain,
% 1.37/1.61 (c0_1(a1549)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[425, 2736])).
% 1.37/1.61 tff(2739,plain,
% 1.37/1.61 (~c1_1(a1549)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[409, 2736])).
% 1.37/1.61 tff(2740,plain,
% 1.37/1.61 (c0_1(a1542)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2052, 2739, 2705, 2702, 2738, 2737, 2691])).
% 1.37/1.61 tff(2741,plain,
% 1.37/1.61 (hskp14),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2667, 2738, 47, 2739])).
% 1.37/1.61 tff(2742,plain,
% 1.37/1.61 (~c2_1(a1558)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[64, 2741])).
% 1.37/1.61 tff(2743,plain,
% 1.37/1.61 (c1_1(a1558)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[72, 2741])).
% 1.37/1.61 tff(2744,plain,
% 1.37/1.61 (c0_1(a1558)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[80, 2741])).
% 1.37/1.61 tff(2745,plain,
% 1.37/1.61 (hskp22),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1304, 319, 2744, 2743, 2738, 2737, 2742, 2739, 111])).
% 1.37/1.61 tff(2746,plain,
% 1.37/1.61 (~c3_1(a1581)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1310, 2745])).
% 1.37/1.61 tff(2747,plain,
% 1.37/1.61 (~c1_1(a1581)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1316, 2745])).
% 1.37/1.61 tff(2748,plain,
% 1.37/1.61 (c2_1(a1581)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1324, 2745])).
% 1.37/1.61 tff(2749,plain,
% 1.37/1.61 (~c0_1(a1581)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1342, 319, 2691, 2705, 2702, 2748, 2747, 2746, 101])).
% 1.37/1.61 tff(2750,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c3_1(a1581) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | c0_1(a1581) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c3_1(a1581) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | c0_1(a1581) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2751,plain,
% 1.37/1.61 (((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c3_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538)) <=> (c3_1(a1581) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | c0_1(a1581) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2752,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c3_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c3_1(a1581) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | c0_1(a1581) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[2751])).
% 1.37/1.61 tff(2753,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c3_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c3_1(a1581) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | c0_1(a1581) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.61 inference(transitivity,[status(thm)],[2752, 2750])).
% 1.37/1.61 tff(2754,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c3_1(a1581) | c0_1(a1581) | (~c2_1(a1581)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(2755,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c3_1(a1581) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | c0_1(a1581) | (~c2_1(a1581)) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 1.37/1.61 tff(2756,plain,
% 1.37/1.61 (c0_1(a1538)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[2755, 319, 2691, 2705, 2748, 2746, 2309, 2308, 650, 2740, 2749])).
% 1.37/1.61 tff(2757,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1565)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2758,plain,
% 1.37/1.61 ((hskp16 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538))) <=> (hskp16 | c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1565)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(2759,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1565))))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[2758])).
% 1.37/1.62 tff(2760,plain,
% 1.37/1.62 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1565)))),
% 1.37/1.62 inference(transitivity,[status(thm)],[2759, 2757])).
% 1.37/1.62 tff(2761,plain,
% 1.37/1.62 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c2_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(2762,plain,
% 1.37/1.62 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a1565) | c3_1(a1565) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c1_1(a1565))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[2761, 2760])).
% 1.37/1.62 tff(2763,plain,
% 1.37/1.62 (hskp16 | (~c0_1(a1538))),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2762, 319, 2005, 1997, 2184, 2309, 2308, 1392])).
% 1.37/1.62 tff(2764,plain,
% 1.37/1.62 (hskp16),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2763, 2756])).
% 1.37/1.62 tff(2765,plain,
% 1.37/1.62 (~c1_1(a1566)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1449, 2764])).
% 1.37/1.62 tff(2766,plain,
% 1.37/1.62 (c2_1(a1566)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1436, 2764])).
% 1.37/1.62 tff(2767,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1566) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c0_1(a1566)) | (~c2_1(a1566)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1566) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c0_1(a1566)) | (~c2_1(a1566)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2768,plain,
% 1.37/1.62 (((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538))) <=> (c1_1(a1566) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c0_1(a1566)) | (~c2_1(a1566)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2769,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1566) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c0_1(a1566)) | (~c2_1(a1566)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542))))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[2768])).
% 1.37/1.62 tff(2770,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1566) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c0_1(a1566)) | (~c2_1(a1566)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.62 inference(transitivity,[status(thm)],[2769, 2767])).
% 1.37/1.62 tff(2771,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542)) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)) | c3_1(a1538) | c1_1(a1538) | (~c0_1(a1538)))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(2772,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1566) | c1_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c0_1(a1538)) | (~c0_1(a1566)) | (~c2_1(a1566)) | (~c1_1(a1542)) | (~c3_1(a1542)) | (~c0_1(a1542))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[2771, 2770])).
% 1.37/1.62 tff(2773,plain,
% 1.37/1.62 (~c0_1(a1566)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2772, 319, 2691, 2702, 2766, 2765, 2309, 2307, 363, 2756, 2740])).
% 1.37/1.62 tff(2774,plain,
% 1.37/1.62 (c3_1(a1566)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1428, 2764])).
% 1.37/1.62 tff(2775,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | c0_1(a1566) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | c0_1(a1566) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2776,plain,
% 1.37/1.62 (((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c1_1(a1566) | c0_1(a1566) | (~c3_1(a1566)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538)) <=> (c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | c0_1(a1566) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2777,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c1_1(a1566) | c0_1(a1566) | (~c3_1(a1566)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | c0_1(a1566) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[2776])).
% 1.37/1.62 tff(2778,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c1_1(a1566) | c0_1(a1566) | (~c3_1(a1566)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | c0_1(a1566) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542)))),
% 1.37/1.62 inference(transitivity,[status(thm)],[2777, 2775])).
% 1.37/1.62 tff(2779,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1542)) | (~c0_1(a1542)) | (~c2_1(a1542)) | c1_1(a1566) | c0_1(a1566) | (~c3_1(a1566)) | c3_1(a1538) | c2_1(a1538) | c1_1(a1538))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(2780,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1566) | c1_1(a1538) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | (~c3_1(a1566)) | c0_1(a1566) | (~c1_1(a1542)) | (~c2_1(a1542)) | (~c0_1(a1542))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 1.37/1.62 tff(2781,plain,
% 1.37/1.62 ($false),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2780, 319, 2691, 2705, 2774, 2765, 2309, 2308, 2307, 2701, 2773, 2740])).
% 1.37/1.62 tff(2782,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 1.37/1.62 tff(2783,plain,
% 1.37/1.62 (c0_1(a1534)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[236, 2782])).
% 1.37/1.62 tff(2784,plain,
% 1.37/1.62 (c2_1(a1534)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[222, 2782])).
% 1.37/1.62 tff(2785,plain,
% 1.37/1.62 (~c3_1(a1534)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[228, 2782])).
% 1.37/1.62 tff(2786,plain,
% 1.37/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c1_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1538))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2787,plain,
% 1.37/1.62 ((hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1538) | c1_1(a1538) | c0_1(a1538)) <=> (hskp5 | c1_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1538))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2788,plain,
% 1.37/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1538) | c1_1(a1538) | c0_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c1_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1538)))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[2787])).
% 1.37/1.62 tff(2789,plain,
% 1.37/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1538) | c1_1(a1538) | c0_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1538))),
% 1.37/1.62 inference(transitivity,[status(thm)],[2788, 2786])).
% 1.37/1.62 tff(2790,plain,
% 1.37/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1538) | c1_1(a1538) | c0_1(a1538))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(2791,plain,
% 1.37/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a1538) | c3_1(a1538) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c0_1(a1538)),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 1.37/1.62 tff(2792,plain,
% 1.37/1.62 (hskp5 | (~c1_1(a1534)) | c0_1(a1538)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2791, 319, 265, 2309, 2307, 264, 462])).
% 1.37/1.62 tff(2793,plain,
% 1.37/1.62 (~c1_1(a1534)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2792, 2394, 1082])).
% 1.37/1.62 tff(2794,plain,
% 1.37/1.62 (^[U: $i] : refl((hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 1.37/1.62 inference(bind,[status(th)],[])).
% 1.37/1.62 tff(2795,plain,
% 1.37/1.62 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.62 inference(quant_intro,[status(thm)],[2794])).
% 1.37/1.62 tff(2796,plain,
% 1.37/1.62 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2797,plain,
% 1.37/1.62 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp6) <=> ((hskp10 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp6))), rewrite(((hskp10 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp6) <=> (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp6) <=> (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 1.37/1.62 inference(bind,[status(th)],[])).
% 1.37/1.62 tff(2798,plain,
% 1.37/1.62 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp6) <=> ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.62 inference(quant_intro,[status(thm)],[2797])).
% 1.37/1.62 tff(2799,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.37/1.62 tff(2800,plain,
% 1.37/1.62 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[2799, 2798])).
% 1.37/1.62 tff(2801,plain,
% 1.37/1.62 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[2800, 2796])).
% 1.37/1.62 tff(2802,plain,(
% 1.37/1.62 ![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.62 inference(skolemize,[status(sab)],[2801])).
% 1.37/1.62 tff(2803,plain,
% 1.37/1.62 (![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[2802, 2795])).
% 1.37/1.62 tff(2804,plain,
% 1.37/1.62 (((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))) <=> ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp10 | hskp6 | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2805,plain,
% 1.37/1.62 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp10 | hskp6 | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(2806,plain,
% 1.37/1.62 ((~![U: $i] : (hskp10 | hskp6 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp10 | hskp6 | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[2805, 2804])).
% 1.37/1.62 tff(2807,plain,
% 1.37/1.62 (hskp10 | hskp6 | c1_1(a1534)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2806, 319, 265, 266, 2803])).
% 1.37/1.62 tff(2808,plain,
% 1.37/1.62 (hskp6),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2807, 2793, 11])).
% 1.37/1.62 tff(2809,plain,
% 1.37/1.62 (~c2_1(a1543)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[912, 2808])).
% 1.37/1.62 tff(2810,plain,
% 1.37/1.62 (c0_1(a1543)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[950, 2808])).
% 1.37/1.62 tff(2811,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2812,plain,
% 1.37/1.62 (((~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(2813,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565)))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[2812])).
% 1.37/1.62 tff(2814,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565))),
% 1.37/1.62 inference(transitivity,[status(thm)],[2813, 2811])).
% 1.37/1.62 tff(2815,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1543) | c3_1(a1543) | (~c0_1(a1543)) | c3_1(a1534) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(2816,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c2_1(a1543) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | c3_1(a1543) | (~c0_1(a1543)) | c0_1(a1565)),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[2815, 2814])).
% 1.37/1.62 tff(2817,plain,
% 1.37/1.62 (c3_1(a1543)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2816, 319, 2810, 265, 1997, 2184, 2809, 264, 35, 2793, 2395])).
% 1.37/1.62 tff(2818,plain,
% 1.37/1.62 ($false),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2421, 319, 2399, 2810, 1997, 2184, 2809, 2368, 2395, 2817])).
% 1.37/1.62 tff(2819,plain,(c2_1(a1545) | (~c0_1(a1534)) | c3_1(a1534) | hskp10 | (~c2_1(a1534)) | hskp5 | c0_1(a1545) | c3_1(a1545)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.62 tff(2820,plain,
% 1.37/1.62 (c2_1(a1545) | hskp10 | hskp5 | c0_1(a1545) | c3_1(a1545)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2819, 2785, 2784, 2783])).
% 1.37/1.62 tff(2821,plain,
% 1.37/1.62 (c2_1(a1545)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2820, 24, 11, 1082, 23])).
% 1.37/1.62 tff(2822,plain,
% 1.37/1.62 (c1_1(a1545) | (~c0_1(a1565))),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2456, 319, 1082, 2005, 2184, 23, 24, 462])).
% 1.37/1.62 tff(2823,plain,
% 1.37/1.62 (~c0_1(a1565)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[2822, 2571])).
% 1.37/1.62 tff(2824,plain,
% 1.37/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c1_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c1_1(a1545))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(2825,plain,
% 1.45/1.62 ((hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545)) <=> (hskp5 | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c1_1(a1545))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(2826,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c1_1(a1545)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[2825])).
% 1.45/1.62 tff(2827,plain,
% 1.45/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c1_1(a1545))),
% 1.45/1.62 inference(transitivity,[status(thm)],[2826, 2824])).
% 1.45/1.62 tff(2828,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c0_1(a1534)) | c3_1(a1545) | c1_1(a1545) | c0_1(a1545))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(2829,plain,
% 1.45/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | c1_1(a1545)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 1.45/1.62 tff(2830,plain,
% 1.45/1.62 ((~c1_1(a1534)) | c1_1(a1545)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[2829, 319, 1082, 2783, 23, 24, 2785, 462])).
% 1.45/1.62 tff(2831,plain,
% 1.45/1.62 (~c1_1(a1534)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[2830, 2571])).
% 1.45/1.62 tff(2832,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)) | c0_1(a1565))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(2833,plain,
% 1.45/1.62 (((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)) | c0_1(a1565))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(2834,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)) | c0_1(a1565)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[2833])).
% 1.45/1.62 tff(2835,plain,
% 1.45/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)) | c0_1(a1565))),
% 1.45/1.62 inference(transitivity,[status(thm)],[2834, 2832])).
% 1.45/1.62 tff(2836,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1534) | c3_1(a1534) | (~c0_1(a1534)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(2837,plain,
% 1.45/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c3_1(a1534) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1545)) | c0_1(a1565)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2836, 2835])).
% 1.45/1.63 tff(2838,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2837, 319, 611, 2783, 1997, 2184, 23, 24, 2785, 714, 2831, 2823])).
% 1.45/1.63 tff(2839,plain,(c1_1(a1545) | (~c2_1(a1545)) | c0_1(a1545) | c3_1(a1545) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(2840,plain,
% 1.45/1.63 (c1_1(a1545)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2839, 2821, 23, 24, 1082])).
% 1.45/1.63 tff(2841,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1565)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2842,plain,
% 1.45/1.63 ((hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545))) <=> (hskp10 | c2_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2843,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1565)) | (~c1_1(a1565))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[2842])).
% 1.45/1.63 tff(2844,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[2843, 2841])).
% 1.45/1.63 tff(2845,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1545) | (~c1_1(a1545)) | (~c2_1(a1545)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(2846,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | c0_1(a1545) | (~ndr1_0) | (~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1565)) | (~c1_1(a1565))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2845, 2844])).
% 1.45/1.63 tff(2847,plain,
% 1.45/1.63 ((~c2_1(a1545)) | (~c1_1(a1545)) | (~c0_1(a1565))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2846, 319, 11, 2005, 1997, 23, 1121])).
% 1.45/1.63 tff(2848,plain,
% 1.45/1.63 (~c0_1(a1565)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2847, 2840, 2821])).
% 1.45/1.63 tff(2849,plain,
% 1.45/1.63 (~c0_1(a1538)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2316, 2848])).
% 1.45/1.63 tff(2850,plain,
% 1.45/1.63 (hskp5 | (~c1_1(a1534)) | c0_1(a1538)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2791, 319, 2783, 2309, 2307, 2785, 462])).
% 1.45/1.63 tff(2851,plain,
% 1.45/1.63 (~c1_1(a1534)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2850, 2849, 1082])).
% 1.45/1.63 tff(2852,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2837, 319, 2821, 2783, 1997, 2184, 23, 24, 2785, 714, 2851, 2848])).
% 1.45/1.63 tff(2853,plain,(c3_1(a1545) | c0_1(a1545) | hskp5 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(2854,plain,
% 1.45/1.63 (c3_1(a1545)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2853, 1082, 23, 11])).
% 1.45/1.63 tff(2855,plain,
% 1.45/1.63 (~hskp7),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[180, 2854])).
% 1.45/1.63 tff(2856,plain,
% 1.45/1.63 (~c1_1(a1534)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2850, 2317, 1082])).
% 1.45/1.63 tff(2857,plain,
% 1.45/1.63 (hskp10 | hskp6 | c1_1(a1534)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2806, 319, 2783, 2784, 2803])).
% 1.45/1.63 tff(2858,plain,
% 1.45/1.63 (hskp6),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2857, 2856, 11])).
% 1.45/1.63 tff(2859,plain,
% 1.45/1.63 (~c2_1(a1543)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[912, 2858])).
% 1.45/1.63 tff(2860,plain,
% 1.45/1.63 (c0_1(a1543)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[950, 2858])).
% 1.45/1.63 tff(2861,plain,
% 1.45/1.63 (c3_1(a1543)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2816, 319, 2860, 2783, 1997, 2184, 2859, 2785, 35, 2856, 25])).
% 1.45/1.63 tff(2862,assumption,(~hskp7), introduced(assumption)).
% 1.45/1.63 tff(2863,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2421, 319, 2862, 2860, 1997, 2184, 2859, 2368, 25, 2861])).
% 1.45/1.63 tff(2864,plain,(c0_1(a1565) | hskp7 | hskp10 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(2865,plain,
% 1.45/1.63 (c0_1(a1565)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2864, 2855, 11, 1082])).
% 1.45/1.63 tff(2866,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a1565) | c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a1565) | c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2867,plain,
% 1.45/1.63 (((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545))) <=> (c3_1(a1565) | c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2868,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a1565) | c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[2867])).
% 1.45/1.63 tff(2869,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a1565) | c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[2868, 2866])).
% 1.45/1.63 tff(2870,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(2871,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a1565) | c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c0_1(a1565)) | (~c1_1(a1565))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 1.45/1.63 tff(2872,plain,
% 1.45/1.63 ((~c3_1(a1545)) | c1_1(a1545) | (~c0_1(a1565))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2871, 319, 2005, 2783, 2784, 2184, 23, 2785, 393])).
% 1.45/1.63 tff(2873,plain,
% 1.45/1.63 (c1_1(a1545)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2872, 2865, 2854])).
% 1.45/1.63 tff(2874,plain,
% 1.45/1.63 (c0_1(a1538)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2357, 2865, 1082])).
% 1.45/1.63 tff(2875,plain,
% 1.45/1.63 (hskp16),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2763, 2874])).
% 1.45/1.63 tff(2876,plain,
% 1.45/1.63 (~c1_1(a1566)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1449, 2875])).
% 1.45/1.63 tff(2877,plain,
% 1.45/1.63 (~c2_1(a1545)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2847, 2873, 2865])).
% 1.45/1.63 tff(2878,plain,
% 1.45/1.63 (c2_1(a1566)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1436, 2875])).
% 1.45/1.63 tff(2879,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a1545) | c1_1(a1566) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | c0_1(a1566) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a1545) | c1_1(a1566) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2880,plain,
% 1.45/1.63 ((hskp28 | (~ndr1_0) | c2_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)) | c1_1(a1566) | c0_1(a1566) | (~c2_1(a1566))) <=> (hskp28 | c2_1(a1545) | c1_1(a1566) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2881,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)) | c1_1(a1566) | c0_1(a1566) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a1545) | c1_1(a1566) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | c0_1(a1566) | (~c2_1(a1566))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[2880])).
% 1.45/1.63 tff(2882,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)) | c1_1(a1566) | c0_1(a1566) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a1545) | c1_1(a1566) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[2881, 2879])).
% 1.45/1.63 tff(2883,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)) | c1_1(a1566) | c0_1(a1566) | (~c2_1(a1566)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(2884,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a1545) | c1_1(a1566) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | c0_1(a1566) | (~c2_1(a1566))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 1.45/1.63 tff(2885,plain,
% 1.45/1.63 (c0_1(a1566)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2884, 319, 12, 2878, 2877, 2876, 2854, 22, 2873])).
% 1.45/1.63 tff(2886,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | c1_1(a1566) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1566)) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp21 | c1_1(a1566) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2887,plain,
% 1.45/1.63 ((hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566))) <=> (hskp21 | c1_1(a1566) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2888,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | c1_1(a1566) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1566)) | (~c2_1(a1566))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[2887])).
% 1.45/1.63 tff(2889,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp21 | c1_1(a1566) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[2888, 2886])).
% 1.45/1.63 tff(2890,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1566) | (~c0_1(a1566)) | (~c2_1(a1566)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(2891,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp21 | c1_1(a1566) | c2_1(a1565) | (~ndr1_0) | (~c0_1(a1565)) | (~c1_1(a1565)) | (~c0_1(a1566)) | (~c2_1(a1566))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2890, 2889])).
% 1.45/1.63 tff(2892,plain,
% 1.45/1.63 (hskp21 | (~c0_1(a1566))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2891, 319, 2878, 2005, 2876, 1997, 2210, 2865])).
% 1.45/1.63 tff(2893,plain,
% 1.45/1.63 (hskp21),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2892, 2885])).
% 1.45/1.63 tff(2894,plain,
% 1.45/1.63 (~c1_1(a1575)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[438, 2893])).
% 1.45/1.63 tff(2895,plain,
% 1.45/1.63 (~c0_1(a1575)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[444, 2893])).
% 1.45/1.63 tff(2896,plain,
% 1.45/1.63 (c2_1(a1575)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[515, 2893])).
% 1.45/1.63 tff(2897,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a1545) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | (~c2_1(a1575)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a1545) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | (~c2_1(a1575)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2898,plain,
% 1.45/1.63 ((hskp28 | (~ndr1_0) | c2_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575))) <=> (hskp28 | c2_1(a1545) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | (~c2_1(a1575)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2899,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a1545) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | (~c2_1(a1575))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[2898])).
% 1.45/1.63 tff(2900,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a1545) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | (~c2_1(a1575)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[2899, 2897])).
% 1.45/1.63 tff(2901,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1545) | (~c1_1(a1545)) | (~c3_1(a1545)) | c1_1(a1575) | c0_1(a1575) | (~c2_1(a1575)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(2902,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a1545) | c0_1(a1575) | c1_1(a1575) | (~c3_1(a1545)) | (~ndr1_0) | (~c1_1(a1545)) | (~c2_1(a1575))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 1.45/1.63 tff(2903,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2902, 319, 12, 2896, 2877, 2895, 2894, 2854, 22, 2873])).
% 1.45/1.63 tff(2904,plain,(hskp5 | hskp28 | hskp10 | c0_1(a1545)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(2905,plain,
% 1.45/1.63 (hskp5),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2904, 23, 11, 12])).
% 1.45/1.63 tff(2906,plain,
% 1.45/1.63 (~c0_1(a1539)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[474, 2905])).
% 1.45/1.63 tff(2907,plain,
% 1.45/1.63 (c3_1(a1539)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[482, 2905])).
% 1.45/1.63 tff(2908,plain,
% 1.45/1.63 (c1_1(a1539)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[490, 2905])).
% 1.45/1.63 tff(2909,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | c2_1(a1565) | c3_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c2_1(a1565) | c3_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)) | c0_1(a1565))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2910,plain,
% 1.45/1.63 ((hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565)) <=> (hskp29 | c2_1(a1565) | c3_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)) | c0_1(a1565))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2911,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | c2_1(a1565) | c3_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)) | c0_1(a1565)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[2910])).
% 1.45/1.63 tff(2912,plain,
% 1.45/1.63 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c2_1(a1565) | c3_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)) | c0_1(a1565))),
% 1.45/1.63 inference(transitivity,[status(thm)],[2911, 2909])).
% 1.45/1.63 tff(2913,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1565) | c2_1(a1565) | c0_1(a1565))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(2914,plain,
% 1.45/1.63 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c2_1(a1565) | c3_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | (~c1_1(a1539)) | c0_1(a1565)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2913, 2912])).
% 1.45/1.63 tff(2915,plain,
% 1.45/1.63 (hskp29 | c0_1(a1565)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2914, 319, 2908, 2907, 1997, 2184, 2906, 2126])).
% 1.45/1.63 tff(2916,plain,
% 1.45/1.63 (hskp29),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2915, 25])).
% 1.45/1.63 tff(2917,plain,
% 1.45/1.63 (c2_1(a1544)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2140, 2916])).
% 1.45/1.63 tff(2918,plain,
% 1.45/1.63 (c1_1(a1544)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2148, 2916])).
% 1.45/1.63 tff(2919,plain,
% 1.45/1.63 (c0_1(a1544)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2156, 2916])).
% 1.45/1.63 tff(2920,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2921,plain,
% 1.45/1.63 (((~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538)) <=> (c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2922,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | (c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[2921])).
% 1.45/1.63 tff(2923,plain,
% 1.45/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[2922, 2920])).
% 1.45/1.63 tff(2924,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | ((~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)) | c3_1(a1545) | c0_1(a1545) | (~c2_1(a1545)) | c2_1(a1538) | c0_1(a1538) | c1_1(a1538))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(2925,plain,
% 1.45/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c1_1(W))) | c0_1(a1545) | c3_1(a1545) | c1_1(a1538) | c2_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c2_1(a1545)) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2924, 2923])).
% 1.45/1.63 tff(2926,plain,
% 1.45/1.63 (~c2_1(a1545)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2925, 319, 2919, 2918, 2917, 23, 24, 2309, 2308, 650, 2317])).
% 1.45/1.63 tff(2927,plain,
% 1.45/1.63 (~hskp7),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[194, 2926])).
% 1.45/1.63 tff(2928,plain,
% 1.45/1.63 (^[U: $i] : refl((hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(2929,plain,
% 1.45/1.63 (![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[2928])).
% 1.45/1.63 tff(2930,plain,
% 1.45/1.63 (![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(2931,plain,
% 1.45/1.63 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp31) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp31))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp31) | hskp7) <=> ((hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp7))), rewrite(((hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp7) <=> (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp31) | hskp7) <=> (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))))),
% 1.45/1.63 inference(bind,[status(th)],[])).
% 1.45/1.63 tff(2932,plain,
% 1.45/1.63 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp31) | hskp7) <=> ![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.45/1.63 inference(quant_intro,[status(thm)],[2931])).
% 1.45/1.63 tff(2933,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp31) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.45/1.63 tff(2934,plain,
% 1.45/1.63 (![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2933, 2932])).
% 1.45/1.63 tff(2935,plain,
% 1.45/1.63 (![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2934, 2930])).
% 1.45/1.63 tff(2936,plain,(
% 1.45/1.63 ![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.45/1.63 inference(skolemize,[status(sab)],[2935])).
% 1.45/1.63 tff(2937,plain,
% 1.45/1.63 (![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[2936, 2929])).
% 1.45/1.63 tff(2938,plain,
% 1.45/1.63 (((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp31 | hskp7 | (~ndr1_0) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))) <=> ((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp31 | hskp7 | (~ndr1_0) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2939,plain,
% 1.45/1.64 ((hskp31 | hskp7 | (~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544))) <=> (hskp31 | hskp7 | (~ndr1_0) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2940,plain,
% 1.45/1.64 (((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)))) <=> ((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp31 | hskp7 | (~ndr1_0) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[2939])).
% 1.45/1.64 tff(2941,plain,
% 1.45/1.64 (((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)))) <=> ((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp31 | hskp7 | (~ndr1_0) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[2940, 2938])).
% 1.45/1.64 tff(2942,plain,
% 1.45/1.64 ((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(a1544)) | (~c0_1(a1544)) | (~c2_1(a1544)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(2943,plain,
% 1.45/1.64 ((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp31 | hskp7 | (~ndr1_0) | (~c2_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 1.45/1.64 tff(2944,plain,
% 1.45/1.64 (hskp31 | hskp7),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2943, 319, 2919, 2918, 2917, 2937])).
% 1.45/1.64 tff(2945,plain,
% 1.45/1.64 (hskp31),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2944, 2927])).
% 1.45/1.64 tff(2946,plain,
% 1.45/1.64 (c3_1(a1562)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1707, 2945])).
% 1.45/1.64 tff(2947,plain,
% 1.45/1.64 (c0_1(a1562)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1723, 2945])).
% 1.45/1.64 tff(2948,plain,
% 1.45/1.64 (~c1_1(a1562)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1792, 319, 11, 2947, 2946, 10])).
% 1.45/1.64 tff(2949,plain,
% 1.45/1.64 (c2_1(a1562)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1715, 2945])).
% 1.45/1.64 tff(2950,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2951,plain,
% 1.45/1.64 (((~ndr1_0) | (~c1_1(a1539)) | (~c3_1(a1539)) | (~c2_1(a1539)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c2_1(a1562)) | (~c0_1(a1562))) <=> (c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2952,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1539)) | (~c3_1(a1539)) | (~c2_1(a1539)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c2_1(a1562)) | (~c0_1(a1562)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[2951])).
% 1.45/1.64 tff(2953,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1539)) | (~c3_1(a1539)) | (~c2_1(a1539)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c2_1(a1562)) | (~c0_1(a1562)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[2952, 2950])).
% 1.45/1.64 tff(2954,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1539)) | (~c3_1(a1539)) | (~c2_1(a1539)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c2_1(a1562)) | (~c0_1(a1562)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(2955,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c3_1(a1539)) | (~c2_1(a1539)) | (~c1_1(a1539))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 1.45/1.64 tff(2956,plain,
% 1.45/1.64 (~c2_1(a1539)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2955, 319, 2947, 2949, 2908, 2907, 2783, 2784, 2785, 101, 2948])).
% 1.45/1.64 tff(2957,plain,
% 1.45/1.64 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2958,plain,
% 1.45/1.64 ((hskp10 | (~ndr1_0) | (~c1_1(a1544)) | (~c3_1(a1544)) | (~c0_1(a1544))) <=> (hskp10 | (~ndr1_0) | (~c3_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2959,plain,
% 1.45/1.64 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1544)) | (~c3_1(a1544)) | (~c0_1(a1544)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c3_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[2958])).
% 1.45/1.64 tff(2960,plain,
% 1.45/1.64 (((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1544)) | (~c3_1(a1544)) | (~c0_1(a1544)))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[2959, 2957])).
% 1.45/1.64 tff(2961,plain,
% 1.45/1.64 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | (~ndr1_0) | (~c1_1(a1544)) | (~c3_1(a1544)) | (~c0_1(a1544)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(2962,plain,
% 1.45/1.64 ((~![U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | (~ndr1_0) | (~c3_1(a1544)) | (~c1_1(a1544)) | (~c0_1(a1544))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[2961, 2960])).
% 1.45/1.64 tff(2963,plain,
% 1.45/1.64 (~c3_1(a1544)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2962, 319, 11, 2919, 2918, 10])).
% 1.45/1.64 tff(2964,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1544)) | (~c1_1(a1544)) | c3_1(a1544))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1544)) | (~c1_1(a1544)) | c3_1(a1544))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2965,plain,
% 1.45/1.64 ((hskp21 | (~ndr1_0) | c3_1(a1544) | (~c1_1(a1544)) | (~c2_1(a1544)) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562))) <=> (hskp21 | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1544)) | (~c1_1(a1544)) | c3_1(a1544))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2966,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1544) | (~c1_1(a1544)) | (~c2_1(a1544)) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1544)) | (~c1_1(a1544)) | c3_1(a1544)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[2965])).
% 1.45/1.64 tff(2967,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1544) | (~c1_1(a1544)) | (~c2_1(a1544)) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1544)) | (~c1_1(a1544)) | c3_1(a1544))),
% 1.45/1.64 inference(transitivity,[status(thm)],[2966, 2964])).
% 1.45/1.64 tff(2968,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1544) | (~c1_1(a1544)) | (~c2_1(a1544)) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(2969,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c2_1(a1544)) | (~c1_1(a1544)) | c3_1(a1544)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[2968, 2967])).
% 1.45/1.64 tff(2970,plain,
% 1.45/1.64 (hskp21),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2969, 319, 2947, 2946, 2918, 2917, 403, 2963, 2948])).
% 1.45/1.64 tff(2971,plain,
% 1.45/1.64 (~c1_1(a1575)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[438, 2970])).
% 1.45/1.64 tff(2972,plain,
% 1.45/1.64 (~c0_1(a1575)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[444, 2970])).
% 1.45/1.64 tff(2973,plain,
% 1.45/1.64 (c2_1(a1575)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[515, 2970])).
% 1.45/1.64 tff(2974,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[522, 319, 12, 2973, 2908, 2907, 2972, 2971, 22, 2956])).
% 1.45/1.64 tff(2975,plain,(c0_1(a1565) | hskp28 | hskp10 | c0_1(a1545) | c3_1(a1545)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(2976,plain,
% 1.45/1.64 (c0_1(a1565)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2975, 24, 11, 23, 12])).
% 1.45/1.64 tff(2977,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c0_1(a1565)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2978,plain,
% 1.45/1.64 ((hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539))) <=> (hskp10 | c2_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2979,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | c2_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c0_1(a1565)) | (~c1_1(a1565))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[2978])).
% 1.45/1.64 tff(2980,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[2979, 2977])).
% 1.45/1.64 tff(2981,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c0_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1539)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(2982,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp10 | c2_1(a1565) | c0_1(a1539) | (~ndr1_0) | (~c2_1(a1539)) | (~c1_1(a1539)) | (~c0_1(a1565)) | (~c1_1(a1565))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[2981, 2980])).
% 1.45/1.64 tff(2983,plain,
% 1.45/1.64 ((~c2_1(a1539)) | (~c0_1(a1565))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2982, 319, 11, 2005, 2908, 1997, 2906, 1121])).
% 1.45/1.64 tff(2984,plain,
% 1.45/1.64 (~c2_1(a1539)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2983, 2976])).
% 1.45/1.64 tff(2985,assumption,(~c2_1(a1539)), introduced(assumption)).
% 1.45/1.64 tff(2986,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2987,plain,
% 1.45/1.64 ((hskp6 | (~ndr1_0) | c2_1(a1539) | c0_1(a1539) | (~c3_1(a1539)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545)) <=> (hskp6 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2988,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1539) | c0_1(a1539) | (~c3_1(a1539)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[2987])).
% 1.45/1.64 tff(2989,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1539) | c0_1(a1539) | (~c3_1(a1539)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539))),
% 1.45/1.64 inference(transitivity,[status(thm)],[2988, 2986])).
% 1.45/1.64 tff(2990,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1539) | c0_1(a1539) | (~c3_1(a1539)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(2991,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c0_1(a1539) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 1.45/1.64 tff(2992,plain,
% 1.45/1.64 (hskp6 | c2_1(a1545)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2991, 319, 1140, 23, 24, 977, 899, 2985])).
% 1.45/1.64 tff(2993,plain,
% 1.45/1.64 (hskp6),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2992, 2386])).
% 1.45/1.64 tff(2994,plain,
% 1.45/1.64 (~c2_1(a1543)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[912, 2993])).
% 1.45/1.64 tff(2995,plain,
% 1.45/1.64 (c0_1(a1543)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[950, 2993])).
% 1.45/1.64 tff(2996,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2997,plain,
% 1.45/1.64 ((hskp7 | (~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545)) <=> (hskp7 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(2998,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[2997])).
% 1.45/1.64 tff(2999,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[2998, 2996])).
% 1.45/1.64 tff(3000,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a1543) | (~c3_1(a1543)) | (~c0_1(a1543)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(3001,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | c2_1(a1543) | (~ndr1_0) | (~c3_1(a1543)) | (~c0_1(a1543))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 1.45/1.64 tff(3002,plain,
% 1.45/1.64 (~c3_1(a1543)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3001, 319, 2399, 2386, 2995, 23, 24, 2994, 2368])).
% 1.45/1.64 tff(3003,assumption,(c0_1(a1565)), introduced(assumption)).
% 1.45/1.64 tff(3004,plain,
% 1.45/1.64 (~c1_1(a1543)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[918, 2993])).
% 1.45/1.64 tff(3005,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1545) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c0_1(a1565)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1545) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c0_1(a1565)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(3006,plain,
% 1.45/1.64 (((~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c0_1(a1565)) | c3_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545)) <=> (c2_1(a1545) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c0_1(a1565)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(3007,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c0_1(a1565)) | c3_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a1545) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c0_1(a1565))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[3006])).
% 1.45/1.64 tff(3008,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c0_1(a1565)) | c3_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1545) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c0_1(a1565)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[3007, 3005])).
% 1.45/1.64 tff(3009,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c0_1(a1565)) | c3_1(a1543) | c1_1(a1543) | (~c0_1(a1543)) | c3_1(a1545) | c2_1(a1545) | c0_1(a1545))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(3010,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a1545) | c2_1(a1565) | c3_1(a1565) | c0_1(a1545) | c3_1(a1545) | c1_1(a1543) | (~ndr1_0) | c3_1(a1543) | (~c0_1(a1543)) | (~c0_1(a1565))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 1.45/1.64 tff(3011,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3010, 319, 2386, 2995, 1997, 2184, 23, 24, 3004, 35, 3003, 3002])).
% 1.45/1.64 tff(3012,plain,(c2_1(a1545) | c0_1(a1545) | c3_1(a1545) | (~c0_1(a1565)) | (~c3_1(a1539)) | c0_1(a1539) | c2_1(a1539)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(3013,plain,
% 1.45/1.64 (c2_1(a1545)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3012, 24, 23, 2976, 2907, 2906, 2984])).
% 1.45/1.64 tff(3014,plain,
% 1.45/1.64 (~c1_1(a1545)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2847, 3013, 2976])).
% 1.45/1.64 tff(3015,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c0_1(a1545) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1545)) | c1_1(a1545))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c0_1(a1545) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1545)) | c1_1(a1545))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(3016,plain,
% 1.45/1.64 ((hskp28 | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c1_1(a1545) | c0_1(a1545) | (~c2_1(a1545))) <=> (hskp28 | c0_1(a1545) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1545)) | c1_1(a1545))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(3017,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c1_1(a1545) | c0_1(a1545) | (~c2_1(a1545)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c0_1(a1545) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1545)) | c1_1(a1545)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[3016])).
% 1.45/1.64 tff(3018,plain,
% 1.45/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c1_1(a1545) | c0_1(a1545) | (~c2_1(a1545)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c0_1(a1545) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1545)) | c1_1(a1545))),
% 1.45/1.64 inference(transitivity,[status(thm)],[3017, 3015])).
% 1.45/1.64 tff(3019,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c1_1(a1545) | c0_1(a1545) | (~c2_1(a1545)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(3020,plain,
% 1.45/1.64 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c0_1(a1545) | (~ndr1_0) | (~c3_1(a1539)) | c2_1(a1539) | (~c1_1(a1539)) | (~c2_1(a1545)) | c1_1(a1545)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[3019, 3018])).
% 1.45/1.64 tff(3021,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3020, 319, 12, 3013, 2908, 2907, 23, 22, 3014, 2984])).
% 1.45/1.64 tff(3022,plain,(c3_1(a1545) | hskp28 | c0_1(a1545) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(3023,plain,
% 1.45/1.64 (c3_1(a1545)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3022, 23, 12, 11])).
% 1.45/1.64 tff(3024,assumption,(hskp29), introduced(assumption)).
% 1.45/1.64 tff(3025,plain,
% 1.45/1.64 (c1_1(a1544)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2148, 3024])).
% 1.45/1.64 tff(3026,plain,
% 1.45/1.64 (c0_1(a1544)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2156, 3024])).
% 1.45/1.64 tff(3027,plain,
% 1.45/1.64 (~c3_1(a1544)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2962, 319, 11, 3026, 3025, 10])).
% 1.45/1.64 tff(3028,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c1_1(a1544)) | c3_1(a1544) | (~c0_1(a1544)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c1_1(a1544)) | c3_1(a1544) | (~c0_1(a1544)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(3029,plain,
% 1.45/1.64 (((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1544) | (~c1_1(a1544)) | (~c0_1(a1544)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545))) <=> (c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c1_1(a1544)) | c3_1(a1544) | (~c0_1(a1544)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(3030,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1544) | (~c1_1(a1544)) | (~c0_1(a1544)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c1_1(a1544)) | c3_1(a1544) | (~c0_1(a1544))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[3029])).
% 1.45/1.64 tff(3031,plain,
% 1.45/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1544) | (~c1_1(a1544)) | (~c0_1(a1544)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c1_1(a1544)) | c3_1(a1544) | (~c0_1(a1544)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[3030, 3028])).
% 1.45/1.64 tff(3032,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c3_1(a1544) | (~c1_1(a1544)) | (~c0_1(a1544)) | c0_1(a1545) | c1_1(a1545) | (~c3_1(a1545)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(3033,plain,
% 1.45/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1545) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1545) | (~c1_1(a1544)) | c3_1(a1544) | (~c0_1(a1544))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[3032, 3031])).
% 1.45/1.65 tff(3034,plain,
% 1.45/1.65 (c1_1(a1545)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3033, 319, 3026, 3025, 2783, 2784, 23, 3023, 2785, 393, 3027])).
% 1.45/1.65 tff(3035,plain,
% 1.45/1.65 (c2_1(a1544)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2140, 3024])).
% 1.45/1.65 tff(3036,plain,
% 1.45/1.65 (~hskp7),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[180, 3023])).
% 1.45/1.65 tff(3037,plain,
% 1.45/1.65 (hskp31),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2943, 319, 3036, 3026, 3025, 3035, 2937])).
% 1.45/1.65 tff(3038,plain,
% 1.45/1.65 (c3_1(a1562)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1707, 3037])).
% 1.45/1.65 tff(3039,plain,
% 1.45/1.65 (c0_1(a1562)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1723, 3037])).
% 1.45/1.65 tff(3040,plain,
% 1.45/1.65 (~c1_1(a1562)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1792, 319, 11, 3039, 3038, 10])).
% 1.45/1.65 tff(3041,plain,
% 1.45/1.65 (hskp21),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2969, 319, 3039, 3038, 3025, 3035, 403, 3027, 3040])).
% 1.45/1.65 tff(3042,plain,
% 1.45/1.65 (~c1_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[438, 3041])).
% 1.45/1.65 tff(3043,plain,
% 1.45/1.65 (~c0_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[444, 3041])).
% 1.45/1.65 tff(3044,plain,
% 1.45/1.65 (c2_1(a1562)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1715, 3037])).
% 1.45/1.65 tff(3045,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | (~c1_1(a1545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | (~c1_1(a1545)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3046,plain,
% 1.45/1.65 (((~ndr1_0) | (~c1_1(a1545)) | (~c3_1(a1545)) | (~c2_1(a1545)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c2_1(a1562)) | (~c0_1(a1562))) <=> ((~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | (~c1_1(a1545)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3047,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1545)) | (~c3_1(a1545)) | (~c2_1(a1545)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c2_1(a1562)) | (~c0_1(a1562)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | (~c1_1(a1545))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[3046])).
% 1.45/1.65 tff(3048,plain,
% 1.45/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1545)) | (~c3_1(a1545)) | (~c2_1(a1545)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c2_1(a1562)) | (~c0_1(a1562)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | (~c1_1(a1545)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[3047, 3045])).
% 1.45/1.65 tff(3049,plain,
% 1.45/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a1545)) | (~c3_1(a1545)) | (~c2_1(a1545)) | c3_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c2_1(a1562)) | (~c0_1(a1562)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(3050,plain,
% 1.45/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (~c3_1(a1545)) | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c2_1(a1545)) | (~c1_1(a1545))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[3049, 3048])).
% 1.45/1.65 tff(3051,plain,
% 1.45/1.65 (~c2_1(a1545)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3050, 319, 3039, 3044, 2783, 2784, 3023, 2785, 101, 3034, 3040])).
% 1.45/1.65 tff(3052,plain,
% 1.45/1.65 (c2_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[515, 3041])).
% 1.45/1.65 tff(3053,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2902, 319, 12, 3052, 3051, 3043, 3042, 3023, 22, 3034])).
% 1.45/1.65 tff(3054,plain,((~hskp29) | hskp28 | hskp10 | c0_1(a1545)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(3055,plain,
% 1.45/1.65 (~hskp29),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3054, 23, 11, 12])).
% 1.45/1.65 tff(3056,plain,
% 1.45/1.65 (c0_1(a1565)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2915, 3055])).
% 1.45/1.65 tff(3057,plain,
% 1.45/1.65 (c1_1(a1545)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2872, 3056, 3023])).
% 1.45/1.65 tff(3058,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | c0_1(a1539) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1539)) | (~c1_1(a1539)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c0_1(a1539) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3059,plain,
% 1.45/1.65 ((hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1538) | c2_1(a1538) | c0_1(a1538)) <=> (hskp29 | c0_1(a1539) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3060,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1538) | c2_1(a1538) | c0_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | c0_1(a1539) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1539)) | (~c1_1(a1539))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[3059])).
% 1.45/1.65 tff(3061,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1538) | c2_1(a1538) | c0_1(a1538))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c0_1(a1539) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1539)) | (~c1_1(a1539)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[3060, 3058])).
% 1.45/1.65 tff(3062,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp29 | (~ndr1_0) | c0_1(a1539) | (~c1_1(a1539)) | (~c3_1(a1539)) | c3_1(a1538) | c2_1(a1538) | c0_1(a1538))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(3063,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp29 | c0_1(a1539) | c2_1(a1538) | c3_1(a1538) | (~ndr1_0) | c0_1(a1538) | (~c3_1(a1539)) | (~c1_1(a1539))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 1.45/1.65 tff(3064,plain,
% 1.45/1.65 (hskp29 | c0_1(a1538)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3063, 319, 2908, 2907, 2906, 2308, 2307, 2126])).
% 1.45/1.65 tff(3065,plain,
% 1.45/1.65 (c0_1(a1538)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3064, 3055])).
% 1.45/1.65 tff(3066,plain,
% 1.45/1.65 (hskp16),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2763, 3065])).
% 1.45/1.65 tff(3067,plain,
% 1.45/1.65 (~c1_1(a1566)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1449, 3066])).
% 1.45/1.65 tff(3068,plain,
% 1.45/1.65 (~c2_1(a1545)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2847, 3056, 3057])).
% 1.45/1.65 tff(3069,plain,
% 1.45/1.65 (c2_1(a1566)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1436, 3066])).
% 1.45/1.65 tff(3070,plain,
% 1.45/1.65 (c0_1(a1566)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2884, 319, 12, 3069, 3068, 3067, 3023, 22, 3057])).
% 1.45/1.65 tff(3071,plain,
% 1.45/1.65 (hskp21 | (~c0_1(a1566))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2891, 319, 3069, 2005, 3067, 1997, 2210, 3056])).
% 1.45/1.65 tff(3072,plain,
% 1.45/1.65 (hskp21),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3071, 3070])).
% 1.45/1.65 tff(3073,plain,
% 1.45/1.65 (~c1_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[438, 3072])).
% 1.45/1.65 tff(3074,plain,
% 1.45/1.65 (~c0_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[444, 3072])).
% 1.45/1.65 tff(3075,plain,
% 1.45/1.65 (c2_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[515, 3072])).
% 1.45/1.65 tff(3076,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2902, 319, 12, 3075, 3068, 3074, 3073, 3023, 22, 3057])).
% 1.45/1.65 tff(3077,plain,(c0_1(a1545) | hskp28 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(3078,plain,
% 1.45/1.65 (c0_1(a1545)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3077, 12, 11])).
% 1.45/1.65 tff(3079,plain,
% 1.45/1.65 (~hskp7),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[186, 3078])).
% 1.45/1.65 tff(3080,plain,
% 1.45/1.65 (((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)))) <=> ((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp31 | hskp7 | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3081,plain,
% 1.45/1.65 ((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(3082,plain,
% 1.45/1.65 ((~![U: $i] : (hskp31 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp31 | hskp7 | (~ndr1_0) | (~c1_1(a1534)) | (~c0_1(a1534)) | (~c2_1(a1534))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[3081, 3080])).
% 1.45/1.65 tff(3083,plain,
% 1.45/1.65 (hskp31 | hskp7 | (~c1_1(a1534))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3082, 319, 2783, 2784, 2937])).
% 1.45/1.65 tff(3084,plain,
% 1.45/1.65 (hskp31),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3083, 383, 3079])).
% 1.45/1.65 tff(3085,plain,
% 1.45/1.65 (c3_1(a1562)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1707, 3084])).
% 1.45/1.65 tff(3086,plain,
% 1.45/1.65 (c0_1(a1562)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1723, 3084])).
% 1.45/1.65 tff(3087,plain,
% 1.45/1.65 (~c1_1(a1562)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1792, 319, 11, 3086, 3085, 10])).
% 1.45/1.65 tff(3088,plain,
% 1.45/1.65 (c2_1(a1562)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1715, 3084])).
% 1.45/1.65 tff(3089,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c1_1(a1565)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3090,plain,
% 1.45/1.65 ((hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562))) <=> (hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c1_1(a1565)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3091,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c1_1(a1565))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[3090])).
% 1.45/1.65 tff(3092,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c1_1(a1565)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[3091, 3089])).
% 1.45/1.65 tff(3093,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(3094,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | c1_1(a1562) | (~c0_1(a1562)) | (~c2_1(a1562)) | (~c1_1(a1565))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[3093, 3092])).
% 1.45/1.65 tff(3095,plain,
% 1.45/1.65 (hskp20),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3094, 319, 3086, 3088, 2005, 1997, 2184, 1804, 3087])).
% 1.45/1.65 tff(3096,plain,
% 1.45/1.65 (~c2_1(a1574)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1764, 3095])).
% 1.45/1.65 tff(3097,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1534)) | (~c2_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1534)) | (~c2_1(a1534)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3098,plain,
% 1.45/1.65 ((hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562))) <=> (hskp21 | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1534)) | (~c2_1(a1534)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3099,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1534)) | (~c2_1(a1534))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[3098])).
% 1.45/1.65 tff(3100,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1534)) | (~c2_1(a1534)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[3099, 3097])).
% 1.45/1.65 tff(3101,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a1534) | (~c1_1(a1534)) | (~c2_1(a1534)) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(3102,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a1534) | (~ndr1_0) | c1_1(a1562) | (~c3_1(a1562)) | (~c0_1(a1562)) | (~c1_1(a1534)) | (~c2_1(a1534))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[3101, 3100])).
% 1.45/1.65 tff(3103,plain,
% 1.45/1.65 (hskp21),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3102, 319, 3086, 3085, 2784, 2785, 403, 383, 3087])).
% 1.45/1.65 tff(3104,plain,
% 1.45/1.65 (~c1_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[438, 3103])).
% 1.45/1.65 tff(3105,plain,
% 1.45/1.65 (~c0_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[444, 3103])).
% 1.45/1.65 tff(3106,plain,
% 1.45/1.65 (c3_1(a1574)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1743, 3095])).
% 1.45/1.65 tff(3107,plain,
% 1.45/1.65 (c1_1(a1574)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1751, 3095])).
% 1.45/1.65 tff(3108,plain,
% 1.45/1.65 (c2_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[515, 3103])).
% 1.45/1.65 tff(3109,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2228, 319, 12, 3108, 3107, 3106, 3105, 3104, 3096, 22])).
% 1.45/1.65 tff(3110,plain,((~c1_1(a1534)) | hskp28 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(3111,plain,
% 1.45/1.65 (~c1_1(a1534)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3110, 12, 11])).
% 1.45/1.65 tff(3112,plain,
% 1.45/1.65 (hskp20),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2251, 319, 2005, 2783, 2784, 1997, 2184, 1804, 267])).
% 1.45/1.65 tff(3113,plain,
% 1.45/1.65 (~c2_1(a1574)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1764, 3112])).
% 1.45/1.65 tff(3114,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | c2_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1565)) | (~c1_1(a1565)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp21 | c2_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3115,plain,
% 1.45/1.65 ((hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534))) <=> (hskp21 | c2_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3116,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | c2_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1565)) | (~c1_1(a1565))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[3115])).
% 1.45/1.65 tff(3117,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp21 | c2_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1565)) | (~c1_1(a1565)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[3116, 3114])).
% 1.45/1.65 tff(3118,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a1565) | (~c1_1(a1565)) | (~c0_1(a1565)) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(3119,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp21 | c2_1(a1565) | (~ndr1_0) | c1_1(a1534) | (~c0_1(a1534)) | (~c2_1(a1534)) | (~c0_1(a1565)) | (~c1_1(a1565))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[3118, 3117])).
% 1.45/1.65 tff(3120,plain,
% 1.45/1.65 (hskp21),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3119, 319, 2005, 2783, 2784, 1997, 2210, 267, 3003])).
% 1.45/1.65 tff(3121,plain,
% 1.45/1.65 (~c1_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[438, 3120])).
% 1.45/1.65 tff(3122,plain,
% 1.45/1.65 (~c0_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[444, 3120])).
% 1.45/1.65 tff(3123,plain,
% 1.45/1.65 (c3_1(a1574)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1743, 3112])).
% 1.45/1.65 tff(3124,plain,
% 1.45/1.65 (c1_1(a1574)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1751, 3112])).
% 1.45/1.65 tff(3125,plain,
% 1.45/1.65 (c2_1(a1575)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[515, 3120])).
% 1.45/1.65 tff(3126,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2228, 319, 12, 3125, 3124, 3123, 3122, 3121, 3113, 22])).
% 1.45/1.65 tff(3127,plain,(c1_1(a1534) | hskp28 | (~c0_1(a1565))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(3128,plain,
% 1.45/1.65 (~c0_1(a1565)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3127, 3111, 12])).
% 1.45/1.65 tff(3129,plain,
% 1.45/1.65 (hskp6),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2857, 3111, 11])).
% 1.45/1.65 tff(3130,plain,
% 1.45/1.65 (~c2_1(a1543)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[912, 3129])).
% 1.45/1.65 tff(3131,plain,
% 1.45/1.65 (c0_1(a1543)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[950, 3129])).
% 1.45/1.65 tff(3132,plain,
% 1.45/1.65 (c3_1(a1543)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2816, 319, 3131, 2783, 1997, 2184, 3130, 2785, 35, 3111, 3128])).
% 1.45/1.65 tff(3133,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2421, 319, 3079, 3131, 1997, 2184, 3130, 2368, 3128, 3132])).
% 1.45/1.65 tff(3134,plain,(hskp28 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(3135,plain,
% 1.45/1.65 (hskp28),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3134, 11])).
% 1.45/1.65 tff(3136,plain,
% 1.45/1.65 (c3_1(a1542)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[530, 3135])).
% 1.45/1.65 tff(3137,plain,
% 1.45/1.65 (c1_1(a1542)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[546, 3135])).
% 1.45/1.65 tff(3138,plain,
% 1.45/1.65 (~c0_1(a1542)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1569, 319, 11, 3137, 3136, 10])).
% 1.45/1.65 tff(3139,plain,
% 1.45/1.65 (c2_1(a1542)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[538, 3135])).
% 1.45/1.65 tff(3140,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp14 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3141,plain,
% 1.45/1.65 ((hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542))) <=> (hskp14 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(3142,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[3141])).
% 1.45/1.65 tff(3143,plain,
% 1.45/1.65 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp14 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542))),
% 1.45/1.65 inference(transitivity,[status(thm)],[3142, 3140])).
% 1.45/1.65 tff(3144,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1565) | c3_1(a1565) | (~c1_1(a1565)) | c0_1(a1542) | (~c1_1(a1542)) | (~c2_1(a1542)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(3145,plain,
% 1.45/1.65 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp14 | c2_1(a1565) | c3_1(a1565) | (~ndr1_0) | (~c1_1(a1565)) | (~c1_1(a1542)) | (~c2_1(a1542)) | c0_1(a1542)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[3144, 3143])).
% 1.45/1.66 tff(3146,plain,
% 1.45/1.66 (hskp14),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[3145, 319, 3137, 3139, 2005, 1997, 2184, 2442, 3138])).
% 1.45/1.66 tff(3147,plain,
% 1.45/1.66 (~c2_1(a1558)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[64, 3146])).
% 1.45/1.66 tff(3148,plain,
% 1.45/1.66 (c1_1(a1558)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[72, 3146])).
% 1.45/1.66 tff(3149,plain,
% 1.45/1.66 (c0_1(a1558)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[80, 3146])).
% 1.45/1.66 tff(3150,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1135, 319, 11, 3137, 3139, 3149, 3148, 3147, 1121, 3138])).
% 1.45/1.66 tff(3151,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(3152,plain,
% 1.45/1.66 ((~hskp10) | (~c1_1(a1534))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[555, 2784, 2785, 2783])).
% 1.45/1.66 tff(3153,plain,
% 1.45/1.66 (~c1_1(a1534)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[3152, 3151])).
% 1.45/1.66 tff(3154,plain,
% 1.45/1.66 (~c1_1(a1549)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[409, 3151])).
% 1.45/1.66 tff(3155,plain,
% 1.45/1.66 (hskp20),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2251, 319, 2005, 2783, 2784, 1997, 2184, 1804, 3153])).
% 1.45/1.66 tff(3156,plain,
% 1.45/1.66 (~c2_1(a1574)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1764, 3155])).
% 1.45/1.66 tff(3157,plain,
% 1.45/1.66 (c3_1(a1549)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[417, 3151])).
% 1.45/1.66 tff(3158,plain,
% 1.45/1.66 (c0_1(a1549)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[425, 3151])).
% 1.45/1.66 tff(3159,plain,
% 1.45/1.66 (c3_1(a1574)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1743, 3155])).
% 1.45/1.66 tff(3160,plain,
% 1.45/1.66 (c1_1(a1574)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1751, 3155])).
% 1.45/1.66 tff(3161,plain,
% 1.45/1.66 (hskp14),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2261, 319, 3160, 3159, 3158, 3157, 3156, 3154, 2245])).
% 1.45/1.66 tff(3162,plain,
% 1.45/1.66 (c1_1(a1558)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[72, 3161])).
% 1.45/1.66 tff(3163,plain,
% 1.45/1.66 (c0_1(a1558)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[80, 3161])).
% 1.45/1.66 tff(3164,plain,
% 1.45/1.66 (~c3_1(a1558)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2270, 319, 3163, 3162, 2783, 2784, 2785, 363, 3153])).
% 1.45/1.66 tff(3165,plain,
% 1.45/1.66 (~c2_1(a1558)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[64, 3161])).
% 1.45/1.66 tff(3166,plain,
% 1.45/1.66 (c0_1(a1565)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2303, 319, 3163, 2783, 1997, 2184, 3165, 2785, 35, 3153, 3164])).
% 1.45/1.66 tff(3167,plain,
% 1.45/1.66 (hskp28),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[3127, 3166, 3153])).
% 1.45/1.66 tff(3168,plain,
% 1.45/1.66 (c1_1(a1542)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[546, 3167])).
% 1.45/1.66 tff(3169,plain,
% 1.45/1.66 (c2_1(a1542)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[538, 3167])).
% 1.45/1.66 tff(3170,plain,
% 1.45/1.66 (c3_1(a1542)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[530, 3167])).
% 1.45/1.66 tff(3171,plain,
% 1.45/1.66 ((~c1_1(a1542)) | (~c2_1(a1542)) | (~c3_1(a1542)) | (~hskp10)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1821, 2782])).
% 1.45/1.66 tff(3172,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[3171, 3170, 3169, 3151, 3168])).
% 1.45/1.66 % SZS output end Proof
% 1.45/1.66 % E exiting
%------------------------------------------------------------------------------