%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN505-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:39:23 AM UTC 2025
% Result : Unsatisfiable 1.05s 1.23s
% Output : Proof 1.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN505-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n011.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 12:37:27 EDT 2025
% 0.12/0.32 % CPUTime :
% 1.05/1.23 % SZS status Unsatisfiable
% 1.05/1.23 % SZS output start Proof
% 1.05/1.23 tff(c3_1_type, type, (
% 1.05/1.23 c3_1: $i > $o)).
% 1.05/1.23 tff(a494_type, type, (
% 1.05/1.23 a494: $i)).
% 1.05/1.23 tff(hskp18_type, type, (
% 1.05/1.23 hskp18: $o)).
% 1.05/1.23 tff(c2_1_type, type, (
% 1.05/1.23 c2_1: $i > $o)).
% 1.05/1.23 tff(a481_type, type, (
% 1.05/1.23 a481: $i)).
% 1.05/1.23 tff(c0_1_type, type, (
% 1.05/1.23 c0_1: $i > $o)).
% 1.05/1.23 tff(c1_1_type, type, (
% 1.05/1.23 c1_1: $i > $o)).
% 1.05/1.23 tff(ndr1_0_type, type, (
% 1.05/1.23 ndr1_0: $o)).
% 1.05/1.23 tff(hskp12_type, type, (
% 1.05/1.23 hskp12: $o)).
% 1.05/1.23 tff(a529_type, type, (
% 1.05/1.23 a529: $i)).
% 1.05/1.23 tff(a507_type, type, (
% 1.05/1.23 a507: $i)).
% 1.05/1.23 tff(hskp7_type, type, (
% 1.05/1.23 hskp7: $o)).
% 1.05/1.23 tff(hskp16_type, type, (
% 1.05/1.23 hskp16: $o)).
% 1.05/1.23 tff(hskp21_type, type, (
% 1.05/1.23 hskp21: $o)).
% 1.05/1.23 tff(a467_type, type, (
% 1.05/1.23 a467: $i)).
% 1.05/1.23 tff(a487_type, type, (
% 1.05/1.23 a487: $i)).
% 1.05/1.23 tff(hskp29_type, type, (
% 1.05/1.23 hskp29: $o)).
% 1.05/1.23 tff(hskp30_type, type, (
% 1.05/1.23 hskp30: $o)).
% 1.05/1.23 tff(a471_type, type, (
% 1.05/1.23 a471: $i)).
% 1.05/1.23 tff(hskp5_type, type, (
% 1.05/1.23 hskp5: $o)).
% 1.05/1.23 tff(hskp10_type, type, (
% 1.05/1.23 hskp10: $o)).
% 1.05/1.23 tff(hskp31_type, type, (
% 1.05/1.23 hskp31: $o)).
% 1.05/1.23 tff(hskp19_type, type, (
% 1.05/1.23 hskp19: $o)).
% 1.05/1.23 tff(a493_type, type, (
% 1.05/1.23 a493: $i)).
% 1.05/1.23 tff(a488_type, type, (
% 1.05/1.23 a488: $i)).
% 1.05/1.23 tff(a500_type, type, (
% 1.05/1.23 a500: $i)).
% 1.05/1.23 tff(hskp2_type, type, (
% 1.05/1.23 hskp2: $o)).
% 1.05/1.23 tff(a464_type, type, (
% 1.05/1.23 a464: $i)).
% 1.05/1.23 tff(hskp3_type, type, (
% 1.05/1.23 hskp3: $o)).
% 1.05/1.23 tff(a465_type, type, (
% 1.05/1.23 a465: $i)).
% 1.05/1.23 tff(a478_type, type, (
% 1.05/1.23 a478: $i)).
% 1.05/1.23 tff(a466_type, type, (
% 1.05/1.23 a466: $i)).
% 1.05/1.23 tff(hskp4_type, type, (
% 1.05/1.23 hskp4: $o)).
% 1.05/1.23 tff(a474_type, type, (
% 1.05/1.23 a474: $i)).
% 1.05/1.23 tff(a482_type, type, (
% 1.05/1.23 a482: $i)).
% 1.05/1.23 tff(hskp17_type, type, (
% 1.05/1.23 hskp17: $o)).
% 1.05/1.23 tff(hskp13_type, type, (
% 1.05/1.23 hskp13: $o)).
% 1.05/1.23 tff(hskp26_type, type, (
% 1.05/1.23 hskp26: $o)).
% 1.05/1.23 tff(a559_type, type, (
% 1.05/1.23 a559: $i)).
% 1.05/1.23 tff(a463_type, type, (
% 1.05/1.23 a463: $i)).
% 1.05/1.23 tff(hskp1_type, type, (
% 1.05/1.23 hskp1: $o)).
% 1.05/1.23 tff(hskp6_type, type, (
% 1.05/1.23 hskp6: $o)).
% 1.05/1.23 tff(a470_type, type, (
% 1.05/1.23 a470: $i)).
% 1.05/1.23 tff(a483_type, type, (
% 1.05/1.23 a483: $i)).
% 1.05/1.23 tff(hskp14_type, type, (
% 1.05/1.23 hskp14: $o)).
% 1.05/1.23 tff(a472_type, type, (
% 1.05/1.23 a472: $i)).
% 1.05/1.23 tff(hskp8_type, type, (
% 1.05/1.23 hskp8: $o)).
% 1.05/1.23 tff(a521_type, type, (
% 1.05/1.23 a521: $i)).
% 1.05/1.23 tff(hskp23_type, type, (
% 1.05/1.23 hskp23: $o)).
% 1.05/1.23 tff(1,plain,
% 1.05/1.23 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(2,plain,
% 1.05/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[1])).
% 1.05/1.23 tff(3,plain,
% 1.05/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(4,plain,
% 1.05/1.23 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(5,plain,
% 1.05/1.23 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[4])).
% 1.05/1.23 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.05/1.23 tff(7,plain,
% 1.05/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.05/1.23 tff(8,plain,
% 1.05/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.05/1.23 tff(9,plain,(
% 1.05/1.23 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.05/1.23 inference(skolemize,[status(sab)],[8])).
% 1.05/1.23 tff(10,plain,
% 1.05/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.05/1.23 tff(11,plain,
% 1.05/1.23 (^[U: $i] : refl((hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(12,plain,
% 1.05/1.23 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[11])).
% 1.05/1.23 tff(13,plain,
% 1.05/1.23 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(14,plain,
% 1.05/1.23 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) | hskp16) <=> ((hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16))), rewrite(((hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(15,plain,
% 1.05/1.23 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) | hskp16) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[14])).
% 1.05/1.23 tff(16,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.05/1.23 tff(17,plain,
% 1.05/1.23 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.05/1.23 tff(18,plain,
% 1.05/1.23 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.05/1.23 tff(19,plain,(
% 1.05/1.23 ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.05/1.23 inference(skolemize,[status(sab)],[18])).
% 1.05/1.23 tff(20,plain,
% 1.05/1.23 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.05/1.23 tff(21,assumption,(~hskp12), introduced(assumption)).
% 1.05/1.23 tff(22,assumption,(hskp16), introduced(assumption)).
% 1.05/1.23 tff(23,plain,
% 1.05/1.23 (((~hskp16) | (~c1_1(a487))) <=> ((~hskp16) | (~c1_1(a487)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(24,plain,
% 1.05/1.23 (((~c1_1(a487)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a487)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(25,axiom,((~c1_1(a487)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.05/1.23 tff(26,plain,
% 1.05/1.23 ((~hskp16) | (~c1_1(a487))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.05/1.23 tff(27,plain,
% 1.05/1.23 ((~hskp16) | (~c1_1(a487))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[26, 23])).
% 1.05/1.23 tff(28,plain,
% 1.05/1.23 (~c1_1(a487)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[27, 22])).
% 1.05/1.23 tff(29,assumption,(~c2_1(a471)), introduced(assumption)).
% 1.05/1.23 tff(30,assumption,(~c0_1(a471)), introduced(assumption)).
% 1.05/1.23 tff(31,assumption,(~hskp5), introduced(assumption)).
% 1.05/1.23 tff(32,plain,
% 1.05/1.23 (^[U: $i] : refl((hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(33,plain,
% 1.05/1.23 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[32])).
% 1.05/1.23 tff(34,plain,
% 1.05/1.23 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(35,plain,
% 1.05/1.23 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | 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)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp12) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp12))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp12) <=> (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp12) <=> (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(36,plain,
% 1.05/1.23 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp12) <=> ![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[35])).
% 1.05/1.23 tff(37,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.05/1.23 tff(38,plain,
% 1.05/1.23 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.05/1.23 tff(39,plain,
% 1.05/1.23 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.05/1.23 tff(40,plain,(
% 1.05/1.23 ![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.05/1.23 inference(skolemize,[status(sab)],[39])).
% 1.05/1.23 tff(41,plain,
% 1.05/1.23 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.05/1.23 tff(42,assumption,(~ndr1_0), introduced(assumption)).
% 1.05/1.23 tff(43,plain,
% 1.05/1.23 ((ndr1_0 | (~hskp10)) <=> (ndr1_0 | (~hskp10))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(44,plain,
% 1.05/1.23 (((~hskp10) | ndr1_0) <=> (ndr1_0 | (~hskp10))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(45,axiom,((~hskp10) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 1.05/1.23 tff(46,plain,
% 1.05/1.23 (ndr1_0 | (~hskp10)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.05/1.23 tff(47,plain,
% 1.05/1.23 (ndr1_0 | (~hskp10)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[46, 43])).
% 1.05/1.23 tff(48,plain,
% 1.05/1.23 (~hskp10),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[47, 42])).
% 1.05/1.23 tff(49,plain,
% 1.05/1.23 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(50,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.05/1.23 tff(51,plain,
% 1.05/1.23 ((~hskp31) | ndr1_0),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.05/1.23 tff(52,plain,
% 1.05/1.23 ((~hskp31) | ndr1_0),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[51, 49])).
% 1.05/1.23 tff(53,plain,
% 1.05/1.23 ((~hskp31) | ndr1_0),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[52, 49])).
% 1.05/1.23 tff(54,plain,
% 1.05/1.23 ((~hskp31) | ndr1_0),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.05/1.23 tff(55,plain,
% 1.05/1.23 ((~hskp31) | ndr1_0),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[54, 49])).
% 1.05/1.23 tff(56,plain,
% 1.05/1.23 (~hskp31),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[55, 42])).
% 1.05/1.23 tff(57,plain,
% 1.05/1.23 ((ndr1_0 | (~hskp19)) <=> (ndr1_0 | (~hskp19))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(58,plain,
% 1.05/1.23 (((~hskp19) | ndr1_0) <=> (ndr1_0 | (~hskp19))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(59,axiom,((~hskp19) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 1.05/1.23 tff(60,plain,
% 1.05/1.23 (ndr1_0 | (~hskp19)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.05/1.23 tff(61,plain,
% 1.05/1.23 (ndr1_0 | (~hskp19)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[60, 57])).
% 1.05/1.23 tff(62,plain,
% 1.05/1.23 (~hskp19),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[61, 42])).
% 1.05/1.23 tff(63,plain,
% 1.05/1.23 ((hskp31 | hskp19 | hskp10) <=> (hskp31 | hskp19 | hskp10)),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(64,plain,
% 1.05/1.23 (((hskp31 | hskp19) | hskp10) <=> (hskp31 | hskp19 | hskp10)),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(65,plain,
% 1.05/1.23 ((hskp31 | hskp19) <=> (hskp31 | hskp19)),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(66,plain,
% 1.05/1.23 (((hskp31 | hskp19) | hskp10) <=> ((hskp31 | hskp19) | hskp10)),
% 1.05/1.23 inference(monotonicity,[status(thm)],[65])).
% 1.05/1.23 tff(67,plain,
% 1.05/1.23 (((hskp31 | hskp19) | hskp10) <=> (hskp31 | hskp19 | hskp10)),
% 1.05/1.23 inference(transitivity,[status(thm)],[66, 64])).
% 1.05/1.23 tff(68,axiom,((hskp31 | hskp19) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 1.05/1.23 tff(69,plain,
% 1.05/1.23 (hskp31 | hskp19 | hskp10),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.05/1.23 tff(70,plain,
% 1.05/1.23 (hskp31 | hskp19 | hskp10),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[69, 63])).
% 1.05/1.23 tff(71,plain,
% 1.05/1.23 (hskp31 | hskp19 | hskp10),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[70, 63])).
% 1.05/1.23 tff(72,plain,
% 1.05/1.23 (hskp31 | hskp19 | hskp10),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[71, 63])).
% 1.05/1.23 tff(73,plain,
% 1.05/1.23 (hskp31 | hskp19 | hskp10),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[72, 63])).
% 1.05/1.23 tff(74,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[73, 62, 56, 48])).
% 1.05/1.23 tff(75,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(76,plain,
% 1.05/1.23 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(77,plain,
% 1.05/1.23 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | (~c3_1(a471))) <=> (hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(78,plain,
% 1.05/1.23 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | (~c3_1(a471)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471))))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[77])).
% 1.05/1.23 tff(79,plain,
% 1.05/1.23 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | (~c3_1(a471)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)))),
% 1.05/1.23 inference(transitivity,[status(thm)],[78, 76])).
% 1.05/1.23 tff(80,plain,
% 1.05/1.23 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | (~c3_1(a471)))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(81,plain,
% 1.05/1.23 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.05/1.23 tff(82,plain,
% 1.05/1.23 (hskp5 | c0_1(a471) | (~c3_1(a471))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[81, 75, 21, 29, 41])).
% 1.05/1.23 tff(83,plain,
% 1.05/1.23 (~c3_1(a471)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[82, 31, 30])).
% 1.05/1.23 tff(84,plain,
% 1.05/1.23 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(85,plain,
% 1.05/1.23 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[84])).
% 1.05/1.23 tff(86,plain,
% 1.05/1.23 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(87,plain,
% 1.05/1.23 (^[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)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(88,plain,
% 1.05/1.23 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[87])).
% 1.05/1.23 tff(89,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.05/1.23 tff(90,plain,
% 1.05/1.23 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.05/1.23 tff(91,plain,
% 1.05/1.23 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[90, 86])).
% 1.05/1.23 tff(92,plain,(
% 1.05/1.23 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.05/1.23 inference(skolemize,[status(sab)],[91])).
% 1.05/1.23 tff(93,plain,
% 1.05/1.23 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[92, 85])).
% 1.05/1.23 tff(94,plain,
% 1.05/1.23 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(95,plain,
% 1.05/1.23 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[94])).
% 1.05/1.23 tff(96,plain,
% 1.05/1.23 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(97,plain,
% 1.05/1.23 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(98,plain,
% 1.05/1.23 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[97])).
% 1.05/1.23 tff(99,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.05/1.23 tff(100,plain,
% 1.05/1.23 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.05/1.23 tff(101,plain,
% 1.05/1.23 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[100, 96])).
% 1.05/1.23 tff(102,plain,(
% 1.05/1.23 ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.05/1.23 inference(skolemize,[status(sab)],[101])).
% 1.05/1.23 tff(103,plain,
% 1.05/1.23 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[102, 95])).
% 1.05/1.23 tff(104,assumption,(~hskp16), introduced(assumption)).
% 1.05/1.23 tff(105,assumption,(hskp19), introduced(assumption)).
% 1.05/1.23 tff(106,plain,
% 1.05/1.23 (((~hskp19) | (~c3_1(a500))) <=> ((~hskp19) | (~c3_1(a500)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(107,plain,
% 1.05/1.23 (((~c3_1(a500)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a500)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(108,axiom,((~c3_1(a500)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.05/1.23 tff(109,plain,
% 1.05/1.23 ((~hskp19) | (~c3_1(a500))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.05/1.23 tff(110,plain,
% 1.05/1.23 ((~hskp19) | (~c3_1(a500))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[109, 106])).
% 1.05/1.23 tff(111,plain,
% 1.05/1.23 (~c3_1(a500)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[110, 105])).
% 1.05/1.23 tff(112,plain,
% 1.05/1.23 (((~hskp19) | (~c2_1(a500))) <=> ((~hskp19) | (~c2_1(a500)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(113,plain,
% 1.05/1.23 (((~c2_1(a500)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a500)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(114,axiom,((~c2_1(a500)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.05/1.23 tff(115,plain,
% 1.05/1.23 ((~hskp19) | (~c2_1(a500))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.05/1.23 tff(116,plain,
% 1.05/1.23 ((~hskp19) | (~c2_1(a500))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[115, 112])).
% 1.05/1.23 tff(117,plain,
% 1.05/1.23 (~c2_1(a500)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[116, 105])).
% 1.05/1.23 tff(118,plain,
% 1.05/1.23 (((~hskp19) | c1_1(a500)) <=> ((~hskp19) | c1_1(a500))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(119,axiom,((~hskp19) | c1_1(a500)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.05/1.23 tff(120,plain,
% 1.05/1.23 ((~hskp19) | c1_1(a500)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.05/1.23 tff(121,plain,
% 1.05/1.23 ((~hskp19) | c1_1(a500)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[120, 118])).
% 1.05/1.23 tff(122,plain,
% 1.05/1.23 ((~hskp19) | c1_1(a500)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[121, 118])).
% 1.05/1.23 tff(123,plain,
% 1.05/1.23 ((~hskp19) | c1_1(a500)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[122, 118])).
% 1.05/1.23 tff(124,plain,
% 1.05/1.23 ((~hskp19) | c1_1(a500)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[123, 118])).
% 1.05/1.23 tff(125,plain,
% 1.05/1.23 (c1_1(a500)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[124, 105])).
% 1.05/1.23 tff(126,assumption,(~c0_1(a500)), introduced(assumption)).
% 1.05/1.23 tff(127,assumption,(~c3_1(a500)), introduced(assumption)).
% 1.05/1.23 tff(128,assumption,(~c2_1(a500)), introduced(assumption)).
% 1.05/1.23 tff(129,assumption,(c1_1(a500)), introduced(assumption)).
% 1.05/1.23 tff(130,plain,
% 1.05/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(131,plain,
% 1.05/1.23 (((~ndr1_0) | c0_1(a500) | c3_1(a500) | (~c1_1(a500)) | c0_1(a500) | c2_1(a500) | (~c1_1(a500)) | c3_1(a500) | c0_1(a500) | c2_1(a500)) <=> (c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(132,plain,
% 1.05/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a500) | c3_1(a500) | (~c1_1(a500)) | c0_1(a500) | c2_1(a500) | (~c1_1(a500)) | c3_1(a500) | c0_1(a500) | c2_1(a500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500)))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[131])).
% 1.05/1.23 tff(133,plain,
% 1.05/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a500) | c3_1(a500) | (~c1_1(a500)) | c0_1(a500) | c2_1(a500) | (~c1_1(a500)) | c3_1(a500) | c0_1(a500) | c2_1(a500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500))),
% 1.05/1.23 inference(transitivity,[status(thm)],[132, 130])).
% 1.05/1.23 tff(134,plain,
% 1.05/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a500) | c3_1(a500) | (~c1_1(a500)) | c0_1(a500) | c2_1(a500) | (~c1_1(a500)) | c3_1(a500) | c0_1(a500) | c2_1(a500))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(135,plain,
% 1.05/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.05/1.23 tff(136,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[135, 75, 129, 128, 127, 10, 126])).
% 1.05/1.23 tff(137,plain,(c0_1(a500) | (~c1_1(a500)) | c2_1(a500) | c3_1(a500)), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(138,plain,
% 1.05/1.23 (c0_1(a500)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[137, 125, 117, 111])).
% 1.05/1.23 tff(139,plain,
% 1.05/1.23 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))))),
% 1.05/1.23 inference(bind,[status(th)],[])).
% 1.05/1.23 tff(140,plain,
% 1.05/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_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)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.05/1.23 inference(quant_intro,[status(thm)],[139])).
% 1.05/1.23 tff(141,plain,
% 1.05/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_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)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(142,plain,
% 1.05/1.23 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))))),
% 1.09/1.24 inference(bind,[status(th)],[])).
% 1.09/1.24 tff(143,plain,
% 1.09/1.24 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.09/1.24 inference(quant_intro,[status(thm)],[142])).
% 1.09/1.24 tff(144,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause208')).
% 1.09/1.24 tff(145,plain,
% 1.09/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.09/1.24 tff(146,plain,
% 1.09/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[145, 141])).
% 1.09/1.24 tff(147,plain,(
% 1.09/1.24 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.09/1.24 inference(skolemize,[status(sab)],[146])).
% 1.09/1.24 tff(148,plain,
% 1.09/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[147, 140])).
% 1.09/1.24 tff(149,plain,
% 1.09/1.24 (^[U: $i] : refl((hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.09/1.24 inference(bind,[status(th)],[])).
% 1.09/1.24 tff(150,plain,
% 1.09/1.24 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.09/1.24 inference(quant_intro,[status(thm)],[149])).
% 1.09/1.24 tff(151,plain,
% 1.09/1.24 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(152,plain,
% 1.09/1.24 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | 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)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp12) <=> ((hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12))), rewrite(((hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp12) <=> (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.09/1.24 inference(bind,[status(th)],[])).
% 1.09/1.24 tff(153,plain,
% 1.09/1.24 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp12) <=> ![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.09/1.24 inference(quant_intro,[status(thm)],[152])).
% 1.09/1.24 tff(154,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.09/1.24 tff(155,plain,
% 1.09/1.24 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.09/1.24 tff(156,plain,
% 1.09/1.24 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[155, 151])).
% 1.09/1.24 tff(157,plain,(
% 1.09/1.24 ![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.09/1.24 inference(skolemize,[status(sab)],[156])).
% 1.09/1.24 tff(158,plain,
% 1.09/1.24 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[157, 150])).
% 1.09/1.24 tff(159,plain,
% 1.09/1.24 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(160,plain,
% 1.09/1.24 ((hskp30 | hskp12 | (~ndr1_0) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500))) <=> (hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(161,plain,
% 1.09/1.24 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500))))),
% 1.09/1.24 inference(monotonicity,[status(thm)],[160])).
% 1.09/1.24 tff(162,plain,
% 1.09/1.24 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.09/1.24 inference(transitivity,[status(thm)],[161, 159])).
% 1.09/1.24 tff(163,plain,
% 1.09/1.24 ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.09/1.24 inference(quant_inst,[status(thm)],[])).
% 1.09/1.24 tff(164,plain,
% 1.09/1.24 ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.09/1.24 tff(165,plain,
% 1.09/1.24 (hskp30 | (~c0_1(a500))),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[164, 75, 21, 125, 111, 158])).
% 1.09/1.24 tff(166,plain,
% 1.09/1.24 (hskp30),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[165, 138])).
% 1.09/1.24 tff(167,plain,
% 1.09/1.24 (((~hskp30) | c3_1(a488)) <=> ((~hskp30) | c3_1(a488))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(168,axiom,((~hskp30) | c3_1(a488)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.09/1.24 tff(169,plain,
% 1.09/1.24 ((~hskp30) | c3_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.09/1.24 tff(170,plain,
% 1.09/1.24 ((~hskp30) | c3_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[169, 167])).
% 1.09/1.24 tff(171,plain,
% 1.09/1.24 ((~hskp30) | c3_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[170, 167])).
% 1.09/1.24 tff(172,plain,
% 1.09/1.24 ((~hskp30) | c3_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[171, 167])).
% 1.09/1.24 tff(173,plain,
% 1.09/1.24 ((~hskp30) | c3_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[172, 167])).
% 1.09/1.24 tff(174,plain,
% 1.09/1.24 (c3_1(a488)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[173, 166])).
% 1.09/1.24 tff(175,plain,
% 1.09/1.24 (((~hskp30) | c2_1(a488)) <=> ((~hskp30) | c2_1(a488))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(176,axiom,((~hskp30) | c2_1(a488)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.09/1.24 tff(177,plain,
% 1.09/1.24 ((~hskp30) | c2_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.09/1.24 tff(178,plain,
% 1.09/1.24 ((~hskp30) | c2_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[177, 175])).
% 1.09/1.24 tff(179,plain,
% 1.09/1.24 ((~hskp30) | c2_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[178, 175])).
% 1.09/1.24 tff(180,plain,
% 1.09/1.24 ((~hskp30) | c2_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[179, 175])).
% 1.09/1.24 tff(181,plain,
% 1.09/1.24 ((~hskp30) | c2_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[180, 175])).
% 1.09/1.24 tff(182,plain,
% 1.09/1.24 (c2_1(a488)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[181, 166])).
% 1.09/1.24 tff(183,plain,
% 1.09/1.24 (((~hskp30) | c1_1(a488)) <=> ((~hskp30) | c1_1(a488))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(184,axiom,((~hskp30) | c1_1(a488)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.09/1.24 tff(185,plain,
% 1.09/1.24 ((~hskp30) | c1_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.09/1.24 tff(186,plain,
% 1.09/1.24 ((~hskp30) | c1_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[185, 183])).
% 1.09/1.24 tff(187,plain,
% 1.09/1.24 ((~hskp30) | c1_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[186, 183])).
% 1.09/1.24 tff(188,plain,
% 1.09/1.24 ((~hskp30) | c1_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[187, 183])).
% 1.09/1.24 tff(189,plain,
% 1.09/1.24 ((~hskp30) | c1_1(a488)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[188, 183])).
% 1.09/1.24 tff(190,plain,
% 1.09/1.24 (c1_1(a488)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[189, 166])).
% 1.09/1.24 tff(191,plain,
% 1.09/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(192,plain,
% 1.09/1.24 (((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500))) <=> (c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(193,plain,
% 1.09/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))))),
% 1.09/1.24 inference(monotonicity,[status(thm)],[192])).
% 1.09/1.24 tff(194,plain,
% 1.09/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.24 inference(transitivity,[status(thm)],[193, 191])).
% 1.09/1.24 tff(195,plain,
% 1.09/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.09/1.24 inference(quant_inst,[status(thm)],[])).
% 1.09/1.24 tff(196,plain,
% 1.09/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[195, 194])).
% 1.09/1.24 tff(197,plain,
% 1.09/1.24 (~c0_1(a488)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[196, 75, 190, 182, 174, 125, 111, 148, 138])).
% 1.09/1.24 tff(198,plain,
% 1.09/1.24 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.09/1.24 inference(bind,[status(th)],[])).
% 1.09/1.24 tff(199,plain,
% 1.09/1.24 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.09/1.24 inference(quant_intro,[status(thm)],[198])).
% 1.09/1.24 tff(200,plain,
% 1.09/1.24 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(201,plain,
% 1.09/1.24 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.09/1.24 inference(bind,[status(th)],[])).
% 1.09/1.24 tff(202,plain,
% 1.09/1.24 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.09/1.24 inference(quant_intro,[status(thm)],[201])).
% 1.09/1.24 tff(203,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.09/1.24 tff(204,plain,
% 1.09/1.24 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.09/1.24 tff(205,plain,
% 1.09/1.24 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[204, 200])).
% 1.09/1.24 tff(206,plain,(
% 1.09/1.24 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.09/1.24 inference(skolemize,[status(sab)],[205])).
% 1.09/1.24 tff(207,plain,
% 1.09/1.24 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[206, 199])).
% 1.09/1.24 tff(208,plain,
% 1.09/1.24 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(209,plain,
% 1.09/1.24 ((hskp16 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c0_1(a488) | (~c3_1(a488)) | (~c1_1(a488))) <=> (hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(210,plain,
% 1.09/1.24 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c0_1(a488) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))))),
% 1.09/1.24 inference(monotonicity,[status(thm)],[209])).
% 1.09/1.24 tff(211,plain,
% 1.09/1.24 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c0_1(a488) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.24 inference(transitivity,[status(thm)],[210, 208])).
% 1.09/1.24 tff(212,plain,
% 1.09/1.24 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c0_1(a488) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.24 inference(quant_inst,[status(thm)],[])).
% 1.09/1.24 tff(213,plain,
% 1.09/1.24 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.09/1.24 tff(214,plain,
% 1.09/1.24 ($false),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[213, 75, 104, 190, 182, 174, 207, 197])).
% 1.09/1.24 tff(215,plain,((~hskp19) | hskp16 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.09/1.24 tff(216,plain,
% 1.09/1.24 (~hskp19),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[215, 104, 21])).
% 1.09/1.24 tff(217,assumption,(~hskp19), introduced(assumption)).
% 1.09/1.24 tff(218,assumption,(~hskp31), introduced(assumption)).
% 1.09/1.24 tff(219,assumption,(~c2_1(a464)), introduced(assumption)).
% 1.09/1.24 tff(220,assumption,(~c0_1(a464)), introduced(assumption)).
% 1.09/1.24 tff(221,plain,
% 1.09/1.24 (hskp10),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[73, 218, 217])).
% 1.09/1.24 tff(222,plain,
% 1.09/1.24 (((~hskp10) | (~c3_1(a478))) <=> ((~hskp10) | (~c3_1(a478)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(223,plain,
% 1.09/1.24 (((~c3_1(a478)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a478)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(224,axiom,((~c3_1(a478)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.09/1.24 tff(225,plain,
% 1.09/1.24 ((~hskp10) | (~c3_1(a478))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.09/1.24 tff(226,plain,
% 1.09/1.24 ((~hskp10) | (~c3_1(a478))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[225, 222])).
% 1.09/1.24 tff(227,plain,
% 1.09/1.24 (~c3_1(a478)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[226, 221])).
% 1.09/1.24 tff(228,plain,
% 1.09/1.24 (((~hskp10) | (~c0_1(a478))) <=> ((~hskp10) | (~c0_1(a478)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(229,plain,
% 1.09/1.24 (((~c0_1(a478)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a478)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(230,axiom,((~c0_1(a478)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.09/1.24 tff(231,plain,
% 1.09/1.24 ((~hskp10) | (~c0_1(a478))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.09/1.24 tff(232,plain,
% 1.09/1.24 ((~hskp10) | (~c0_1(a478))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[231, 228])).
% 1.09/1.24 tff(233,plain,
% 1.09/1.24 (~c0_1(a478)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[232, 221])).
% 1.09/1.24 tff(234,plain,
% 1.09/1.24 (((~hskp10) | c2_1(a478)) <=> ((~hskp10) | c2_1(a478))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(235,axiom,((~hskp10) | c2_1(a478)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.09/1.24 tff(236,plain,
% 1.09/1.24 ((~hskp10) | c2_1(a478)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.09/1.24 tff(237,plain,
% 1.09/1.24 ((~hskp10) | c2_1(a478)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[236, 234])).
% 1.09/1.24 tff(238,plain,
% 1.09/1.24 ((~hskp10) | c2_1(a478)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[237, 234])).
% 1.09/1.24 tff(239,plain,
% 1.09/1.24 ((~hskp10) | c2_1(a478)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[238, 234])).
% 1.09/1.24 tff(240,plain,
% 1.09/1.24 ((~hskp10) | c2_1(a478)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[239, 234])).
% 1.09/1.24 tff(241,plain,
% 1.09/1.24 (c2_1(a478)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[240, 221])).
% 1.09/1.24 tff(242,assumption,(~c1_1(a465)), introduced(assumption)).
% 1.09/1.24 tff(243,assumption,(~c0_1(a465)), introduced(assumption)).
% 1.09/1.24 tff(244,assumption,(~c3_1(a478)), introduced(assumption)).
% 1.09/1.24 tff(245,assumption,(~c0_1(a478)), introduced(assumption)).
% 1.09/1.24 tff(246,assumption,(c2_1(a478)), introduced(assumption)).
% 1.09/1.24 tff(247,assumption,(~c3_1(a467)), introduced(assumption)).
% 1.09/1.24 tff(248,assumption,(~c1_1(a467)), introduced(assumption)).
% 1.09/1.24 tff(249,plain,
% 1.09/1.24 (^[U: $i] : refl((hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.09/1.24 inference(bind,[status(th)],[])).
% 1.09/1.24 tff(250,plain,
% 1.09/1.24 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.09/1.24 inference(quant_intro,[status(thm)],[249])).
% 1.09/1.24 tff(251,plain,
% 1.09/1.24 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(252,plain,
% 1.09/1.24 (^[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)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.09/1.24 inference(bind,[status(th)],[])).
% 1.09/1.24 tff(253,plain,
% 1.09/1.24 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.09/1.24 inference(quant_intro,[status(thm)],[252])).
% 1.09/1.24 tff(254,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.09/1.24 tff(255,plain,
% 1.09/1.24 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[254, 253])).
% 1.09/1.24 tff(256,plain,
% 1.09/1.24 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[255, 251])).
% 1.09/1.24 tff(257,plain,(
% 1.09/1.24 ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.09/1.24 inference(skolemize,[status(sab)],[256])).
% 1.09/1.24 tff(258,plain,
% 1.09/1.24 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[257, 250])).
% 1.09/1.24 tff(259,plain,
% 1.09/1.24 (((~hskp16) | (~c2_1(a487))) <=> ((~hskp16) | (~c2_1(a487)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(260,plain,
% 1.09/1.24 (((~c2_1(a487)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a487)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(261,axiom,((~c2_1(a487)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.09/1.24 tff(262,plain,
% 1.09/1.24 ((~hskp16) | (~c2_1(a487))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[261, 260])).
% 1.09/1.24 tff(263,plain,
% 1.09/1.24 ((~hskp16) | (~c2_1(a487))),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[262, 259])).
% 1.09/1.24 tff(264,plain,
% 1.09/1.24 (~c2_1(a487)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[263, 22])).
% 1.09/1.24 tff(265,plain,
% 1.09/1.24 (((~hskp16) | c0_1(a487)) <=> ((~hskp16) | c0_1(a487))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(266,axiom,((~hskp16) | c0_1(a487)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.09/1.24 tff(267,plain,
% 1.09/1.24 ((~hskp16) | c0_1(a487)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.09/1.24 tff(268,plain,
% 1.09/1.24 ((~hskp16) | c0_1(a487)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[267, 265])).
% 1.09/1.24 tff(269,plain,
% 1.09/1.24 ((~hskp16) | c0_1(a487)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[268, 265])).
% 1.09/1.24 tff(270,plain,
% 1.09/1.24 ((~hskp16) | c0_1(a487)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[269, 265])).
% 1.09/1.24 tff(271,plain,
% 1.09/1.24 ((~hskp16) | c0_1(a487)),
% 1.09/1.24 inference(modus_ponens,[status(thm)],[270, 265])).
% 1.09/1.24 tff(272,plain,
% 1.09/1.24 (c0_1(a487)),
% 1.09/1.24 inference(unit_resolution,[status(thm)],[271, 22])).
% 1.09/1.24 tff(273,plain,
% 1.09/1.24 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(274,plain,
% 1.09/1.24 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487))) <=> (hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)))),
% 1.09/1.24 inference(rewrite,[status(thm)],[])).
% 1.09/1.24 tff(275,plain,
% 1.09/1.24 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487))))),
% 1.09/1.24 inference(monotonicity,[status(thm)],[274])).
% 1.09/1.24 tff(276,plain,
% 1.09/1.24 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[275, 273])).
% 1.09/1.25 tff(277,plain,
% 1.09/1.25 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(278,plain,
% 1.09/1.25 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[277, 276])).
% 1.09/1.25 tff(279,plain,
% 1.09/1.25 (hskp18),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[278, 75, 217, 272, 28, 264, 258])).
% 1.09/1.25 tff(280,plain,
% 1.09/1.25 (((~hskp18) | (~c3_1(a494))) <=> ((~hskp18) | (~c3_1(a494)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(281,plain,
% 1.09/1.25 (((~c3_1(a494)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a494)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(282,axiom,((~c3_1(a494)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.09/1.25 tff(283,plain,
% 1.09/1.25 ((~hskp18) | (~c3_1(a494))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[282, 281])).
% 1.09/1.25 tff(284,plain,
% 1.09/1.25 ((~hskp18) | (~c3_1(a494))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[283, 280])).
% 1.09/1.25 tff(285,plain,
% 1.09/1.25 (~c3_1(a494)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[284, 279])).
% 1.09/1.25 tff(286,plain,
% 1.09/1.25 (((~hskp18) | (~c2_1(a494))) <=> ((~hskp18) | (~c2_1(a494)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(287,plain,
% 1.09/1.25 (((~c2_1(a494)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a494)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(288,axiom,((~c2_1(a494)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.09/1.25 tff(289,plain,
% 1.09/1.25 ((~hskp18) | (~c2_1(a494))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[288, 287])).
% 1.09/1.25 tff(290,plain,
% 1.09/1.25 ((~hskp18) | (~c2_1(a494))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[289, 286])).
% 1.09/1.25 tff(291,plain,
% 1.09/1.25 (~c2_1(a494)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[290, 279])).
% 1.09/1.25 tff(292,plain,
% 1.09/1.25 (((~hskp18) | c0_1(a494)) <=> ((~hskp18) | c0_1(a494))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(293,axiom,((~hskp18) | c0_1(a494)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.09/1.25 tff(294,plain,
% 1.09/1.25 ((~hskp18) | c0_1(a494)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[293, 292])).
% 1.09/1.25 tff(295,plain,
% 1.09/1.25 ((~hskp18) | c0_1(a494)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[294, 292])).
% 1.09/1.25 tff(296,plain,
% 1.09/1.25 ((~hskp18) | c0_1(a494)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[295, 292])).
% 1.09/1.25 tff(297,plain,
% 1.09/1.25 ((~hskp18) | c0_1(a494)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[296, 292])).
% 1.09/1.25 tff(298,plain,
% 1.09/1.25 ((~hskp18) | c0_1(a494)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[297, 292])).
% 1.09/1.25 tff(299,plain,
% 1.09/1.25 (c0_1(a494)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[298, 279])).
% 1.09/1.25 tff(300,assumption,(~c3_1(a494)), introduced(assumption)).
% 1.09/1.25 tff(301,assumption,(~c2_1(a494)), introduced(assumption)).
% 1.09/1.25 tff(302,assumption,(c0_1(a494)), introduced(assumption)).
% 1.09/1.25 tff(303,assumption,(hskp29), introduced(assumption)).
% 1.09/1.25 tff(304,plain,
% 1.09/1.25 (((~hskp29) | c2_1(a474)) <=> ((~hskp29) | c2_1(a474))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(305,axiom,((~hskp29) | c2_1(a474)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.09/1.25 tff(306,plain,
% 1.09/1.25 ((~hskp29) | c2_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.09/1.25 tff(307,plain,
% 1.09/1.25 ((~hskp29) | c2_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[306, 304])).
% 1.09/1.25 tff(308,plain,
% 1.09/1.25 ((~hskp29) | c2_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[307, 304])).
% 1.09/1.25 tff(309,plain,
% 1.09/1.25 ((~hskp29) | c2_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[308, 304])).
% 1.09/1.25 tff(310,plain,
% 1.09/1.25 ((~hskp29) | c2_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[309, 304])).
% 1.09/1.25 tff(311,plain,
% 1.09/1.25 (c2_1(a474)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[310, 303])).
% 1.09/1.25 tff(312,plain,
% 1.09/1.25 (((~hskp29) | c1_1(a474)) <=> ((~hskp29) | c1_1(a474))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(313,axiom,((~hskp29) | c1_1(a474)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.09/1.25 tff(314,plain,
% 1.09/1.25 ((~hskp29) | c1_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[313, 312])).
% 1.09/1.25 tff(315,plain,
% 1.09/1.25 ((~hskp29) | c1_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[314, 312])).
% 1.09/1.25 tff(316,plain,
% 1.09/1.25 ((~hskp29) | c1_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[315, 312])).
% 1.09/1.25 tff(317,plain,
% 1.09/1.25 ((~hskp29) | c1_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[316, 312])).
% 1.09/1.25 tff(318,plain,
% 1.09/1.25 ((~hskp29) | c1_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[317, 312])).
% 1.09/1.25 tff(319,plain,
% 1.09/1.25 (c1_1(a474)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[318, 303])).
% 1.09/1.25 tff(320,plain,
% 1.09/1.25 (((~hskp29) | c0_1(a474)) <=> ((~hskp29) | c0_1(a474))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(321,axiom,((~hskp29) | c0_1(a474)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.09/1.25 tff(322,plain,
% 1.09/1.25 ((~hskp29) | c0_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[321, 320])).
% 1.09/1.25 tff(323,plain,
% 1.09/1.25 ((~hskp29) | c0_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[322, 320])).
% 1.09/1.25 tff(324,plain,
% 1.09/1.25 ((~hskp29) | c0_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[323, 320])).
% 1.09/1.25 tff(325,plain,
% 1.09/1.25 ((~hskp29) | c0_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[324, 320])).
% 1.09/1.25 tff(326,plain,
% 1.09/1.25 ((~hskp29) | c0_1(a474)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[325, 320])).
% 1.09/1.25 tff(327,plain,
% 1.09/1.25 (c0_1(a474)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[326, 303])).
% 1.09/1.25 tff(328,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(329,plain,
% 1.09/1.25 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a494) | c2_1(a494) | (~c0_1(a494))) <=> (c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(330,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a494) | c2_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[329])).
% 1.09/1.25 tff(331,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a494) | c2_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[330, 328])).
% 1.09/1.25 tff(332,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a494) | c2_1(a494) | (~c0_1(a494)))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(333,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[332, 331])).
% 1.09/1.25 tff(334,plain,
% 1.09/1.25 ($false),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[333, 75, 327, 319, 311, 302, 301, 300, 103])).
% 1.09/1.25 tff(335,plain,((~hskp29) | (~c0_1(a494)) | c2_1(a494) | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.25 tff(336,plain,
% 1.09/1.25 (~hskp29),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[335, 299, 291, 285])).
% 1.09/1.25 tff(337,assumption,(c3_1(a465)), introduced(assumption)).
% 1.09/1.25 tff(338,plain,
% 1.09/1.25 (~hskp29),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[335, 302, 301, 300])).
% 1.09/1.25 tff(339,plain,
% 1.09/1.25 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.09/1.25 inference(bind,[status(th)],[])).
% 1.09/1.25 tff(340,plain,
% 1.09/1.25 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/1.25 inference(quant_intro,[status(thm)],[339])).
% 1.09/1.25 tff(341,plain,
% 1.09/1.25 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(342,plain,
% 1.09/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.09/1.25 inference(bind,[status(th)],[])).
% 1.09/1.25 tff(343,plain,
% 1.09/1.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/1.25 inference(quant_intro,[status(thm)],[342])).
% 1.09/1.25 tff(344,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.09/1.25 tff(345,plain,
% 1.09/1.25 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.09/1.25 tff(346,plain,
% 1.09/1.25 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[345, 341])).
% 1.09/1.25 tff(347,plain,(
% 1.09/1.25 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/1.25 inference(skolemize,[status(sab)],[346])).
% 1.09/1.25 tff(348,plain,
% 1.09/1.25 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[347, 340])).
% 1.09/1.25 tff(349,assumption,(~c2_1(a487)), introduced(assumption)).
% 1.09/1.25 tff(350,assumption,(~c1_1(a487)), introduced(assumption)).
% 1.09/1.25 tff(351,assumption,(c0_1(a487)), introduced(assumption)).
% 1.09/1.25 tff(352,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(353,plain,
% 1.09/1.25 ((hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465))) <=> (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(354,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[353])).
% 1.09/1.25 tff(355,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[354, 352])).
% 1.09/1.25 tff(356,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(357,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[356, 355])).
% 1.09/1.25 tff(358,plain,
% 1.09/1.25 (hskp29 | (~c3_1(a465)) | c2_1(a465)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[357, 75, 351, 350, 349, 243, 348])).
% 1.09/1.25 tff(359,plain,
% 1.09/1.25 (c2_1(a465)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[358, 337, 338])).
% 1.09/1.25 tff(360,plain,
% 1.09/1.25 (^[V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.09/1.25 inference(bind,[status(th)],[])).
% 1.09/1.25 tff(361,plain,
% 1.09/1.25 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.09/1.25 inference(quant_intro,[status(thm)],[360])).
% 1.09/1.25 tff(362,plain,
% 1.09/1.25 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(363,plain,
% 1.09/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | 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)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | 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)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.09/1.25 inference(bind,[status(th)],[])).
% 1.09/1.25 tff(364,plain,
% 1.09/1.25 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.09/1.25 inference(quant_intro,[status(thm)],[363])).
% 1.09/1.25 tff(365,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.09/1.25 tff(366,plain,
% 1.09/1.25 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[365, 364])).
% 1.09/1.25 tff(367,plain,
% 1.09/1.25 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[366, 362])).
% 1.09/1.25 tff(368,plain,(
% 1.09/1.25 ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.09/1.25 inference(skolemize,[status(sab)],[367])).
% 1.09/1.25 tff(369,plain,
% 1.09/1.25 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[368, 361])).
% 1.09/1.25 tff(370,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(371,plain,
% 1.09/1.25 (((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a478) | (~c1_1(a478)) | (~c2_1(a478))) <=> (c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(372,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a478) | (~c1_1(a478)) | (~c2_1(a478)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[371])).
% 1.09/1.25 tff(373,plain,
% 1.09/1.25 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a478) | (~c1_1(a478)) | (~c2_1(a478)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[372, 370])).
% 1.09/1.25 tff(374,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a478) | (~c1_1(a478)) | (~c2_1(a478)))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(375,plain,
% 1.09/1.25 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.09/1.25 tff(376,plain,
% 1.09/1.25 (~c1_1(a478)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[375, 75, 351, 246, 350, 349, 245, 369])).
% 1.09/1.25 tff(377,plain,
% 1.09/1.25 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.09/1.25 inference(bind,[status(th)],[])).
% 1.09/1.25 tff(378,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/1.25 inference(quant_intro,[status(thm)],[377])).
% 1.09/1.25 tff(379,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(380,plain,
% 1.09/1.25 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_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)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.09/1.25 inference(bind,[status(th)],[])).
% 1.09/1.25 tff(381,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/1.25 inference(quant_intro,[status(thm)],[380])).
% 1.09/1.25 tff(382,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 1.09/1.25 tff(383,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[382, 381])).
% 1.09/1.25 tff(384,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[383, 379])).
% 1.09/1.25 tff(385,plain,(
% 1.09/1.25 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/1.25 inference(skolemize,[status(sab)],[384])).
% 1.09/1.25 tff(386,plain,
% 1.09/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[385, 378])).
% 1.09/1.25 tff(387,plain,
% 1.09/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(388,plain,
% 1.09/1.25 (((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | c0_1(a478) | (~c2_1(a478))) <=> (c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(389,plain,
% 1.09/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | c0_1(a478) | (~c2_1(a478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494))))),
% 1.09/1.25 inference(monotonicity,[status(thm)],[388])).
% 1.09/1.25 tff(390,plain,
% 1.09/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | c0_1(a478) | (~c2_1(a478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494)))),
% 1.09/1.25 inference(transitivity,[status(thm)],[389, 387])).
% 1.09/1.25 tff(391,plain,
% 1.09/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | c0_1(a478) | (~c2_1(a478)))),
% 1.09/1.25 inference(quant_inst,[status(thm)],[])).
% 1.09/1.25 tff(392,plain,
% 1.09/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[391, 390])).
% 1.09/1.25 tff(393,plain,
% 1.09/1.25 ((~c3_1(a465)) | (~c2_1(a465))),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[392, 75, 302, 246, 301, 300, 245, 242, 386, 376])).
% 1.09/1.25 tff(394,plain,
% 1.09/1.25 ($false),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[393, 359, 337])).
% 1.09/1.25 tff(395,plain,((~c3_1(a465)) | (~c0_1(a494)) | (~c2_1(a478)) | c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~c0_1(a487)) | c1_1(a487) | c2_1(a487) | c0_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.25 tff(396,plain,
% 1.09/1.25 (~c3_1(a465)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[395, 299, 246, 291, 285, 245, 242, 272, 28, 264, 243])).
% 1.09/1.25 tff(397,plain,
% 1.09/1.25 (((~hskp3) | c3_1(a465)) <=> ((~hskp3) | c3_1(a465))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(398,axiom,((~hskp3) | c3_1(a465)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.09/1.25 tff(399,plain,
% 1.09/1.25 ((~hskp3) | c3_1(a465)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[398, 397])).
% 1.09/1.25 tff(400,plain,
% 1.09/1.25 ((~hskp3) | c3_1(a465)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[399, 397])).
% 1.09/1.25 tff(401,plain,
% 1.09/1.25 ((~hskp3) | c3_1(a465)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[400, 397])).
% 1.09/1.25 tff(402,plain,
% 1.09/1.25 ((~hskp3) | c3_1(a465)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[401, 397])).
% 1.09/1.25 tff(403,plain,
% 1.09/1.25 ((~hskp3) | c3_1(a465)),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[402, 397])).
% 1.09/1.25 tff(404,plain,
% 1.09/1.25 (~hskp3),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[403, 396])).
% 1.09/1.25 tff(405,plain,
% 1.09/1.25 ((hskp29 | hskp12 | hskp3) <=> (hskp29 | hskp12 | hskp3)),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(406,plain,
% 1.09/1.25 (((hskp29 | hskp12) | hskp3) <=> (hskp29 | hskp12 | hskp3)),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(407,plain,
% 1.09/1.25 ((hskp29 | hskp12) <=> (hskp29 | hskp12)),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(408,plain,
% 1.09/1.25 (((hskp29 | hskp12) | hskp3) <=> ((hskp29 | hskp12) | hskp3)),
% 1.09/1.25 inference(monotonicity,[status(thm)],[407])).
% 1.09/1.25 tff(409,plain,
% 1.09/1.25 (((hskp29 | hskp12) | hskp3) <=> (hskp29 | hskp12 | hskp3)),
% 1.09/1.25 inference(transitivity,[status(thm)],[408, 406])).
% 1.09/1.25 tff(410,axiom,((hskp29 | hskp12) | hskp3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.09/1.25 tff(411,plain,
% 1.09/1.25 (hskp29 | hskp12 | hskp3),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.09/1.25 tff(412,plain,
% 1.09/1.25 (hskp29 | hskp12 | hskp3),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[411, 405])).
% 1.09/1.25 tff(413,plain,
% 1.09/1.25 (hskp29 | hskp12 | hskp3),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[412, 405])).
% 1.09/1.25 tff(414,plain,
% 1.09/1.25 (hskp29 | hskp12 | hskp3),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[413, 405])).
% 1.09/1.25 tff(415,plain,
% 1.09/1.25 (hskp29 | hskp12 | hskp3),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[414, 405])).
% 1.09/1.25 tff(416,plain,
% 1.09/1.25 (hskp12),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[415, 404, 336])).
% 1.09/1.25 tff(417,plain,
% 1.09/1.25 (((~hskp12) | (~c3_1(a481))) <=> ((~hskp12) | (~c3_1(a481)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(418,plain,
% 1.09/1.25 (((~c3_1(a481)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a481)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(419,axiom,((~c3_1(a481)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.09/1.25 tff(420,plain,
% 1.09/1.25 ((~hskp12) | (~c3_1(a481))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[419, 418])).
% 1.09/1.25 tff(421,plain,
% 1.09/1.25 ((~hskp12) | (~c3_1(a481))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[420, 417])).
% 1.09/1.25 tff(422,plain,
% 1.09/1.25 (~c3_1(a481)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[421, 416])).
% 1.09/1.25 tff(423,plain,
% 1.09/1.25 (((~hskp12) | (~c0_1(a481))) <=> ((~hskp12) | (~c0_1(a481)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(424,plain,
% 1.09/1.25 (((~c0_1(a481)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a481)))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(425,axiom,((~c0_1(a481)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.09/1.25 tff(426,plain,
% 1.09/1.25 ((~hskp12) | (~c0_1(a481))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[425, 424])).
% 1.09/1.25 tff(427,plain,
% 1.09/1.25 ((~hskp12) | (~c0_1(a481))),
% 1.09/1.25 inference(modus_ponens,[status(thm)],[426, 423])).
% 1.09/1.25 tff(428,plain,
% 1.09/1.25 (~c0_1(a481)),
% 1.09/1.25 inference(unit_resolution,[status(thm)],[427, 416])).
% 1.09/1.25 tff(429,plain,
% 1.09/1.25 (((~hskp12) | c1_1(a481)) <=> ((~hskp12) | c1_1(a481))),
% 1.09/1.25 inference(rewrite,[status(thm)],[])).
% 1.09/1.25 tff(430,axiom,((~hskp12) | c1_1(a481)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.09/1.26 tff(431,plain,
% 1.09/1.26 ((~hskp12) | c1_1(a481)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[430, 429])).
% 1.09/1.26 tff(432,plain,
% 1.09/1.26 ((~hskp12) | c1_1(a481)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[431, 429])).
% 1.09/1.26 tff(433,plain,
% 1.09/1.26 ((~hskp12) | c1_1(a481)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[432, 429])).
% 1.09/1.26 tff(434,plain,
% 1.09/1.26 ((~hskp12) | c1_1(a481)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[433, 429])).
% 1.09/1.26 tff(435,plain,
% 1.09/1.26 ((~hskp12) | c1_1(a481)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[434, 429])).
% 1.09/1.26 tff(436,plain,
% 1.09/1.26 (c1_1(a481)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[435, 416])).
% 1.09/1.26 tff(437,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(438,plain,
% 1.09/1.26 (((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a481) | c0_1(a481) | c2_1(a481)) <=> (c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(439,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a481) | c0_1(a481) | c2_1(a481))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481)))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[438])).
% 1.09/1.26 tff(440,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a481) | c0_1(a481) | c2_1(a481))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.09/1.26 inference(transitivity,[status(thm)],[439, 437])).
% 1.09/1.26 tff(441,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a481) | c0_1(a481) | c2_1(a481))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(442,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[441, 440])).
% 1.09/1.26 tff(443,plain,
% 1.09/1.26 (c2_1(a481)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[442, 75, 436, 428, 422, 10])).
% 1.09/1.26 tff(444,plain,
% 1.09/1.26 (~c1_1(a478)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[375, 75, 272, 246, 28, 264, 245, 369])).
% 1.09/1.26 tff(445,plain,
% 1.09/1.26 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.09/1.26 inference(bind,[status(th)],[])).
% 1.09/1.26 tff(446,plain,
% 1.09/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.09/1.26 inference(quant_intro,[status(thm)],[445])).
% 1.09/1.26 tff(447,plain,
% 1.09/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(448,plain,
% 1.09/1.26 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.09/1.26 inference(bind,[status(th)],[])).
% 1.09/1.26 tff(449,plain,
% 1.09/1.26 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.09/1.26 inference(quant_intro,[status(thm)],[448])).
% 1.09/1.26 tff(450,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 1.09/1.26 tff(451,plain,
% 1.09/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[450, 449])).
% 1.09/1.26 tff(452,plain,
% 1.09/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[451, 447])).
% 1.09/1.26 tff(453,plain,(
% 1.09/1.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.09/1.26 inference(skolemize,[status(sab)],[452])).
% 1.09/1.26 tff(454,plain,
% 1.09/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[453, 446])).
% 1.09/1.26 tff(455,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(456,plain,
% 1.09/1.26 (((~ndr1_0) | c2_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481))) <=> (c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(457,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[456])).
% 1.09/1.26 tff(458,plain,
% 1.09/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[457, 455])).
% 1.09/1.26 tff(459,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(460,plain,
% 1.09/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.09/1.26 tff(461,plain,
% 1.09/1.26 (~c1_1(a494)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[460, 75, 299, 436, 246, 291, 428, 422, 244, 454, 444])).
% 1.09/1.26 tff(462,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(463,plain,
% 1.09/1.26 (((~ndr1_0) | c2_1(a494) | c1_1(a494) | (~c0_1(a494)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(464,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a494) | c1_1(a494) | (~c0_1(a494)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[463])).
% 1.09/1.26 tff(465,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a494) | c1_1(a494) | (~c0_1(a494)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[464, 462])).
% 1.09/1.26 tff(466,plain,
% 1.09/1.26 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a494) | c1_1(a494) | (~c0_1(a494)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(467,plain,
% 1.09/1.26 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[466, 465])).
% 1.09/1.26 tff(468,plain,
% 1.09/1.26 ($false),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[467, 75, 299, 436, 291, 428, 369, 461, 443])).
% 1.09/1.26 tff(469,plain,((~hskp16) | (~c2_1(a478)) | c3_1(a478) | c0_1(a478) | c1_1(a465) | c0_1(a465) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.09/1.26 tff(470,plain,
% 1.09/1.26 (~hskp16),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[469, 243, 244, 245, 242, 246, 217])).
% 1.09/1.26 tff(471,plain,
% 1.09/1.26 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(472,plain,
% 1.09/1.26 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478))) <=> (hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(473,plain,
% 1.09/1.26 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478))))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[472])).
% 1.09/1.26 tff(474,plain,
% 1.09/1.26 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))),
% 1.09/1.26 inference(transitivity,[status(thm)],[473, 471])).
% 1.09/1.26 tff(475,plain,
% 1.09/1.26 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(476,plain,
% 1.09/1.26 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[475, 474])).
% 1.09/1.26 tff(477,plain,
% 1.09/1.26 (hskp16 | hskp7),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[476, 75, 246, 245, 244, 20])).
% 1.09/1.26 tff(478,plain,
% 1.09/1.26 (hskp7),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[477, 470])).
% 1.09/1.26 tff(479,plain,
% 1.09/1.26 (((~hskp7) | (~c2_1(a471))) <=> ((~hskp7) | (~c2_1(a471)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(480,plain,
% 1.09/1.26 (((~c2_1(a471)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a471)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(481,axiom,((~c2_1(a471)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.09/1.26 tff(482,plain,
% 1.09/1.26 ((~hskp7) | (~c2_1(a471))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[481, 480])).
% 1.09/1.26 tff(483,plain,
% 1.09/1.26 ((~hskp7) | (~c2_1(a471))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[482, 479])).
% 1.09/1.26 tff(484,plain,
% 1.09/1.26 (~c2_1(a471)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[483, 478])).
% 1.09/1.26 tff(485,plain,
% 1.09/1.26 (((~hskp7) | c3_1(a471)) <=> ((~hskp7) | c3_1(a471))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(486,axiom,((~hskp7) | c3_1(a471)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.09/1.26 tff(487,plain,
% 1.09/1.26 ((~hskp7) | c3_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[486, 485])).
% 1.09/1.26 tff(488,plain,
% 1.09/1.26 ((~hskp7) | c3_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[487, 485])).
% 1.09/1.26 tff(489,plain,
% 1.09/1.26 ((~hskp7) | c3_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[488, 485])).
% 1.09/1.26 tff(490,plain,
% 1.09/1.26 ((~hskp7) | c3_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[489, 485])).
% 1.09/1.26 tff(491,plain,
% 1.09/1.26 ((~hskp7) | c3_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[490, 485])).
% 1.09/1.26 tff(492,plain,
% 1.09/1.26 (c3_1(a471)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[491, 478])).
% 1.09/1.26 tff(493,plain,
% 1.09/1.26 (((~hskp7) | c0_1(a471)) <=> ((~hskp7) | c0_1(a471))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(494,axiom,((~hskp7) | c0_1(a471)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.09/1.26 tff(495,plain,
% 1.09/1.26 ((~hskp7) | c0_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[494, 493])).
% 1.09/1.26 tff(496,plain,
% 1.09/1.26 ((~hskp7) | c0_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[495, 493])).
% 1.09/1.26 tff(497,plain,
% 1.09/1.26 ((~hskp7) | c0_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[496, 493])).
% 1.09/1.26 tff(498,plain,
% 1.09/1.26 ((~hskp7) | c0_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[497, 493])).
% 1.09/1.26 tff(499,plain,
% 1.09/1.26 ((~hskp7) | c0_1(a471)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[498, 493])).
% 1.09/1.26 tff(500,plain,
% 1.09/1.26 (c0_1(a471)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[499, 478])).
% 1.09/1.26 tff(501,assumption,(c0_1(a471)), introduced(assumption)).
% 1.09/1.26 tff(502,assumption,(c3_1(a471)), introduced(assumption)).
% 1.09/1.26 tff(503,assumption,(c0_1(a467)), introduced(assumption)).
% 1.09/1.26 tff(504,plain,
% 1.09/1.26 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 1.09/1.26 inference(bind,[status(th)],[])).
% 1.09/1.26 tff(505,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.26 inference(quant_intro,[status(thm)],[504])).
% 1.09/1.26 tff(506,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(507,plain,
% 1.09/1.26 (^[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(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | 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)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 1.09/1.26 inference(bind,[status(th)],[])).
% 1.09/1.26 tff(508,plain,
% 1.09/1.26 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.26 inference(quant_intro,[status(thm)],[507])).
% 1.09/1.26 tff(509,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.09/1.26 tff(510,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.09/1.26 tff(511,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[510, 506])).
% 1.09/1.26 tff(512,plain,(
% 1.09/1.26 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.26 inference(skolemize,[status(sab)],[511])).
% 1.09/1.26 tff(513,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[512, 505])).
% 1.09/1.26 tff(514,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(515,plain,
% 1.09/1.26 ((hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a467) | c1_1(a467) | c2_1(a467)) <=> (hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(516,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a467) | c1_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467)))),
% 1.09/1.26 inference(monotonicity,[status(thm)],[515])).
% 1.09/1.26 tff(517,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a467) | c1_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467))),
% 1.09/1.26 inference(transitivity,[status(thm)],[516, 514])).
% 1.09/1.26 tff(518,plain,
% 1.09/1.26 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a467) | c1_1(a467) | c2_1(a467))),
% 1.09/1.26 inference(quant_inst,[status(thm)],[])).
% 1.09/1.26 tff(519,plain,
% 1.09/1.26 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467)),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[518, 517])).
% 1.09/1.26 tff(520,plain,
% 1.09/1.26 (hskp16 | (~c0_1(a467)) | c2_1(a467)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[519, 75, 248, 247, 513])).
% 1.09/1.26 tff(521,plain,
% 1.09/1.26 (c2_1(a467)),
% 1.09/1.26 inference(unit_resolution,[status(thm)],[520, 503, 104])).
% 1.09/1.26 tff(522,plain,
% 1.09/1.26 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.09/1.26 inference(bind,[status(th)],[])).
% 1.09/1.26 tff(523,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.26 inference(quant_intro,[status(thm)],[522])).
% 1.09/1.26 tff(524,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(525,plain,
% 1.09/1.26 (^[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(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.09/1.26 inference(bind,[status(th)],[])).
% 1.09/1.26 tff(526,plain,
% 1.09/1.26 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.26 inference(quant_intro,[status(thm)],[525])).
% 1.09/1.26 tff(527,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.09/1.26 tff(528,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[527, 526])).
% 1.09/1.26 tff(529,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[528, 524])).
% 1.09/1.26 tff(530,plain,(
% 1.09/1.26 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.26 inference(skolemize,[status(sab)],[529])).
% 1.09/1.26 tff(531,plain,
% 1.09/1.26 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.26 inference(modus_ponens,[status(thm)],[530, 523])).
% 1.09/1.26 tff(532,plain,
% 1.09/1.26 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.09/1.26 inference(rewrite,[status(thm)],[])).
% 1.09/1.26 tff(533,plain,
% 1.09/1.26 ((hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(534,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471))))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[533])).
% 1.09/1.27 tff(535,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.09/1.27 inference(transitivity,[status(thm)],[534, 532])).
% 1.09/1.27 tff(536,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(537,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.09/1.27 tff(538,plain,
% 1.09/1.27 (hskp12 | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[537, 75, 29, 248, 531])).
% 1.09/1.27 tff(539,plain,
% 1.09/1.27 ($false),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[538, 521, 503, 502, 501, 21])).
% 1.09/1.27 tff(540,plain,((~c0_1(a467)) | (~c3_1(a471)) | (~c0_1(a471)) | hskp12 | c2_1(a471) | c1_1(a467) | hskp16 | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.27 tff(541,plain,
% 1.09/1.27 (~c0_1(a467)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[540, 21, 500, 492, 484, 248, 470, 247])).
% 1.09/1.27 tff(542,plain,
% 1.09/1.27 (((~hskp5) | c0_1(a467)) <=> ((~hskp5) | c0_1(a467))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(543,axiom,((~hskp5) | c0_1(a467)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.09/1.27 tff(544,plain,
% 1.09/1.27 ((~hskp5) | c0_1(a467)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.09/1.27 tff(545,plain,
% 1.09/1.27 ((~hskp5) | c0_1(a467)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[544, 542])).
% 1.09/1.27 tff(546,plain,
% 1.09/1.27 ((~hskp5) | c0_1(a467)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[545, 542])).
% 1.09/1.27 tff(547,plain,
% 1.09/1.27 ((~hskp5) | c0_1(a467)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[546, 542])).
% 1.09/1.27 tff(548,plain,
% 1.09/1.27 ((~hskp5) | c0_1(a467)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[547, 542])).
% 1.09/1.27 tff(549,plain,
% 1.09/1.27 (~hskp5),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[548, 541])).
% 1.09/1.27 tff(550,plain,
% 1.09/1.27 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.09/1.27 inference(bind,[status(th)],[])).
% 1.09/1.27 tff(551,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.09/1.27 inference(quant_intro,[status(thm)],[550])).
% 1.09/1.27 tff(552,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(553,plain,
% 1.09/1.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | 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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.09/1.27 inference(bind,[status(th)],[])).
% 1.09/1.27 tff(554,plain,
% 1.09/1.27 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.09/1.27 inference(quant_intro,[status(thm)],[553])).
% 1.09/1.27 tff(555,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 1.09/1.27 tff(556,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.09/1.27 tff(557,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[556, 552])).
% 1.09/1.27 tff(558,plain,(
% 1.09/1.27 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.09/1.27 inference(skolemize,[status(sab)],[557])).
% 1.09/1.27 tff(559,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[558, 551])).
% 1.09/1.27 tff(560,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(561,plain,
% 1.09/1.27 ((hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a467) | c1_1(a467) | c0_1(a467)) <=> (hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(562,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a467) | c1_1(a467) | c0_1(a467))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[561])).
% 1.09/1.27 tff(563,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a467) | c1_1(a467) | c0_1(a467))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.09/1.27 inference(transitivity,[status(thm)],[562, 560])).
% 1.09/1.27 tff(564,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a467) | c1_1(a467) | c0_1(a467))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(565,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[564, 563])).
% 1.09/1.27 tff(566,plain,
% 1.09/1.27 (hskp5 | c0_1(a467) | c1_1(a467) | (~c1_1(a464))),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[565, 75, 247, 220, 219, 559])).
% 1.09/1.27 tff(567,plain,
% 1.09/1.27 (~c1_1(a464)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[566, 549, 248, 541])).
% 1.09/1.27 tff(568,plain,
% 1.09/1.27 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(569,plain,
% 1.09/1.27 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c3_1(a464))) <=> (hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(570,plain,
% 1.09/1.27 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c3_1(a464)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464))))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[569])).
% 1.09/1.27 tff(571,plain,
% 1.09/1.27 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c3_1(a464)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)))),
% 1.09/1.27 inference(transitivity,[status(thm)],[570, 568])).
% 1.09/1.27 tff(572,plain,
% 1.09/1.27 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c3_1(a464)))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(573,plain,
% 1.09/1.27 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.09/1.27 tff(574,plain,
% 1.09/1.27 (hskp12 | hskp5 | c0_1(a464) | (~c3_1(a464))),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[573, 75, 219, 41])).
% 1.09/1.27 tff(575,plain,
% 1.09/1.27 (~c3_1(a464)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[574, 549, 21, 220])).
% 1.09/1.27 tff(576,plain,
% 1.09/1.27 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(577,plain,
% 1.09/1.27 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | (~c3_1(a465))) <=> (hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(578,plain,
% 1.09/1.27 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | (~c3_1(a465)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465)))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[577])).
% 1.09/1.27 tff(579,plain,
% 1.09/1.27 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | (~c3_1(a465)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465))),
% 1.09/1.27 inference(transitivity,[status(thm)],[578, 576])).
% 1.09/1.27 tff(580,plain,
% 1.09/1.27 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | (~c3_1(a465)))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(581,plain,
% 1.09/1.27 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.09/1.27 tff(582,plain,
% 1.09/1.27 (hskp12 | hskp5 | (~c3_1(a465)) | c2_1(a465)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[581, 75, 243, 41])).
% 1.09/1.27 tff(583,plain,
% 1.09/1.27 (c2_1(a465)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[582, 337, 21, 31])).
% 1.09/1.27 tff(584,assumption,(~c1_1(a464)), introduced(assumption)).
% 1.09/1.27 tff(585,plain,
% 1.09/1.27 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 1.09/1.27 inference(bind,[status(th)],[])).
% 1.09/1.27 tff(586,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.27 inference(quant_intro,[status(thm)],[585])).
% 1.09/1.27 tff(587,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(588,plain,
% 1.09/1.27 (^[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)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 1.09/1.27 inference(bind,[status(th)],[])).
% 1.09/1.27 tff(589,plain,
% 1.09/1.27 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.27 inference(quant_intro,[status(thm)],[588])).
% 1.09/1.27 tff(590,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.09/1.27 tff(591,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.09/1.27 tff(592,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[591, 587])).
% 1.09/1.27 tff(593,plain,(
% 1.09/1.27 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.27 inference(skolemize,[status(sab)],[592])).
% 1.09/1.27 tff(594,plain,
% 1.09/1.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[593, 586])).
% 1.09/1.27 tff(595,assumption,(~c3_1(a464)), introduced(assumption)).
% 1.09/1.27 tff(596,plain,
% 1.09/1.27 (((~hskp2) | c3_1(a464)) <=> ((~hskp2) | c3_1(a464))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(597,axiom,((~hskp2) | c3_1(a464)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.09/1.27 tff(598,plain,
% 1.09/1.27 ((~hskp2) | c3_1(a464)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[597, 596])).
% 1.09/1.27 tff(599,plain,
% 1.09/1.27 ((~hskp2) | c3_1(a464)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[598, 596])).
% 1.09/1.27 tff(600,plain,
% 1.09/1.27 ((~hskp2) | c3_1(a464)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[599, 596])).
% 1.09/1.27 tff(601,plain,
% 1.09/1.27 ((~hskp2) | c3_1(a464)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[600, 596])).
% 1.09/1.27 tff(602,plain,
% 1.09/1.27 ((~hskp2) | c3_1(a464)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[601, 596])).
% 1.09/1.27 tff(603,plain,
% 1.09/1.27 (~hskp2),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[602, 595])).
% 1.09/1.27 tff(604,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(605,plain,
% 1.09/1.27 ((hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(606,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465))))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[605])).
% 1.09/1.27 tff(607,plain,
% 1.09/1.27 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.09/1.27 inference(transitivity,[status(thm)],[606, 604])).
% 1.09/1.27 tff(608,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(609,plain,
% 1.09/1.27 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[608, 607])).
% 1.09/1.27 tff(610,plain,
% 1.09/1.27 ((~c3_1(a465)) | (~c2_1(a465))),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[609, 75, 603, 595, 242, 219, 594, 584])).
% 1.09/1.27 tff(611,plain,
% 1.09/1.27 ($false),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[610, 583, 337])).
% 1.09/1.27 tff(612,plain,((~c3_1(a465)) | c3_1(a464) | c1_1(a465) | c2_1(a464) | c1_1(a464) | hskp12 | hskp5 | c0_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.27 tff(613,plain,
% 1.09/1.27 (~c3_1(a465)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[612, 575, 242, 219, 567, 21, 549, 243])).
% 1.09/1.27 tff(614,plain,
% 1.09/1.27 (~hskp3),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[403, 613])).
% 1.09/1.27 tff(615,plain,
% 1.09/1.27 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.09/1.27 inference(bind,[status(th)],[])).
% 1.09/1.27 tff(616,plain,
% 1.09/1.27 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.27 inference(quant_intro,[status(thm)],[615])).
% 1.09/1.27 tff(617,plain,
% 1.09/1.27 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(618,plain,
% 1.09/1.27 (^[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)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.09/1.27 inference(bind,[status(th)],[])).
% 1.09/1.27 tff(619,plain,
% 1.09/1.27 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.27 inference(quant_intro,[status(thm)],[618])).
% 1.09/1.27 tff(620,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 1.09/1.27 tff(621,plain,
% 1.09/1.27 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[620, 619])).
% 1.09/1.27 tff(622,plain,
% 1.09/1.27 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[621, 617])).
% 1.09/1.27 tff(623,plain,(
% 1.09/1.27 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.27 inference(skolemize,[status(sab)],[622])).
% 1.09/1.27 tff(624,plain,
% 1.09/1.27 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[623, 616])).
% 1.09/1.27 tff(625,plain,
% 1.09/1.27 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(626,plain,
% 1.09/1.27 ((hskp4 | hskp3 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464)) <=> (hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(627,plain,
% 1.09/1.27 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464)))),
% 1.09/1.27 inference(monotonicity,[status(thm)],[626])).
% 1.09/1.27 tff(628,plain,
% 1.09/1.27 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.09/1.27 inference(transitivity,[status(thm)],[627, 625])).
% 1.09/1.27 tff(629,plain,
% 1.09/1.27 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))),
% 1.09/1.27 inference(quant_inst,[status(thm)],[])).
% 1.09/1.27 tff(630,plain,
% 1.09/1.27 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464)),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[629, 628])).
% 1.09/1.27 tff(631,plain,
% 1.09/1.27 (hskp4 | hskp3 | c0_1(a464) | c1_1(a464)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[630, 75, 219, 624])).
% 1.09/1.27 tff(632,plain,
% 1.09/1.27 (hskp4),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[631, 614, 220, 567])).
% 1.09/1.27 tff(633,plain,
% 1.09/1.27 (((~hskp4) | (~c0_1(a466))) <=> ((~hskp4) | (~c0_1(a466)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(634,plain,
% 1.09/1.27 (((~c0_1(a466)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a466)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.27 tff(635,axiom,((~c0_1(a466)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.09/1.27 tff(636,plain,
% 1.09/1.27 ((~hskp4) | (~c0_1(a466))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.09/1.27 tff(637,plain,
% 1.09/1.27 ((~hskp4) | (~c0_1(a466))),
% 1.09/1.27 inference(modus_ponens,[status(thm)],[636, 633])).
% 1.09/1.27 tff(638,plain,
% 1.09/1.27 (~c0_1(a466)),
% 1.09/1.27 inference(unit_resolution,[status(thm)],[637, 632])).
% 1.09/1.27 tff(639,plain,
% 1.09/1.27 (((~hskp4) | (~c1_1(a466))) <=> ((~hskp4) | (~c1_1(a466)))),
% 1.09/1.27 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(640,plain,
% 1.09/1.28 (((~c1_1(a466)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a466)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(641,axiom,((~c1_1(a466)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.09/1.28 tff(642,plain,
% 1.09/1.28 ((~hskp4) | (~c1_1(a466))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[641, 640])).
% 1.09/1.28 tff(643,plain,
% 1.09/1.28 ((~hskp4) | (~c1_1(a466))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[642, 639])).
% 1.09/1.28 tff(644,plain,
% 1.09/1.28 (~c1_1(a466)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[643, 632])).
% 1.09/1.28 tff(645,plain,
% 1.09/1.28 (((~hskp4) | (~c3_1(a466))) <=> ((~hskp4) | (~c3_1(a466)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(646,plain,
% 1.09/1.28 (((~c3_1(a466)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a466)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(647,axiom,((~c3_1(a466)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.09/1.28 tff(648,plain,
% 1.09/1.28 ((~hskp4) | (~c3_1(a466))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[647, 646])).
% 1.09/1.28 tff(649,plain,
% 1.09/1.28 ((~hskp4) | (~c3_1(a466))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[648, 645])).
% 1.09/1.28 tff(650,plain,
% 1.09/1.28 (~c3_1(a466)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[649, 632])).
% 1.09/1.28 tff(651,assumption,(~c3_1(a466)), introduced(assumption)).
% 1.09/1.28 tff(652,assumption,(~c0_1(a466)), introduced(assumption)).
% 1.09/1.28 tff(653,assumption,(~c1_1(a466)), introduced(assumption)).
% 1.09/1.28 tff(654,plain,
% 1.09/1.28 (hskp7),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[477, 104])).
% 1.09/1.28 tff(655,plain,
% 1.09/1.28 (c0_1(a471)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[499, 654])).
% 1.09/1.28 tff(656,plain,
% 1.09/1.28 (c3_1(a471)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[491, 654])).
% 1.09/1.28 tff(657,plain,
% 1.09/1.28 (~c0_1(a467)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[540, 655, 21, 656, 29, 248, 104, 247])).
% 1.09/1.28 tff(658,plain,
% 1.09/1.28 (~hskp5),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[548, 657])).
% 1.09/1.28 tff(659,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(660,plain,
% 1.09/1.28 ((hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a466) | c1_1(a466) | c0_1(a466)) <=> (hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(661,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a466) | c1_1(a466) | c0_1(a466))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[660])).
% 1.09/1.28 tff(662,plain,
% 1.09/1.28 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a466) | c1_1(a466) | c0_1(a466))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[661, 659])).
% 1.09/1.28 tff(663,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a466) | c1_1(a466) | c0_1(a466))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(664,plain,
% 1.09/1.28 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[663, 662])).
% 1.09/1.28 tff(665,plain,
% 1.09/1.28 (hskp5 | c0_1(a466) | c1_1(a466) | (~c1_1(a464))),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[664, 75, 651, 220, 219, 559])).
% 1.09/1.28 tff(666,plain,
% 1.09/1.28 (~c1_1(a464)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[665, 658, 653, 652])).
% 1.09/1.28 tff(667,plain,
% 1.09/1.28 (^[U: $i] : refl((hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.09/1.28 inference(bind,[status(th)],[])).
% 1.09/1.28 tff(668,plain,
% 1.09/1.28 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.28 inference(quant_intro,[status(thm)],[667])).
% 1.09/1.28 tff(669,plain,
% 1.09/1.28 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(670,plain,
% 1.09/1.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.09/1.28 inference(bind,[status(th)],[])).
% 1.09/1.28 tff(671,plain,
% 1.09/1.28 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.28 inference(quant_intro,[status(thm)],[670])).
% 1.09/1.28 tff(672,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.09/1.28 tff(673,plain,
% 1.09/1.28 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[672, 671])).
% 1.09/1.28 tff(674,plain,
% 1.09/1.28 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[673, 669])).
% 1.09/1.28 tff(675,plain,(
% 1.09/1.28 ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.28 inference(skolemize,[status(sab)],[674])).
% 1.09/1.28 tff(676,plain,
% 1.09/1.28 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[675, 668])).
% 1.09/1.28 tff(677,plain,
% 1.09/1.28 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(678,plain,
% 1.09/1.28 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471))) <=> (hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(679,plain,
% 1.09/1.28 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[678])).
% 1.09/1.28 tff(680,plain,
% 1.09/1.28 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[679, 677])).
% 1.09/1.28 tff(681,plain,
% 1.09/1.28 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(682,plain,
% 1.09/1.28 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[681, 680])).
% 1.09/1.28 tff(683,plain,
% 1.09/1.28 (hskp17 | hskp5 | (~c0_1(a471)) | (~c3_1(a471))),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[682, 75, 29, 676])).
% 1.09/1.28 tff(684,plain,
% 1.09/1.28 (hskp17),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[683, 658, 655, 656])).
% 1.09/1.28 tff(685,plain,
% 1.09/1.28 (((~hskp17) | c2_1(a493)) <=> ((~hskp17) | c2_1(a493))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(686,axiom,((~hskp17) | c2_1(a493)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.09/1.28 tff(687,plain,
% 1.09/1.28 ((~hskp17) | c2_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[686, 685])).
% 1.09/1.28 tff(688,plain,
% 1.09/1.28 ((~hskp17) | c2_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[687, 685])).
% 1.09/1.28 tff(689,plain,
% 1.09/1.28 ((~hskp17) | c2_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[688, 685])).
% 1.09/1.28 tff(690,plain,
% 1.09/1.28 ((~hskp17) | c2_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[689, 685])).
% 1.09/1.28 tff(691,plain,
% 1.09/1.28 ((~hskp17) | c2_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[690, 685])).
% 1.09/1.28 tff(692,plain,
% 1.09/1.28 (c2_1(a493)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[691, 684])).
% 1.09/1.28 tff(693,plain,
% 1.09/1.28 (((~hskp17) | (~c0_1(a493))) <=> ((~hskp17) | (~c0_1(a493)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(694,plain,
% 1.09/1.28 (((~c0_1(a493)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a493)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(695,axiom,((~c0_1(a493)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.09/1.28 tff(696,plain,
% 1.09/1.28 ((~hskp17) | (~c0_1(a493))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[695, 694])).
% 1.09/1.28 tff(697,plain,
% 1.09/1.28 ((~hskp17) | (~c0_1(a493))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[696, 693])).
% 1.09/1.28 tff(698,plain,
% 1.09/1.28 (~c0_1(a493)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[697, 684])).
% 1.09/1.28 tff(699,plain,
% 1.09/1.28 (((~hskp17) | c3_1(a493)) <=> ((~hskp17) | c3_1(a493))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(700,axiom,((~hskp17) | c3_1(a493)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.09/1.28 tff(701,plain,
% 1.09/1.28 ((~hskp17) | c3_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[700, 699])).
% 1.09/1.28 tff(702,plain,
% 1.09/1.28 ((~hskp17) | c3_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[701, 699])).
% 1.09/1.28 tff(703,plain,
% 1.09/1.28 ((~hskp17) | c3_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[702, 699])).
% 1.09/1.28 tff(704,plain,
% 1.09/1.28 ((~hskp17) | c3_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[703, 699])).
% 1.09/1.28 tff(705,plain,
% 1.09/1.28 ((~hskp17) | c3_1(a493)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[704, 699])).
% 1.09/1.28 tff(706,plain,
% 1.09/1.28 (c3_1(a493)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[705, 684])).
% 1.09/1.28 tff(707,plain,
% 1.09/1.28 (~c0_1(a467)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[540, 501, 21, 502, 29, 248, 104, 247])).
% 1.09/1.28 tff(708,plain,
% 1.09/1.28 (~hskp5),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[548, 707])).
% 1.09/1.28 tff(709,plain,
% 1.09/1.28 (hskp17),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[683, 708, 501, 502])).
% 1.09/1.28 tff(710,plain,
% 1.09/1.28 (~c0_1(a493)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[697, 709])).
% 1.09/1.28 tff(711,assumption,(hskp26), introduced(assumption)).
% 1.09/1.28 tff(712,plain,
% 1.09/1.28 (((~hskp26) | (~c3_1(a559))) <=> ((~hskp26) | (~c3_1(a559)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(713,plain,
% 1.09/1.28 (((~c3_1(a559)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a559)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(714,axiom,((~c3_1(a559)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.09/1.28 tff(715,plain,
% 1.09/1.28 ((~hskp26) | (~c3_1(a559))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[714, 713])).
% 1.09/1.28 tff(716,plain,
% 1.09/1.28 ((~hskp26) | (~c3_1(a559))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[715, 712])).
% 1.09/1.28 tff(717,plain,
% 1.09/1.28 (~c3_1(a559)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[716, 711])).
% 1.09/1.28 tff(718,plain,
% 1.09/1.28 (c3_1(a493)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[705, 709])).
% 1.09/1.28 tff(719,plain,
% 1.09/1.28 (c2_1(a493)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[691, 709])).
% 1.09/1.28 tff(720,plain,
% 1.09/1.28 (((~hskp26) | c0_1(a559)) <=> ((~hskp26) | c0_1(a559))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(721,axiom,((~hskp26) | c0_1(a559)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.09/1.28 tff(722,plain,
% 1.09/1.28 ((~hskp26) | c0_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[721, 720])).
% 1.09/1.28 tff(723,plain,
% 1.09/1.28 ((~hskp26) | c0_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[722, 720])).
% 1.09/1.28 tff(724,plain,
% 1.09/1.28 ((~hskp26) | c0_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[723, 720])).
% 1.09/1.28 tff(725,plain,
% 1.09/1.28 ((~hskp26) | c0_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[724, 720])).
% 1.09/1.28 tff(726,plain,
% 1.09/1.28 ((~hskp26) | c0_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[725, 720])).
% 1.09/1.28 tff(727,plain,
% 1.09/1.28 (c0_1(a559)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[726, 711])).
% 1.09/1.28 tff(728,plain,
% 1.09/1.28 (((~hskp26) | c1_1(a559)) <=> ((~hskp26) | c1_1(a559))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(729,axiom,((~hskp26) | c1_1(a559)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.09/1.28 tff(730,plain,
% 1.09/1.28 ((~hskp26) | c1_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[729, 728])).
% 1.09/1.28 tff(731,plain,
% 1.09/1.28 ((~hskp26) | c1_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[730, 728])).
% 1.09/1.28 tff(732,plain,
% 1.09/1.28 ((~hskp26) | c1_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[731, 728])).
% 1.09/1.28 tff(733,plain,
% 1.09/1.28 ((~hskp26) | c1_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[732, 728])).
% 1.09/1.28 tff(734,plain,
% 1.09/1.28 ((~hskp26) | c1_1(a559)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[733, 728])).
% 1.09/1.28 tff(735,plain,
% 1.09/1.28 (c1_1(a559)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[734, 711])).
% 1.09/1.28 tff(736,plain,
% 1.09/1.28 (~c0_1(a467)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[540, 21, 501, 502, 29, 248, 104, 247])).
% 1.09/1.28 tff(737,plain,
% 1.09/1.28 (~hskp5),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[548, 736])).
% 1.09/1.28 tff(738,plain,
% 1.09/1.28 (~c1_1(a464)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[665, 737, 653, 652])).
% 1.09/1.28 tff(739,plain,
% 1.09/1.28 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 1.09/1.28 inference(bind,[status(th)],[])).
% 1.09/1.28 tff(740,plain,
% 1.09/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.09/1.28 inference(quant_intro,[status(thm)],[739])).
% 1.09/1.28 tff(741,plain,
% 1.09/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(742,plain,
% 1.09/1.28 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 1.09/1.28 inference(bind,[status(th)],[])).
% 1.09/1.28 tff(743,plain,
% 1.09/1.28 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.09/1.28 inference(quant_intro,[status(thm)],[742])).
% 1.09/1.28 tff(744,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 1.09/1.28 tff(745,plain,
% 1.09/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[744, 743])).
% 1.09/1.28 tff(746,plain,
% 1.09/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[745, 741])).
% 1.09/1.28 tff(747,plain,(
% 1.09/1.28 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.09/1.28 inference(skolemize,[status(sab)],[746])).
% 1.09/1.28 tff(748,plain,
% 1.09/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[747, 740])).
% 1.09/1.28 tff(749,assumption,(~c0_1(a493)), introduced(assumption)).
% 1.09/1.28 tff(750,assumption,(~c3_1(a559)), introduced(assumption)).
% 1.09/1.28 tff(751,plain,
% 1.09/1.28 (~c3_1(a464)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[574, 737, 21, 220])).
% 1.09/1.28 tff(752,assumption,(c3_1(a493)), introduced(assumption)).
% 1.09/1.28 tff(753,assumption,(c2_1(a493)), introduced(assumption)).
% 1.09/1.28 tff(754,assumption,(c1_1(a559)), introduced(assumption)).
% 1.09/1.28 tff(755,assumption,(c0_1(a559)), introduced(assumption)).
% 1.09/1.28 tff(756,plain,
% 1.09/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(757,plain,
% 1.09/1.28 (((~ndr1_0) | c3_1(a559) | (~c1_1(a559)) | (~c0_1(a559)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(758,plain,
% 1.09/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a559) | (~c1_1(a559)) | (~c0_1(a559)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[757])).
% 1.09/1.28 tff(759,plain,
% 1.09/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a559) | (~c1_1(a559)) | (~c0_1(a559)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[758, 756])).
% 1.09/1.28 tff(760,plain,
% 1.09/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a559) | (~c1_1(a559)) | (~c0_1(a559)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(761,plain,
% 1.09/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.09/1.28 tff(762,plain,
% 1.09/1.28 ($false),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[761, 75, 755, 754, 753, 752, 751, 750, 749, 219, 748, 738])).
% 1.09/1.28 tff(763,plain,(hskp12 | (~c0_1(a559)) | (~c1_1(a559)) | (~c2_1(a493)) | (~c3_1(a493)) | c3_1(a559) | c0_1(a493) | c2_1(a464) | c0_1(a464) | c1_1(a466) | c0_1(a466) | c3_1(a466) | (~c0_1(a471)) | (~c3_1(a471)) | c2_1(a471) | c1_1(a467) | hskp16 | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.28 tff(764,plain,
% 1.09/1.28 ($false),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[763, 735, 727, 21, 719, 718, 717, 710, 219, 220, 653, 652, 651, 501, 502, 29, 248, 104, 247])).
% 1.09/1.28 tff(765,plain,((~hskp26) | hskp12 | c2_1(a464) | c0_1(a464) | c1_1(a466) | c0_1(a466) | c3_1(a466) | (~c0_1(a471)) | (~c3_1(a471)) | c2_1(a471) | c1_1(a467) | hskp16 | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.28 tff(766,plain,
% 1.09/1.28 (~hskp26),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[765, 655, 219, 220, 653, 652, 651, 21, 656, 29, 248, 104, 247])).
% 1.09/1.28 tff(767,plain,
% 1.09/1.28 ((hskp26 | hskp16 | hskp13) <=> (hskp26 | hskp16 | hskp13)),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(768,plain,
% 1.09/1.28 (((hskp26 | hskp16) | hskp13) <=> (hskp26 | hskp16 | hskp13)),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(769,plain,
% 1.09/1.28 ((hskp26 | hskp16) <=> (hskp26 | hskp16)),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(770,plain,
% 1.09/1.28 (((hskp26 | hskp16) | hskp13) <=> ((hskp26 | hskp16) | hskp13)),
% 1.09/1.28 inference(monotonicity,[status(thm)],[769])).
% 1.09/1.28 tff(771,plain,
% 1.09/1.28 (((hskp26 | hskp16) | hskp13) <=> (hskp26 | hskp16 | hskp13)),
% 1.09/1.28 inference(transitivity,[status(thm)],[770, 768])).
% 1.09/1.28 tff(772,axiom,((hskp26 | hskp16) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.09/1.28 tff(773,plain,
% 1.09/1.28 (hskp26 | hskp16 | hskp13),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.09/1.28 tff(774,plain,
% 1.09/1.28 (hskp26 | hskp16 | hskp13),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[773, 767])).
% 1.09/1.28 tff(775,plain,
% 1.09/1.28 (hskp26 | hskp16 | hskp13),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[774, 767])).
% 1.09/1.28 tff(776,plain,
% 1.09/1.28 (hskp26 | hskp16 | hskp13),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[775, 767])).
% 1.09/1.28 tff(777,plain,
% 1.09/1.28 (hskp26 | hskp16 | hskp13),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[776, 767])).
% 1.09/1.28 tff(778,plain,
% 1.09/1.28 (hskp13),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[777, 766, 104])).
% 1.09/1.28 tff(779,plain,
% 1.09/1.28 (((~hskp13) | (~c2_1(a482))) <=> ((~hskp13) | (~c2_1(a482)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(780,plain,
% 1.09/1.28 (((~c2_1(a482)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a482)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(781,axiom,((~c2_1(a482)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.09/1.28 tff(782,plain,
% 1.09/1.28 ((~hskp13) | (~c2_1(a482))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.09/1.28 tff(783,plain,
% 1.09/1.28 ((~hskp13) | (~c2_1(a482))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[782, 779])).
% 1.09/1.28 tff(784,plain,
% 1.09/1.28 (~c2_1(a482)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[783, 778])).
% 1.09/1.28 tff(785,assumption,(~c0_1(a482)), introduced(assumption)).
% 1.09/1.28 tff(786,assumption,(~c2_1(a482)), introduced(assumption)).
% 1.09/1.28 tff(787,plain,
% 1.09/1.28 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(788,plain,
% 1.09/1.28 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a482) | c0_1(a482) | (~c3_1(a482))) <=> (hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(789,plain,
% 1.09/1.28 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a482) | c0_1(a482) | (~c3_1(a482)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[788])).
% 1.09/1.28 tff(790,plain,
% 1.09/1.28 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a482) | c0_1(a482) | (~c3_1(a482)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[789, 787])).
% 1.09/1.28 tff(791,plain,
% 1.09/1.28 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a482) | c0_1(a482) | (~c3_1(a482)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(792,plain,
% 1.09/1.28 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[791, 790])).
% 1.09/1.28 tff(793,plain,
% 1.09/1.28 (hskp12 | hskp5 | c0_1(a482) | (~c3_1(a482))),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[792, 75, 786, 41])).
% 1.09/1.28 tff(794,plain,
% 1.09/1.28 (~c3_1(a482)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[793, 737, 785, 21])).
% 1.09/1.28 tff(795,plain,
% 1.09/1.28 (((~hskp13) | c3_1(a482)) <=> ((~hskp13) | c3_1(a482))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(796,axiom,((~hskp13) | c3_1(a482)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.09/1.28 tff(797,plain,
% 1.09/1.28 ((~hskp13) | c3_1(a482)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[796, 795])).
% 1.09/1.28 tff(798,plain,
% 1.09/1.28 ((~hskp13) | c3_1(a482)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[797, 795])).
% 1.09/1.28 tff(799,plain,
% 1.09/1.28 ((~hskp13) | c3_1(a482)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[798, 795])).
% 1.09/1.28 tff(800,plain,
% 1.09/1.28 ((~hskp13) | c3_1(a482)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[799, 795])).
% 1.09/1.28 tff(801,plain,
% 1.09/1.28 ((~hskp13) | c3_1(a482)),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[800, 795])).
% 1.09/1.28 tff(802,plain,
% 1.09/1.28 (~hskp13),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[801, 794])).
% 1.09/1.28 tff(803,plain,
% 1.09/1.28 (hskp26),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[777, 802, 104])).
% 1.09/1.28 tff(804,plain,
% 1.09/1.28 (~c3_1(a559)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[716, 803])).
% 1.09/1.28 tff(805,plain,
% 1.09/1.28 (c1_1(a559)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[734, 803])).
% 1.09/1.28 tff(806,plain,
% 1.09/1.28 (c0_1(a559)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[726, 803])).
% 1.09/1.28 tff(807,plain,
% 1.09/1.28 ($false),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[761, 75, 806, 805, 753, 752, 751, 804, 749, 219, 748, 738])).
% 1.09/1.28 tff(808,plain,(hskp12 | (~c2_1(a493)) | (~c3_1(a493)) | c0_1(a493) | c2_1(a464) | hskp16 | c0_1(a482) | c2_1(a482) | c0_1(a464) | c1_1(a466) | c0_1(a466) | c3_1(a466) | (~c0_1(a471)) | (~c3_1(a471)) | c2_1(a471) | c1_1(a467) | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.28 tff(809,plain,
% 1.09/1.28 (c0_1(a482)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[808, 784, 21, 656, 219, 104, 706, 698, 220, 653, 652, 651, 655, 692, 29, 248, 247])).
% 1.09/1.28 tff(810,plain,
% 1.09/1.28 (((~hskp13) | (~c1_1(a482))) <=> ((~hskp13) | (~c1_1(a482)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(811,plain,
% 1.09/1.28 (((~c1_1(a482)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a482)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(812,axiom,((~c1_1(a482)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.09/1.28 tff(813,plain,
% 1.09/1.28 ((~hskp13) | (~c1_1(a482))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[812, 811])).
% 1.09/1.28 tff(814,plain,
% 1.09/1.28 ((~hskp13) | (~c1_1(a482))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[813, 810])).
% 1.09/1.28 tff(815,plain,
% 1.09/1.28 (~c1_1(a482)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[814, 778])).
% 1.09/1.28 tff(816,plain,
% 1.09/1.28 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(817,plain,
% 1.09/1.28 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a482) | c1_1(a482) | (~c0_1(a482))) <=> (hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(818,plain,
% 1.09/1.28 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a482) | c1_1(a482) | (~c0_1(a482)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[817])).
% 1.09/1.28 tff(819,plain,
% 1.09/1.28 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a482) | c1_1(a482) | (~c0_1(a482)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[818, 816])).
% 1.09/1.28 tff(820,plain,
% 1.09/1.28 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a482) | c1_1(a482) | (~c0_1(a482)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(821,plain,
% 1.09/1.28 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[820, 819])).
% 1.09/1.28 tff(822,plain,
% 1.09/1.28 (hskp18),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[821, 75, 217, 815, 784, 258, 809])).
% 1.09/1.28 tff(823,plain,
% 1.09/1.28 (~c2_1(a494)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[290, 822])).
% 1.09/1.28 tff(824,plain,
% 1.09/1.28 (~c3_1(a494)),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[284, 822])).
% 1.09/1.28 tff(825,assumption,(~c0_1(a494)), introduced(assumption)).
% 1.09/1.28 tff(826,plain,
% 1.09/1.28 (~hskp18),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[298, 825])).
% 1.09/1.28 tff(827,plain,
% 1.09/1.28 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(828,plain,
% 1.09/1.28 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471))) <=> (hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)))),
% 1.09/1.28 inference(rewrite,[status(thm)],[])).
% 1.09/1.28 tff(829,plain,
% 1.09/1.28 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471))))),
% 1.09/1.28 inference(monotonicity,[status(thm)],[828])).
% 1.09/1.28 tff(830,plain,
% 1.09/1.28 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)))),
% 1.09/1.28 inference(transitivity,[status(thm)],[829, 827])).
% 1.09/1.28 tff(831,plain,
% 1.09/1.28 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)))),
% 1.09/1.28 inference(quant_inst,[status(thm)],[])).
% 1.09/1.28 tff(832,plain,
% 1.09/1.28 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471))),
% 1.09/1.28 inference(modus_ponens,[status(thm)],[831, 830])).
% 1.09/1.28 tff(833,plain,
% 1.09/1.28 (hskp18 | c1_1(a471) | (~c0_1(a471))),
% 1.09/1.28 inference(unit_resolution,[status(thm)],[832, 75, 217, 29, 258])).
% 1.09/1.29 tff(834,plain,
% 1.09/1.29 (c1_1(a471)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[833, 826, 501])).
% 1.09/1.29 tff(835,plain,
% 1.09/1.29 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.09/1.29 inference(bind,[status(th)],[])).
% 1.09/1.29 tff(836,plain,
% 1.09/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.09/1.29 inference(quant_intro,[status(thm)],[835])).
% 1.09/1.29 tff(837,plain,
% 1.09/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(838,plain,
% 1.09/1.29 (^[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))) | (~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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.09/1.29 inference(bind,[status(th)],[])).
% 1.09/1.29 tff(839,plain,
% 1.09/1.29 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_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)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.09/1.29 inference(quant_intro,[status(thm)],[838])).
% 1.09/1.29 tff(840,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause207')).
% 1.09/1.29 tff(841,plain,
% 1.09/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[840, 839])).
% 1.09/1.29 tff(842,plain,
% 1.09/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[841, 837])).
% 1.09/1.29 tff(843,plain,(
% 1.09/1.29 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.09/1.29 inference(skolemize,[status(sab)],[842])).
% 1.09/1.29 tff(844,plain,
% 1.09/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[843, 836])).
% 1.09/1.29 tff(845,plain,
% 1.09/1.29 (hskp17),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[683, 31, 501, 502])).
% 1.09/1.29 tff(846,plain,
% 1.09/1.29 (~c0_1(a493)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[697, 845])).
% 1.09/1.29 tff(847,plain,
% 1.09/1.29 (c3_1(a493)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[705, 845])).
% 1.09/1.29 tff(848,plain,
% 1.09/1.29 (c2_1(a493)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[691, 845])).
% 1.09/1.29 tff(849,plain,
% 1.09/1.29 (~c3_1(a464)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[574, 31, 21, 220])).
% 1.09/1.29 tff(850,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(851,plain,
% 1.09/1.29 ((hskp5 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | (~c1_1(a494)) | c3_1(a464) | c1_1(a464) | c0_1(a464)) <=> (hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(852,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | (~c1_1(a494)) | c3_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494))))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[851])).
% 1.09/1.29 tff(853,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | (~c1_1(a494)) | c3_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494)))),
% 1.09/1.29 inference(transitivity,[status(thm)],[852, 850])).
% 1.09/1.29 tff(854,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | (~c1_1(a494)) | c3_1(a464) | c1_1(a464) | c0_1(a464))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(855,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[854, 853])).
% 1.09/1.29 tff(856,plain,
% 1.09/1.29 (c0_1(a494) | (~c1_1(a494))),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[855, 75, 31, 849, 301, 220, 559, 584])).
% 1.09/1.29 tff(857,plain,
% 1.09/1.29 (~c1_1(a494)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[856, 825])).
% 1.09/1.29 tff(858,assumption,(~c1_1(a494)), introduced(assumption)).
% 1.09/1.29 tff(859,plain,
% 1.09/1.29 (c2_1(a465)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[582, 21, 337, 31])).
% 1.09/1.29 tff(860,plain,
% 1.09/1.29 (~c3_1(a464)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[574, 21, 31, 220])).
% 1.09/1.29 tff(861,plain,
% 1.09/1.29 (~hskp2),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[602, 860])).
% 1.09/1.29 tff(862,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(863,plain,
% 1.09/1.29 ((hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a494) | c1_1(a494) | c2_1(a494)) <=> (hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(864,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a494) | c1_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494)))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[863])).
% 1.09/1.29 tff(865,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a494) | c1_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494))),
% 1.09/1.29 inference(transitivity,[status(thm)],[864, 862])).
% 1.09/1.29 tff(866,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a494) | c1_1(a494) | c2_1(a494))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(867,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494)),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[866, 865])).
% 1.09/1.29 tff(868,plain,
% 1.09/1.29 (hskp2 | c2_1(a494) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[867, 75, 300, 242, 594])).
% 1.09/1.29 tff(869,plain,
% 1.09/1.29 ($false),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[868, 861, 859, 301, 337, 858])).
% 1.09/1.29 tff(870,plain,(hskp12 | c2_1(a494) | (~c3_1(a465)) | c1_1(a494) | c3_1(a494) | c1_1(a465) | hskp5 | c0_1(a465) | c0_1(a464) | c2_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.29 tff(871,plain,
% 1.09/1.29 (~c3_1(a465)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[870, 857, 21, 31, 300, 242, 301, 243, 220, 219])).
% 1.09/1.29 tff(872,plain,
% 1.09/1.29 (~hskp3),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[403, 871])).
% 1.09/1.29 tff(873,plain,
% 1.09/1.29 (hskp29),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[415, 872, 21])).
% 1.09/1.29 tff(874,plain,
% 1.09/1.29 (c2_1(a474)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[310, 873])).
% 1.09/1.29 tff(875,plain,
% 1.09/1.29 (c1_1(a474)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[318, 873])).
% 1.09/1.29 tff(876,plain,
% 1.09/1.29 (c0_1(a474)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[326, 873])).
% 1.09/1.29 tff(877,plain,
% 1.09/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(878,plain,
% 1.09/1.29 (((~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493))) <=> (c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(879,plain,
% 1.09/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[878])).
% 1.09/1.29 tff(880,plain,
% 1.09/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.29 inference(transitivity,[status(thm)],[879, 877])).
% 1.09/1.29 tff(881,plain,
% 1.09/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(882,plain,
% 1.09/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[881, 880])).
% 1.09/1.29 tff(883,plain,
% 1.09/1.29 ($false),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[882, 75, 876, 875, 874, 848, 847, 501, 502, 846, 844, 834])).
% 1.09/1.29 tff(884,plain,(c0_1(a494) | (~c0_1(a471)) | (~c3_1(a471)) | hskp12 | hskp5 | c3_1(a494) | c1_1(a465) | c2_1(a494) | c0_1(a465) | c0_1(a464) | c2_1(a464) | hskp19 | c2_1(a471) | c1_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.29 tff(885,plain,
% 1.09/1.29 (c0_1(a494)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[884, 301, 502, 21, 31, 300, 242, 501, 243, 220, 219, 217, 29, 584])).
% 1.09/1.29 tff(886,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(887,plain,
% 1.09/1.29 ((hskp16 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | c2_1(a494)) <=> (hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(888,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494))))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[887])).
% 1.09/1.29 tff(889,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494)))),
% 1.09/1.29 inference(transitivity,[status(thm)],[888, 886])).
% 1.09/1.29 tff(890,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | c2_1(a494))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(891,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[890, 889])).
% 1.09/1.29 tff(892,plain,
% 1.09/1.29 ($false),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[891, 75, 104, 302, 301, 300, 513, 858])).
% 1.09/1.29 tff(893,plain,(c1_1(a494) | hskp16 | (~c0_1(a494)) | c2_1(a494) | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.29 tff(894,plain,
% 1.09/1.29 (c1_1(a494)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[893, 885, 300, 301, 104])).
% 1.09/1.29 tff(895,plain,
% 1.09/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(896,plain,
% 1.09/1.29 (((~ndr1_0) | c3_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(897,plain,
% 1.09/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494))))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[896])).
% 1.09/1.29 tff(898,plain,
% 1.09/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.09/1.29 inference(transitivity,[status(thm)],[897, 895])).
% 1.09/1.29 tff(899,plain,
% 1.09/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(900,plain,
% 1.09/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[899, 898])).
% 1.09/1.29 tff(901,plain,
% 1.09/1.29 ((~c1_1(a494)) | (~c0_1(a494))),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[900, 75, 848, 847, 849, 300, 846, 219, 748, 584])).
% 1.09/1.29 tff(902,plain,
% 1.09/1.29 ($false),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[901, 894, 885])).
% 1.09/1.29 tff(903,plain,(c2_1(a494) | c3_1(a494) | c2_1(a464) | c1_1(a464) | hskp16 | (~c3_1(a471)) | hskp12 | hskp5 | c1_1(a465) | (~c0_1(a471)) | c0_1(a465) | c0_1(a464) | hskp19 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.29 tff(904,plain,
% 1.09/1.29 ($false),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[903, 824, 823, 219, 666, 104, 656, 21, 658, 242, 655, 243, 220, 217, 29])).
% 1.09/1.29 tff(905,plain,(hskp16 | c2_1(a464) | hskp12 | c1_1(a465) | c0_1(a465) | c0_1(a464) | hskp19 | c2_1(a471) | c1_1(a466) | c0_1(a466) | c3_1(a466) | c1_1(a467) | c3_1(a467) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.29 tff(906,plain,
% 1.09/1.29 (hskp16),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[905, 21, 219, 242, 243, 220, 217, 29, 653, 652, 651, 248, 247, 246, 245, 244])).
% 1.09/1.29 tff(907,plain,
% 1.09/1.29 (~c2_1(a487)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[263, 906])).
% 1.09/1.29 tff(908,plain,
% 1.09/1.29 (~c1_1(a487)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[27, 906])).
% 1.09/1.29 tff(909,plain,
% 1.09/1.29 (c0_1(a487)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[271, 906])).
% 1.09/1.29 tff(910,plain,
% 1.09/1.29 (hskp18),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[278, 75, 217, 909, 908, 907, 258])).
% 1.09/1.29 tff(911,plain,
% 1.09/1.29 (~c3_1(a494)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[284, 910])).
% 1.09/1.29 tff(912,plain,
% 1.09/1.29 (~c2_1(a494)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[290, 910])).
% 1.09/1.29 tff(913,plain,
% 1.09/1.29 (c0_1(a494)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[298, 910])).
% 1.09/1.29 tff(914,plain,
% 1.09/1.29 (~hskp29),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[335, 913, 912, 911])).
% 1.09/1.29 tff(915,plain,
% 1.09/1.29 (hskp3),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[415, 914, 21])).
% 1.09/1.29 tff(916,plain,
% 1.09/1.29 (c3_1(a465)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[403, 915])).
% 1.09/1.29 tff(917,plain,
% 1.09/1.29 (hskp29 | (~c3_1(a465)) | c2_1(a465)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[357, 75, 909, 908, 907, 243, 348])).
% 1.09/1.29 tff(918,plain,
% 1.09/1.29 (c2_1(a465)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[917, 916, 914])).
% 1.09/1.29 tff(919,plain,
% 1.09/1.29 (~c1_1(a478)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[375, 75, 909, 246, 908, 907, 245, 369])).
% 1.09/1.29 tff(920,plain,
% 1.09/1.29 ($false),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[392, 75, 913, 246, 916, 912, 911, 245, 242, 386, 919, 918])).
% 1.09/1.29 tff(921,plain,(hskp12 | (~c2_1(a478)) | c0_1(a478) | c1_1(a465) | c0_1(a465) | hskp19 | c2_1(a464) | c0_1(a464) | c2_1(a471) | c1_1(a466) | c0_1(a466) | c3_1(a466) | c1_1(a467) | c3_1(a467) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.29 tff(922,plain,
% 1.09/1.29 ($false),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[921, 650, 644, 245, 242, 243, 217, 219, 220, 246, 484, 21, 638, 248, 247, 244])).
% 1.09/1.29 tff(923,plain,(hskp12 | c0_1(a478) | c1_1(a465) | c0_1(a465) | hskp19 | c2_1(a464) | c0_1(a464) | (~c2_1(a478)) | c1_1(a467) | c3_1(a467) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.29 tff(924,plain,
% 1.09/1.29 (hskp12),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[923, 248, 242, 243, 217, 219, 220, 246, 245, 247, 244])).
% 1.09/1.29 tff(925,plain,
% 1.09/1.29 (~c3_1(a481)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[421, 924])).
% 1.09/1.29 tff(926,plain,
% 1.09/1.29 (~c0_1(a481)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[427, 924])).
% 1.09/1.29 tff(927,plain,
% 1.09/1.29 (c1_1(a481)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[435, 924])).
% 1.09/1.29 tff(928,plain,
% 1.09/1.29 (c2_1(a481)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[442, 75, 927, 926, 925, 10])).
% 1.09/1.29 tff(929,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(930,plain,
% 1.09/1.29 (((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.29 inference(rewrite,[status(thm)],[])).
% 1.09/1.29 tff(931,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.09/1.29 inference(monotonicity,[status(thm)],[930])).
% 1.09/1.29 tff(932,plain,
% 1.09/1.29 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.29 inference(transitivity,[status(thm)],[931, 929])).
% 1.09/1.29 tff(933,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.29 inference(quant_inst,[status(thm)],[])).
% 1.09/1.29 tff(934,plain,
% 1.09/1.29 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.09/1.29 inference(modus_ponens,[status(thm)],[933, 932])).
% 1.09/1.29 tff(935,plain,
% 1.09/1.29 (c1_1(a471)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[934, 75, 927, 500, 926, 484, 369, 928])).
% 1.09/1.29 tff(936,assumption,(~hskp17), introduced(assumption)).
% 1.09/1.29 tff(937,plain,
% 1.09/1.29 (hskp5),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[683, 655, 936, 656])).
% 1.09/1.29 tff(938,plain,
% 1.09/1.29 (c0_1(a467)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[548, 937])).
% 1.09/1.29 tff(939,plain,
% 1.09/1.29 (hskp12),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[540, 938, 655, 656, 29, 248, 104, 247])).
% 1.09/1.29 tff(940,plain,
% 1.09/1.29 (c1_1(a481)),
% 1.09/1.29 inference(unit_resolution,[status(thm)],[435, 939])).
% 1.09/1.29 tff(941,assumption,(~c3_1(a481)), introduced(assumption)).
% 1.09/1.29 tff(942,assumption,(~c0_1(a481)), introduced(assumption)).
% 1.09/1.30 tff(943,plain,
% 1.09/1.30 ((~c1_1(a481)) | c2_1(a481)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[442, 75, 942, 941, 10])).
% 1.09/1.30 tff(944,plain,
% 1.09/1.30 (c2_1(a481)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[943, 940])).
% 1.09/1.30 tff(945,plain,
% 1.09/1.30 (c2_1(a467)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[520, 938, 104])).
% 1.09/1.30 tff(946,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(947,plain,
% 1.09/1.30 (((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a467) | c1_1(a467) | (~c2_1(a467)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481))) <=> (c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(948,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a467) | c1_1(a467) | (~c2_1(a467)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481))))),
% 1.09/1.30 inference(monotonicity,[status(thm)],[947])).
% 1.09/1.30 tff(949,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a467) | c1_1(a467) | (~c2_1(a467)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)))),
% 1.09/1.30 inference(transitivity,[status(thm)],[948, 946])).
% 1.09/1.30 tff(950,plain,
% 1.09/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a467) | c1_1(a467) | (~c2_1(a467)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))),
% 1.09/1.30 inference(quant_inst,[status(thm)],[])).
% 1.09/1.30 tff(951,plain,
% 1.09/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[950, 949])).
% 1.09/1.30 tff(952,plain,
% 1.09/1.30 (c0_1(a481) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481))),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[951, 75, 941, 29, 248, 247, 454])).
% 1.09/1.30 tff(953,plain,
% 1.09/1.30 (~c1_1(a471)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[952, 940, 942, 655, 945])).
% 1.09/1.30 tff(954,plain,
% 1.09/1.30 (c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[934, 75, 942, 29, 369])).
% 1.09/1.30 tff(955,plain,
% 1.09/1.30 ($false),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[954, 953, 944, 655, 940])).
% 1.09/1.30 tff(956,plain,(hskp16 | c0_1(a481) | c2_1(a471) | c3_1(a481) | c1_1(a467) | c3_1(a467) | hskp17 | (~c2_1(a478)) | c0_1(a478) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.30 tff(957,plain,
% 1.09/1.30 (hskp17),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[956, 925, 470, 484, 248, 247, 926, 246, 245, 244])).
% 1.09/1.30 tff(958,plain,
% 1.09/1.30 (~c0_1(a493)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[697, 957])).
% 1.09/1.30 tff(959,plain,
% 1.09/1.30 (c3_1(a493)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[705, 957])).
% 1.09/1.30 tff(960,plain,
% 1.09/1.30 (c2_1(a493)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[691, 957])).
% 1.09/1.30 tff(961,plain,
% 1.09/1.30 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.09/1.30 inference(bind,[status(th)],[])).
% 1.09/1.30 tff(962,plain,
% 1.09/1.30 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.09/1.30 inference(quant_intro,[status(thm)],[961])).
% 1.09/1.30 tff(963,plain,
% 1.09/1.30 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(964,plain,
% 1.09/1.30 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.09/1.30 inference(bind,[status(th)],[])).
% 1.09/1.30 tff(965,plain,
% 1.09/1.30 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.09/1.30 inference(quant_intro,[status(thm)],[964])).
% 1.09/1.30 tff(966,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.09/1.30 tff(967,plain,
% 1.09/1.30 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[966, 965])).
% 1.09/1.30 tff(968,plain,
% 1.09/1.30 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[967, 963])).
% 1.09/1.30 tff(969,plain,(
% 1.09/1.30 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.09/1.30 inference(skolemize,[status(sab)],[968])).
% 1.09/1.30 tff(970,plain,
% 1.09/1.30 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[969, 962])).
% 1.09/1.30 tff(971,plain,
% 1.09/1.30 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(972,plain,
% 1.09/1.30 ((hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471))) <=> (hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(973,plain,
% 1.09/1.30 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.09/1.30 inference(monotonicity,[status(thm)],[972])).
% 1.09/1.30 tff(974,plain,
% 1.09/1.30 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.30 inference(transitivity,[status(thm)],[973, 971])).
% 1.09/1.30 tff(975,plain,
% 1.09/1.30 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)))),
% 1.09/1.30 inference(quant_inst,[status(thm)],[])).
% 1.09/1.30 tff(976,plain,
% 1.09/1.30 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.09/1.30 tff(977,plain,
% 1.09/1.30 (hskp29 | (~c1_1(a471))),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[976, 75, 927, 500, 925, 484, 970, 928])).
% 1.09/1.30 tff(978,plain,
% 1.09/1.30 (hskp29),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[977, 935])).
% 1.09/1.30 tff(979,plain,
% 1.09/1.30 (c2_1(a474)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[310, 978])).
% 1.09/1.30 tff(980,plain,
% 1.09/1.30 (c1_1(a474)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[318, 978])).
% 1.09/1.30 tff(981,plain,
% 1.09/1.30 (c0_1(a474)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[326, 978])).
% 1.09/1.30 tff(982,plain,
% 1.09/1.30 ($false),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[882, 75, 981, 980, 979, 960, 959, 500, 492, 958, 844, 935])).
% 1.09/1.30 tff(983,plain,(c1_1(a467) | c3_1(a467) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478) | c1_1(a465) | c0_1(a465) | hskp19 | c2_1(a464) | c0_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.30 tff(984,plain,
% 1.09/1.30 (c1_1(a467)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[983, 247, 246, 245, 244, 242, 243, 217, 219, 220])).
% 1.09/1.30 tff(985,plain,
% 1.09/1.30 (((~hskp5) | (~c1_1(a467))) <=> ((~hskp5) | (~c1_1(a467)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(986,plain,
% 1.09/1.30 (((~c1_1(a467)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a467)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(987,axiom,((~c1_1(a467)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.09/1.30 tff(988,plain,
% 1.09/1.30 ((~hskp5) | (~c1_1(a467))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[987, 986])).
% 1.09/1.30 tff(989,plain,
% 1.09/1.30 ((~hskp5) | (~c1_1(a467))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[988, 985])).
% 1.09/1.30 tff(990,plain,
% 1.09/1.30 (~hskp5),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[989, 984])).
% 1.09/1.30 tff(991,plain,
% 1.09/1.30 (hskp17 | hskp5),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[682, 75, 500, 492, 484, 676])).
% 1.09/1.30 tff(992,plain,
% 1.09/1.30 (hskp17),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[991, 990])).
% 1.09/1.30 tff(993,plain,
% 1.09/1.30 (~c0_1(a493)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[697, 992])).
% 1.09/1.30 tff(994,plain,
% 1.09/1.30 (c3_1(a493)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[705, 992])).
% 1.09/1.30 tff(995,plain,
% 1.09/1.30 (c2_1(a493)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[691, 992])).
% 1.09/1.30 tff(996,assumption,(c1_1(a467)), introduced(assumption)).
% 1.09/1.30 tff(997,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(998,plain,
% 1.09/1.30 (((~ndr1_0) | c0_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a464) | c0_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(999,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))))),
% 1.09/1.30 inference(monotonicity,[status(thm)],[998])).
% 1.09/1.30 tff(1000,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.09/1.30 inference(transitivity,[status(thm)],[999, 997])).
% 1.09/1.30 tff(1001,plain,
% 1.09/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a464) | c0_1(a464) | c2_1(a464))),
% 1.09/1.30 inference(quant_inst,[status(thm)],[])).
% 1.09/1.30 tff(1002,plain,
% 1.09/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 1.09/1.30 tff(1003,plain,
% 1.09/1.30 (~c1_1(a464)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[1002, 75, 595, 220, 219, 10])).
% 1.09/1.30 tff(1004,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1005,plain,
% 1.09/1.30 (((~ndr1_0) | c3_1(a467) | (~c1_1(a467)) | (~c0_1(a467)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1006,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a467) | (~c1_1(a467)) | (~c0_1(a467)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493))))),
% 1.09/1.30 inference(monotonicity,[status(thm)],[1005])).
% 1.09/1.30 tff(1007,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a467) | (~c1_1(a467)) | (~c0_1(a467)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.09/1.30 inference(transitivity,[status(thm)],[1006, 1004])).
% 1.09/1.30 tff(1008,plain,
% 1.09/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a467) | (~c1_1(a467)) | (~c0_1(a467)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.09/1.30 inference(quant_inst,[status(thm)],[])).
% 1.09/1.30 tff(1009,plain,
% 1.09/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 1.09/1.30 tff(1010,plain,
% 1.09/1.30 (c1_1(a464) | (~c0_1(a467))),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[1009, 75, 753, 752, 595, 749, 996, 247, 219, 748])).
% 1.09/1.30 tff(1011,plain,
% 1.09/1.30 (~c0_1(a467)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[1010, 1003])).
% 1.09/1.30 tff(1012,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1013,plain,
% 1.09/1.30 (((~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c1_1(a467)) | c0_1(a467) | c2_1(a467) | (~c1_1(a467)) | c3_1(a464) | c0_1(a464) | c2_1(a464)) <=> (c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1014,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c1_1(a467)) | c0_1(a467) | c2_1(a467) | (~c1_1(a467)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467)))),
% 1.09/1.30 inference(monotonicity,[status(thm)],[1013])).
% 1.09/1.30 tff(1015,plain,
% 1.09/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c1_1(a467)) | c0_1(a467) | c2_1(a467) | (~c1_1(a467)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467))),
% 1.09/1.30 inference(transitivity,[status(thm)],[1014, 1012])).
% 1.09/1.30 tff(1016,plain,
% 1.09/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c1_1(a467)) | c0_1(a467) | c2_1(a467) | (~c1_1(a467)) | c3_1(a464) | c0_1(a464) | c2_1(a464))),
% 1.09/1.30 inference(quant_inst,[status(thm)],[])).
% 1.09/1.30 tff(1017,plain,
% 1.09/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467)),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 1.09/1.30 tff(1018,plain,
% 1.09/1.30 (c2_1(a467)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[1017, 75, 1011, 595, 996, 247, 220, 219, 10])).
% 1.09/1.30 tff(1019,plain,
% 1.09/1.30 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1020,plain,
% 1.09/1.30 (((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a467) | (~c1_1(a467)) | (~c2_1(a467))) <=> (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1021,plain,
% 1.09/1.30 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a467) | (~c1_1(a467)) | (~c2_1(a467)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471))))),
% 1.09/1.30 inference(monotonicity,[status(thm)],[1020])).
% 1.09/1.30 tff(1022,plain,
% 1.09/1.30 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a467) | (~c1_1(a467)) | (~c2_1(a467)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471)))),
% 1.09/1.30 inference(transitivity,[status(thm)],[1021, 1019])).
% 1.09/1.30 tff(1023,plain,
% 1.09/1.30 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a467) | (~c1_1(a467)) | (~c2_1(a467)))),
% 1.09/1.30 inference(quant_inst,[status(thm)],[])).
% 1.09/1.30 tff(1024,plain,
% 1.09/1.30 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 1.09/1.30 tff(1025,plain,
% 1.09/1.30 (c1_1(a471)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[1024, 75, 501, 1011, 29, 996, 369, 1018])).
% 1.09/1.30 tff(1026,plain,
% 1.09/1.30 (^[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)))),
% 1.09/1.30 inference(bind,[status(th)],[])).
% 1.09/1.30 tff(1027,plain,
% 1.09/1.30 (![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))),
% 1.09/1.30 inference(quant_intro,[status(thm)],[1026])).
% 1.09/1.30 tff(1028,plain,
% 1.09/1.30 (![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))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1029,plain,
% 1.09/1.30 (^[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))))),
% 1.09/1.30 inference(bind,[status(th)],[])).
% 1.09/1.30 tff(1030,plain,
% 1.09/1.30 (![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))),
% 1.09/1.30 inference(quant_intro,[status(thm)],[1029])).
% 1.09/1.30 tff(1031,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.09/1.30 tff(1032,plain,
% 1.09/1.30 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 1.09/1.30 tff(1033,plain,
% 1.09/1.30 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1032, 1028])).
% 1.09/1.30 tff(1034,plain,(
% 1.09/1.30 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.30 inference(skolemize,[status(sab)],[1033])).
% 1.09/1.30 tff(1035,plain,
% 1.09/1.30 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1034, 1027])).
% 1.09/1.30 tff(1036,plain,
% 1.09/1.30 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1037,plain,
% 1.09/1.30 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464)) <=> (hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1038,plain,
% 1.09/1.30 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464)))),
% 1.09/1.30 inference(monotonicity,[status(thm)],[1037])).
% 1.09/1.30 tff(1039,plain,
% 1.09/1.30 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.09/1.30 inference(transitivity,[status(thm)],[1038, 1036])).
% 1.09/1.30 tff(1040,plain,
% 1.09/1.30 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))),
% 1.09/1.30 inference(quant_inst,[status(thm)],[])).
% 1.09/1.30 tff(1041,plain,
% 1.09/1.30 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464)),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 1.09/1.30 tff(1042,plain,
% 1.09/1.30 (hskp2 | hskp1 | c0_1(a464) | c1_1(a464)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[1041, 75, 219, 1035])).
% 1.09/1.30 tff(1043,plain,
% 1.09/1.30 (hskp1),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[1042, 1003, 220, 603])).
% 1.09/1.30 tff(1044,plain,
% 1.09/1.30 (((~hskp1) | (~c3_1(a463))) <=> ((~hskp1) | (~c3_1(a463)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1045,plain,
% 1.09/1.30 (((~c3_1(a463)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a463)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1046,axiom,((~c3_1(a463)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.09/1.30 tff(1047,plain,
% 1.09/1.30 ((~hskp1) | (~c3_1(a463))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 1.09/1.30 tff(1048,plain,
% 1.09/1.30 ((~hskp1) | (~c3_1(a463))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1047, 1044])).
% 1.09/1.30 tff(1049,plain,
% 1.09/1.30 (~c3_1(a463)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[1048, 1043])).
% 1.09/1.30 tff(1050,plain,
% 1.09/1.30 (((~hskp1) | (~c1_1(a463))) <=> ((~hskp1) | (~c1_1(a463)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1051,plain,
% 1.09/1.30 (((~c1_1(a463)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a463)))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1052,axiom,((~c1_1(a463)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.09/1.30 tff(1053,plain,
% 1.09/1.30 ((~hskp1) | (~c1_1(a463))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 1.09/1.30 tff(1054,plain,
% 1.09/1.30 ((~hskp1) | (~c1_1(a463))),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1053, 1050])).
% 1.09/1.30 tff(1055,plain,
% 1.09/1.30 (~c1_1(a463)),
% 1.09/1.30 inference(unit_resolution,[status(thm)],[1054, 1043])).
% 1.09/1.30 tff(1056,plain,
% 1.09/1.30 (((~hskp1) | c2_1(a463)) <=> ((~hskp1) | c2_1(a463))),
% 1.09/1.30 inference(rewrite,[status(thm)],[])).
% 1.09/1.30 tff(1057,axiom,((~hskp1) | c2_1(a463)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.09/1.30 tff(1058,plain,
% 1.09/1.30 ((~hskp1) | c2_1(a463)),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 1.09/1.30 tff(1059,plain,
% 1.09/1.30 ((~hskp1) | c2_1(a463)),
% 1.09/1.30 inference(modus_ponens,[status(thm)],[1058, 1056])).
% 1.09/1.31 tff(1060,plain,
% 1.09/1.31 ((~hskp1) | c2_1(a463)),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1059, 1056])).
% 1.09/1.31 tff(1061,plain,
% 1.09/1.31 ((~hskp1) | c2_1(a463)),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1060, 1056])).
% 1.09/1.31 tff(1062,plain,
% 1.09/1.31 ((~hskp1) | c2_1(a463)),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1061, 1056])).
% 1.09/1.31 tff(1063,plain,
% 1.09/1.31 (c2_1(a463)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1062, 1043])).
% 1.09/1.31 tff(1064,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1065,plain,
% 1.09/1.31 (((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a467) | c0_1(a467) | (~c1_1(a467))) <=> (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1066,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a467) | c0_1(a467) | (~c1_1(a467)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471))))),
% 1.09/1.31 inference(monotonicity,[status(thm)],[1065])).
% 1.09/1.31 tff(1067,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a467) | c0_1(a467) | (~c1_1(a467)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)))),
% 1.09/1.31 inference(transitivity,[status(thm)],[1066, 1064])).
% 1.09/1.31 tff(1068,plain,
% 1.09/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a467) | c0_1(a467) | (~c1_1(a467)))),
% 1.09/1.31 inference(quant_inst,[status(thm)],[])).
% 1.09/1.31 tff(1069,plain,
% 1.09/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 1.09/1.31 tff(1070,plain,
% 1.09/1.31 ($false),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1069, 75, 501, 1011, 1063, 29, 996, 247, 1055, 1049, 454, 1025])).
% 1.09/1.31 tff(1071,plain,(c3_1(a464) | (~c0_1(a471)) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~c2_1(a493)) | (~c3_1(a493)) | c0_1(a493)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.31 tff(1072,plain,
% 1.09/1.31 (c3_1(a464)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1071, 984, 484, 500, 247, 220, 219, 995, 994, 993])).
% 1.09/1.31 tff(1073,plain,
% 1.09/1.31 (hskp12),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[574, 1072, 990, 220])).
% 1.09/1.31 tff(1074,plain,
% 1.09/1.31 (~c3_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[421, 1073])).
% 1.09/1.31 tff(1075,plain,
% 1.09/1.31 (~c0_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[427, 1073])).
% 1.09/1.31 tff(1076,plain,
% 1.09/1.31 (c1_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[435, 1073])).
% 1.09/1.31 tff(1077,plain,
% 1.09/1.31 (c2_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[442, 75, 1076, 1075, 1074, 10])).
% 1.09/1.31 tff(1078,plain,
% 1.09/1.31 (c1_1(a471)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[934, 75, 1076, 500, 1075, 484, 369, 1077])).
% 1.09/1.31 tff(1079,plain,
% 1.09/1.31 (hskp29 | (~c1_1(a471))),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[976, 75, 1076, 500, 1074, 484, 970, 1077])).
% 1.09/1.31 tff(1080,plain,
% 1.09/1.31 (hskp29),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1079, 1078])).
% 1.09/1.31 tff(1081,plain,
% 1.09/1.31 (c2_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[310, 1080])).
% 1.09/1.31 tff(1082,plain,
% 1.09/1.31 (c1_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[318, 1080])).
% 1.09/1.31 tff(1083,plain,
% 1.09/1.31 (c0_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[326, 1080])).
% 1.09/1.31 tff(1084,plain,
% 1.09/1.31 ($false),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[882, 75, 1083, 1082, 1081, 995, 994, 500, 492, 993, 844, 1078])).
% 1.09/1.31 tff(1085,plain,(c3_1(a467) | c0_1(a464) | c2_1(a464) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478) | c1_1(a465) | c0_1(a465) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.09/1.31 tff(1086,plain,
% 1.09/1.31 (c3_1(a467)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1085, 243, 219, 246, 245, 244, 242, 220, 217])).
% 1.09/1.31 tff(1087,plain,
% 1.09/1.31 (((~hskp5) | (~c3_1(a467))) <=> ((~hskp5) | (~c3_1(a467)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1088,plain,
% 1.09/1.31 (((~c3_1(a467)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a467)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1089,axiom,((~c3_1(a467)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.09/1.31 tff(1090,plain,
% 1.09/1.31 ((~hskp5) | (~c3_1(a467))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 1.09/1.31 tff(1091,plain,
% 1.09/1.31 ((~hskp5) | (~c3_1(a467))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1090, 1087])).
% 1.09/1.31 tff(1092,plain,
% 1.09/1.31 (~hskp5),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1091, 1086])).
% 1.09/1.31 tff(1093,plain,
% 1.09/1.31 (hskp17),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[991, 1092])).
% 1.09/1.31 tff(1094,plain,
% 1.09/1.31 (~c0_1(a493)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[697, 1093])).
% 1.09/1.31 tff(1095,plain,
% 1.09/1.31 (c3_1(a493)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[705, 1093])).
% 1.09/1.31 tff(1096,plain,
% 1.09/1.31 (c2_1(a493)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[691, 1093])).
% 1.09/1.31 tff(1097,plain,
% 1.09/1.31 (~c1_1(a464)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1002, 75, 860, 220, 219, 10])).
% 1.09/1.31 tff(1098,plain,
% 1.09/1.31 (~c3_1(a465)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[612, 1097, 242, 219, 860, 21, 31, 243])).
% 1.09/1.31 tff(1099,plain,
% 1.09/1.31 (~hskp3),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[403, 1098])).
% 1.09/1.31 tff(1100,plain,
% 1.09/1.31 (hskp29),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[415, 1099, 21])).
% 1.09/1.31 tff(1101,plain,
% 1.09/1.31 (c2_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[310, 1100])).
% 1.09/1.31 tff(1102,plain,
% 1.09/1.31 (c1_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[318, 1100])).
% 1.09/1.31 tff(1103,plain,
% 1.09/1.31 (c0_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[326, 1100])).
% 1.09/1.31 tff(1104,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1105,plain,
% 1.09/1.31 (((~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493))) <=> (c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1106,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.09/1.31 inference(monotonicity,[status(thm)],[1105])).
% 1.09/1.31 tff(1107,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.31 inference(transitivity,[status(thm)],[1106, 1104])).
% 1.09/1.31 tff(1108,plain,
% 1.09/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.09/1.31 inference(quant_inst,[status(thm)],[])).
% 1.09/1.31 tff(1109,plain,
% 1.09/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.09/1.31 tff(1110,plain,
% 1.09/1.31 (~c3_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1109, 75, 1103, 1102, 1101, 753, 752, 749, 844])).
% 1.09/1.31 tff(1111,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1112,plain,
% 1.09/1.31 (((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1113,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.09/1.31 inference(monotonicity,[status(thm)],[1112])).
% 1.09/1.31 tff(1114,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.31 inference(transitivity,[status(thm)],[1113, 1111])).
% 1.09/1.31 tff(1115,plain,
% 1.09/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.09/1.31 inference(quant_inst,[status(thm)],[])).
% 1.09/1.31 tff(1116,plain,
% 1.09/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 1.09/1.31 tff(1117,plain,
% 1.09/1.31 ($false),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1116, 75, 1103, 1102, 753, 752, 860, 749, 219, 748, 1097, 1110])).
% 1.09/1.31 tff(1118,plain,(hskp12 | (~c2_1(a493)) | (~c3_1(a493)) | c0_1(a493) | c2_1(a464) | c1_1(a465) | hskp5 | c0_1(a465) | c0_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.31 tff(1119,plain,
% 1.09/1.31 (hskp12),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1118, 1096, 1095, 1094, 219, 242, 1092, 243, 220])).
% 1.09/1.31 tff(1120,plain,
% 1.09/1.31 (~c3_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[421, 1119])).
% 1.09/1.31 tff(1121,plain,
% 1.09/1.31 (~c0_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[427, 1119])).
% 1.09/1.31 tff(1122,plain,
% 1.09/1.31 (c1_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[435, 1119])).
% 1.09/1.31 tff(1123,plain,
% 1.09/1.31 (c2_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[442, 75, 1122, 1121, 1120, 10])).
% 1.09/1.31 tff(1124,plain,
% 1.09/1.31 (c1_1(a471)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[934, 75, 1122, 500, 1121, 484, 369, 1123])).
% 1.09/1.31 tff(1125,plain,
% 1.09/1.31 (hskp29),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[976, 75, 1122, 500, 1120, 484, 970, 1124, 1123])).
% 1.09/1.31 tff(1126,plain,
% 1.09/1.31 (c2_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[310, 1125])).
% 1.09/1.31 tff(1127,plain,
% 1.09/1.31 (c1_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[318, 1125])).
% 1.09/1.31 tff(1128,plain,
% 1.09/1.31 (c0_1(a474)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[326, 1125])).
% 1.09/1.31 tff(1129,plain,
% 1.09/1.31 ($false),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[882, 75, 1128, 1127, 1126, 1096, 1095, 500, 492, 1094, 844, 1124])).
% 1.09/1.31 tff(1130,plain,(c0_1(a465) | c2_1(a464) | c1_1(a465) | c0_1(a464) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.09/1.31 tff(1131,plain,
% 1.09/1.31 (c0_1(a465)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1130, 242, 219, 220, 241, 233, 227, 217])).
% 1.09/1.31 tff(1132,plain,
% 1.09/1.31 (((~hskp3) | (~c0_1(a465))) <=> ((~hskp3) | (~c0_1(a465)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1133,plain,
% 1.09/1.31 (((~c0_1(a465)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a465)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1134,axiom,((~c0_1(a465)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.09/1.31 tff(1135,plain,
% 1.09/1.31 ((~hskp3) | (~c0_1(a465))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 1.09/1.31 tff(1136,plain,
% 1.09/1.31 ((~hskp3) | (~c0_1(a465))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1135, 1132])).
% 1.09/1.31 tff(1137,plain,
% 1.09/1.31 (~hskp3),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1136, 1131])).
% 1.09/1.31 tff(1138,assumption,(~hskp3), introduced(assumption)).
% 1.09/1.31 tff(1139,plain,
% 1.09/1.31 (~hskp29),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[335, 291, 299, 285])).
% 1.09/1.31 tff(1140,plain,
% 1.09/1.31 (hskp12),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[415, 1139, 1138])).
% 1.09/1.31 tff(1141,plain,
% 1.09/1.31 (~c3_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[421, 1140])).
% 1.09/1.31 tff(1142,plain,
% 1.09/1.31 (~c0_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[427, 1140])).
% 1.09/1.31 tff(1143,plain,
% 1.09/1.31 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1144,plain,
% 1.09/1.31 ((hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464))) <=> (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1145,plain,
% 1.09/1.31 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487))))),
% 1.09/1.31 inference(monotonicity,[status(thm)],[1144])).
% 1.09/1.31 tff(1146,plain,
% 1.09/1.31 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487)))),
% 1.09/1.31 inference(transitivity,[status(thm)],[1145, 1143])).
% 1.09/1.31 tff(1147,plain,
% 1.09/1.31 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))),
% 1.09/1.31 inference(quant_inst,[status(thm)],[])).
% 1.09/1.31 tff(1148,plain,
% 1.09/1.31 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 1.09/1.31 tff(1149,plain,
% 1.09/1.31 (hskp29 | (~c3_1(a464))),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1148, 75, 272, 28, 264, 220, 219, 348])).
% 1.09/1.31 tff(1150,plain,
% 1.09/1.31 (~c3_1(a464)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1149, 1139])).
% 1.09/1.31 tff(1151,plain,
% 1.09/1.31 (c1_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[435, 1140])).
% 1.09/1.31 tff(1152,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1153,plain,
% 1.09/1.31 (((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a464) | c0_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1154,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481)))),
% 1.09/1.31 inference(monotonicity,[status(thm)],[1153])).
% 1.09/1.31 tff(1155,plain,
% 1.09/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.09/1.31 inference(transitivity,[status(thm)],[1154, 1152])).
% 1.09/1.31 tff(1156,plain,
% 1.09/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a464) | c0_1(a464) | c2_1(a464))),
% 1.09/1.31 inference(quant_inst,[status(thm)],[])).
% 1.09/1.31 tff(1157,plain,
% 1.09/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481)),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 1.09/1.31 tff(1158,plain,
% 1.09/1.31 (c2_1(a481)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1157, 75, 1151, 1150, 1142, 1141, 220, 219, 10])).
% 1.09/1.31 tff(1159,plain,
% 1.09/1.31 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1160,plain,
% 1.09/1.31 (((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1161,plain,
% 1.09/1.31 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487))))),
% 1.09/1.31 inference(monotonicity,[status(thm)],[1160])).
% 1.09/1.31 tff(1162,plain,
% 1.09/1.31 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487)))),
% 1.09/1.31 inference(transitivity,[status(thm)],[1161, 1159])).
% 1.09/1.31 tff(1163,plain,
% 1.09/1.31 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.31 inference(quant_inst,[status(thm)],[])).
% 1.09/1.31 tff(1164,plain,
% 1.09/1.31 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.09/1.31 tff(1165,plain,
% 1.09/1.31 ($false),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1164, 75, 272, 1151, 28, 264, 1142, 369, 1158])).
% 1.09/1.31 tff(1166,plain,((~hskp16) | c0_1(a464) | c2_1(a464) | hskp3 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.09/1.31 tff(1167,plain,
% 1.09/1.31 (~hskp16),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1166, 1137, 219, 220, 217])).
% 1.09/1.31 tff(1168,plain,
% 1.09/1.31 (hskp16 | hskp7),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[476, 75, 241, 233, 227, 20])).
% 1.09/1.31 tff(1169,plain,
% 1.09/1.31 (hskp7),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1168, 1167])).
% 1.09/1.31 tff(1170,plain,
% 1.09/1.31 (~c2_1(a471)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[483, 1169])).
% 1.09/1.31 tff(1171,plain,
% 1.09/1.31 (c0_1(a471)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[499, 1169])).
% 1.09/1.31 tff(1172,plain,
% 1.09/1.31 (c3_1(a471)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[491, 1169])).
% 1.09/1.31 tff(1173,assumption,(c0_1(a465)), introduced(assumption)).
% 1.09/1.31 tff(1174,plain,
% 1.09/1.31 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1175,plain,
% 1.09/1.31 ((hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a465) | (~c2_1(a465)) | (~c0_1(a465))) <=> (hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1176,plain,
% 1.09/1.31 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a465) | (~c2_1(a465)) | (~c0_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471))))),
% 1.09/1.31 inference(monotonicity,[status(thm)],[1175])).
% 1.09/1.31 tff(1177,plain,
% 1.09/1.31 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a465) | (~c2_1(a465)) | (~c0_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.09/1.31 inference(transitivity,[status(thm)],[1176, 1174])).
% 1.09/1.31 tff(1178,plain,
% 1.09/1.31 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a465) | (~c2_1(a465)) | (~c0_1(a465)))),
% 1.09/1.31 inference(quant_inst,[status(thm)],[])).
% 1.09/1.31 tff(1179,plain,
% 1.09/1.31 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.09/1.31 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 1.09/1.31 tff(1180,plain,
% 1.09/1.31 (hskp12 | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1179, 75, 29, 1173, 242, 531])).
% 1.09/1.31 tff(1181,plain,
% 1.09/1.31 (~c2_1(a465)),
% 1.09/1.31 inference(unit_resolution,[status(thm)],[1180, 21, 502, 501])).
% 1.09/1.31 tff(1182,plain,
% 1.09/1.31 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1183,plain,
% 1.09/1.31 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a465) | c1_1(a465) | (~c0_1(a465))) <=> (hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465))),
% 1.09/1.31 inference(rewrite,[status(thm)],[])).
% 1.09/1.31 tff(1184,plain,
% 1.09/1.31 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a465) | c1_1(a465) | (~c0_1(a465)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465)))),
% 1.09/1.32 inference(monotonicity,[status(thm)],[1183])).
% 1.09/1.32 tff(1185,plain,
% 1.09/1.32 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a465) | c1_1(a465) | (~c0_1(a465)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465))),
% 1.09/1.32 inference(transitivity,[status(thm)],[1184, 1182])).
% 1.09/1.32 tff(1186,plain,
% 1.09/1.32 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a465) | c1_1(a465) | (~c0_1(a465)))),
% 1.09/1.32 inference(quant_inst,[status(thm)],[])).
% 1.09/1.32 tff(1187,plain,
% 1.09/1.32 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465)),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 1.09/1.32 tff(1188,plain,
% 1.09/1.32 (hskp18 | (~c0_1(a465)) | c2_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1187, 75, 217, 242, 258])).
% 1.09/1.32 tff(1189,plain,
% 1.09/1.32 (hskp18),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1188, 1181, 1173])).
% 1.09/1.32 tff(1190,plain,
% 1.09/1.32 (~c3_1(a494)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[284, 1189])).
% 1.09/1.32 tff(1191,plain,
% 1.09/1.32 (~hskp3),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1136, 1173])).
% 1.09/1.32 tff(1192,plain,
% 1.09/1.32 (hskp29),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[415, 21, 1191])).
% 1.09/1.32 tff(1193,plain,
% 1.09/1.32 (c0_1(a494)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[298, 1189])).
% 1.09/1.32 tff(1194,plain,
% 1.09/1.32 (~c2_1(a494)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[290, 1189])).
% 1.09/1.32 tff(1195,plain,
% 1.09/1.32 ($false),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[335, 1194, 1193, 1192, 1190])).
% 1.09/1.32 tff(1196,plain,(hskp12 | (~c0_1(a465)) | hskp19 | c1_1(a465) | (~c3_1(a471)) | (~c0_1(a471)) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.32 tff(1197,plain,
% 1.09/1.32 (hskp12),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1196, 1172, 217, 242, 1131, 1171, 1170])).
% 1.09/1.32 tff(1198,plain,
% 1.09/1.32 (~c3_1(a481)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[421, 1197])).
% 1.09/1.32 tff(1199,plain,
% 1.09/1.32 (~c0_1(a481)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[427, 1197])).
% 1.09/1.32 tff(1200,plain,
% 1.09/1.32 (c1_1(a481)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[435, 1197])).
% 1.09/1.32 tff(1201,plain,
% 1.09/1.32 (c2_1(a481)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[442, 75, 1200, 1199, 1198, 10])).
% 1.09/1.32 tff(1202,plain,
% 1.09/1.32 (c1_1(a471)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[934, 75, 1200, 1171, 1199, 1170, 369, 1201])).
% 1.09/1.32 tff(1203,plain,
% 1.09/1.32 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))),
% 1.09/1.32 inference(bind,[status(th)],[])).
% 1.09/1.32 tff(1204,plain,
% 1.09/1.32 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.32 inference(quant_intro,[status(thm)],[1203])).
% 1.09/1.32 tff(1205,plain,
% 1.09/1.32 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1206,plain,
% 1.09/1.32 (^[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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp31) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp31))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.09/1.32 inference(bind,[status(th)],[])).
% 1.09/1.32 tff(1207,plain,
% 1.09/1.32 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.32 inference(quant_intro,[status(thm)],[1206])).
% 1.09/1.32 tff(1208,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.09/1.32 tff(1209,plain,
% 1.09/1.32 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 1.09/1.32 tff(1210,plain,
% 1.09/1.32 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1209, 1205])).
% 1.09/1.32 tff(1211,plain,(
% 1.09/1.32 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.32 inference(skolemize,[status(sab)],[1210])).
% 1.09/1.32 tff(1212,plain,
% 1.09/1.32 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1211, 1204])).
% 1.09/1.32 tff(1213,plain,
% 1.09/1.32 (hskp29),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[976, 75, 1200, 1171, 1198, 1170, 970, 1202, 1201])).
% 1.09/1.32 tff(1214,plain,
% 1.09/1.32 (c2_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[310, 1213])).
% 1.09/1.32 tff(1215,plain,
% 1.09/1.32 (c1_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[318, 1213])).
% 1.09/1.32 tff(1216,plain,
% 1.09/1.32 (c0_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[326, 1213])).
% 1.09/1.32 tff(1217,plain,
% 1.09/1.32 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1218,plain,
% 1.09/1.32 ((hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1219,plain,
% 1.09/1.32 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.09/1.32 inference(monotonicity,[status(thm)],[1218])).
% 1.09/1.32 tff(1220,plain,
% 1.09/1.32 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.32 inference(transitivity,[status(thm)],[1219, 1217])).
% 1.09/1.32 tff(1221,plain,
% 1.09/1.32 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.09/1.32 inference(quant_inst,[status(thm)],[])).
% 1.09/1.32 tff(1222,plain,
% 1.09/1.32 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 1.09/1.32 tff(1223,plain,
% 1.09/1.32 ($false),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1222, 218, 75, 1216, 1215, 1214, 1171, 1172, 1212, 1202])).
% 1.09/1.32 tff(1224,plain,(c1_1(a465) | hskp31 | hskp19 | c2_1(a464) | c0_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.32 tff(1225,plain,
% 1.09/1.32 (c1_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1224, 220, 217, 219, 218])).
% 1.09/1.32 tff(1226,plain,
% 1.09/1.32 (((~hskp3) | (~c1_1(a465))) <=> ((~hskp3) | (~c1_1(a465)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1227,plain,
% 1.09/1.32 (((~c1_1(a465)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a465)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1228,axiom,((~c1_1(a465)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.09/1.32 tff(1229,plain,
% 1.09/1.32 ((~hskp3) | (~c1_1(a465))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 1.09/1.32 tff(1230,plain,
% 1.09/1.32 ((~hskp3) | (~c1_1(a465))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1229, 1226])).
% 1.09/1.32 tff(1231,plain,
% 1.09/1.32 (~hskp3),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1230, 1225])).
% 1.09/1.32 tff(1232,plain,
% 1.09/1.32 (~hskp16),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1166, 1231, 219, 220, 217])).
% 1.09/1.32 tff(1233,plain,
% 1.09/1.32 (hskp29),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[415, 21, 1138])).
% 1.09/1.32 tff(1234,plain,
% 1.09/1.32 (c2_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[310, 1233])).
% 1.09/1.32 tff(1235,plain,
% 1.09/1.32 (c1_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[318, 1233])).
% 1.09/1.32 tff(1236,plain,
% 1.09/1.32 (c0_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[326, 1233])).
% 1.09/1.32 tff(1237,plain,
% 1.09/1.32 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1238,plain,
% 1.09/1.32 ((hskp31 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1239,plain,
% 1.09/1.32 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.09/1.32 inference(monotonicity,[status(thm)],[1238])).
% 1.09/1.32 tff(1240,plain,
% 1.09/1.32 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.32 inference(transitivity,[status(thm)],[1239, 1237])).
% 1.09/1.32 tff(1241,plain,
% 1.09/1.32 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.09/1.32 inference(quant_inst,[status(thm)],[])).
% 1.09/1.32 tff(1242,plain,
% 1.09/1.32 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 1.09/1.32 tff(1243,plain,
% 1.09/1.32 (~c3_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1242, 218, 75, 1236, 1235, 1234, 1212])).
% 1.09/1.32 tff(1244,plain,
% 1.09/1.32 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1245,plain,
% 1.09/1.32 ((hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474))) <=> (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1246,plain,
% 1.09/1.32 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.09/1.32 inference(monotonicity,[status(thm)],[1245])).
% 1.09/1.32 tff(1247,plain,
% 1.09/1.32 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.32 inference(transitivity,[status(thm)],[1246, 1244])).
% 1.09/1.32 tff(1248,plain,
% 1.09/1.32 ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))),
% 1.09/1.32 inference(quant_inst,[status(thm)],[])).
% 1.09/1.32 tff(1249,plain,
% 1.09/1.32 ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 1.09/1.32 tff(1250,plain,
% 1.09/1.32 (hskp30 | c3_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1249, 75, 21, 1236, 1235, 158])).
% 1.09/1.32 tff(1251,plain,
% 1.09/1.32 (hskp30),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1250, 1243])).
% 1.09/1.32 tff(1252,plain,
% 1.09/1.32 (c3_1(a488)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[173, 1251])).
% 1.09/1.32 tff(1253,plain,
% 1.09/1.32 (c2_1(a488)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[181, 1251])).
% 1.09/1.32 tff(1254,plain,
% 1.09/1.32 (c1_1(a488)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[189, 1251])).
% 1.09/1.32 tff(1255,plain,
% 1.09/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1256,plain,
% 1.09/1.32 (((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474))) <=> ((~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1257,plain,
% 1.09/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))))),
% 1.09/1.32 inference(monotonicity,[status(thm)],[1256])).
% 1.09/1.32 tff(1258,plain,
% 1.09/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.09/1.32 inference(transitivity,[status(thm)],[1257, 1255])).
% 1.09/1.32 tff(1259,plain,
% 1.09/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))),
% 1.09/1.32 inference(quant_inst,[status(thm)],[])).
% 1.09/1.32 tff(1260,plain,
% 1.09/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 1.09/1.32 tff(1261,plain,
% 1.09/1.32 (~c0_1(a488)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1260, 75, 1254, 1253, 1252, 1236, 1235, 148, 1243])).
% 1.09/1.32 tff(1262,plain,
% 1.09/1.32 ($false),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[213, 75, 104, 1254, 1253, 1252, 207, 1261])).
% 1.09/1.32 tff(1263,plain,(hskp12 | hskp16 | hskp31 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.09/1.32 tff(1264,plain,
% 1.09/1.32 (hskp12),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1263, 1232, 218, 1231])).
% 1.09/1.32 tff(1265,plain,
% 1.09/1.32 (~c3_1(a481)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[421, 1264])).
% 1.09/1.32 tff(1266,plain,
% 1.09/1.32 (~c0_1(a481)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[427, 1264])).
% 1.09/1.32 tff(1267,plain,
% 1.09/1.32 (c1_1(a481)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[435, 1264])).
% 1.09/1.32 tff(1268,plain,
% 1.09/1.32 (c2_1(a481)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[442, 75, 1267, 1266, 1265, 10])).
% 1.09/1.32 tff(1269,plain,
% 1.09/1.32 (hskp7),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1168, 1232])).
% 1.09/1.32 tff(1270,plain,
% 1.09/1.32 (~c2_1(a471)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[483, 1269])).
% 1.09/1.32 tff(1271,plain,
% 1.09/1.32 (c0_1(a471)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[499, 1269])).
% 1.09/1.32 tff(1272,plain,
% 1.09/1.32 (c1_1(a471)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[934, 75, 1267, 1271, 1266, 1270, 369, 1268])).
% 1.09/1.32 tff(1273,plain,
% 1.09/1.32 (c3_1(a471)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[491, 1269])).
% 1.09/1.32 tff(1274,plain,
% 1.09/1.32 (hskp29),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[976, 75, 1267, 1271, 1265, 1270, 970, 1272, 1268])).
% 1.09/1.32 tff(1275,plain,
% 1.09/1.32 (c2_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[310, 1274])).
% 1.09/1.32 tff(1276,plain,
% 1.09/1.32 (c1_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[318, 1274])).
% 1.09/1.32 tff(1277,plain,
% 1.09/1.32 (c0_1(a474)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[326, 1274])).
% 1.09/1.32 tff(1278,plain,
% 1.09/1.32 ($false),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1222, 218, 75, 1277, 1276, 1275, 1271, 1273, 1212, 1272])).
% 1.09/1.32 tff(1279,plain,(c0_1(a464) | hskp31 | c2_1(a464) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.09/1.32 tff(1280,plain,
% 1.09/1.32 (c0_1(a464)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1279, 219, 218, 217])).
% 1.09/1.32 tff(1281,plain,
% 1.09/1.32 (((~hskp2) | (~c0_1(a464))) <=> ((~hskp2) | (~c0_1(a464)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1282,plain,
% 1.09/1.32 (((~c0_1(a464)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a464)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1283,axiom,((~c0_1(a464)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.09/1.32 tff(1284,plain,
% 1.09/1.32 ((~hskp2) | (~c0_1(a464))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 1.09/1.32 tff(1285,plain,
% 1.09/1.32 ((~hskp2) | (~c0_1(a464))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1284, 1281])).
% 1.09/1.32 tff(1286,plain,
% 1.09/1.32 (~hskp2),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1285, 1280])).
% 1.09/1.32 tff(1287,plain,
% 1.09/1.32 (hskp3),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[415, 1139, 21])).
% 1.09/1.32 tff(1288,plain,
% 1.09/1.32 (~c1_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1230, 1287])).
% 1.09/1.32 tff(1289,plain,
% 1.09/1.32 (c3_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[403, 1287])).
% 1.09/1.32 tff(1290,plain,
% 1.09/1.32 (~c0_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1136, 1287])).
% 1.09/1.32 tff(1291,plain,
% 1.09/1.32 ($false),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[395, 1290, 1289, 246, 272, 28, 245, 1288, 285, 299, 264, 291])).
% 1.09/1.32 tff(1292,plain,((~hskp16) | (~c2_1(a478)) | c0_1(a478) | hskp12 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.09/1.32 tff(1293,plain,
% 1.09/1.32 (~hskp16),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1292, 21, 233, 241, 217])).
% 1.09/1.32 tff(1294,plain,
% 1.09/1.32 (hskp7),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1168, 1293])).
% 1.09/1.32 tff(1295,assumption,(~hskp2), introduced(assumption)).
% 1.09/1.32 tff(1296,plain,
% 1.09/1.32 (hskp3),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1263, 104, 218, 21])).
% 1.09/1.32 tff(1297,plain,
% 1.09/1.32 (~c1_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1230, 1296])).
% 1.09/1.32 tff(1298,plain,
% 1.09/1.32 (~c0_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1136, 1296])).
% 1.09/1.32 tff(1299,plain,
% 1.09/1.32 (c3_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[403, 1296])).
% 1.09/1.32 tff(1300,plain,
% 1.09/1.32 (hskp5 | c2_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[581, 75, 21, 337, 243, 41])).
% 1.09/1.32 tff(1301,plain,
% 1.09/1.32 (c2_1(a465)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1300, 31])).
% 1.09/1.32 tff(1302,assumption,(hskp6), introduced(assumption)).
% 1.09/1.32 tff(1303,plain,
% 1.09/1.32 (((~hskp6) | (~c2_1(a470))) <=> ((~hskp6) | (~c2_1(a470)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1304,plain,
% 1.09/1.32 (((~c2_1(a470)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a470)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1305,axiom,((~c2_1(a470)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.09/1.32 tff(1306,plain,
% 1.09/1.32 ((~hskp6) | (~c2_1(a470))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 1.09/1.32 tff(1307,plain,
% 1.09/1.32 ((~hskp6) | (~c2_1(a470))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1306, 1303])).
% 1.09/1.32 tff(1308,plain,
% 1.09/1.32 (~c2_1(a470)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1307, 1302])).
% 1.09/1.32 tff(1309,plain,
% 1.09/1.32 (((~hskp6) | (~c0_1(a470))) <=> ((~hskp6) | (~c0_1(a470)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1310,plain,
% 1.09/1.32 (((~c0_1(a470)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a470)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1311,axiom,((~c0_1(a470)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.09/1.32 tff(1312,plain,
% 1.09/1.32 ((~hskp6) | (~c0_1(a470))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 1.09/1.32 tff(1313,plain,
% 1.09/1.32 ((~hskp6) | (~c0_1(a470))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1312, 1309])).
% 1.09/1.32 tff(1314,plain,
% 1.09/1.32 (~c0_1(a470)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1313, 1302])).
% 1.09/1.32 tff(1315,plain,
% 1.09/1.32 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1316,plain,
% 1.09/1.32 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a470) | c0_1(a470) | (~c3_1(a470))) <=> (hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1317,plain,
% 1.09/1.32 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a470) | c0_1(a470) | (~c3_1(a470)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470))))),
% 1.09/1.32 inference(monotonicity,[status(thm)],[1316])).
% 1.09/1.32 tff(1318,plain,
% 1.09/1.32 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a470) | c0_1(a470) | (~c3_1(a470)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470)))),
% 1.09/1.32 inference(transitivity,[status(thm)],[1317, 1315])).
% 1.09/1.32 tff(1319,plain,
% 1.09/1.32 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a470) | c0_1(a470) | (~c3_1(a470)))),
% 1.09/1.32 inference(quant_inst,[status(thm)],[])).
% 1.09/1.32 tff(1320,plain,
% 1.09/1.32 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 1.09/1.32 tff(1321,plain,
% 1.09/1.32 (~c3_1(a470)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1320, 75, 21, 31, 1314, 1308, 41])).
% 1.09/1.32 tff(1322,assumption,(c2_1(a465)), introduced(assumption)).
% 1.09/1.32 tff(1323,plain,
% 1.09/1.32 (((~hskp6) | (~c1_1(a470))) <=> ((~hskp6) | (~c1_1(a470)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1324,plain,
% 1.09/1.32 (((~c1_1(a470)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a470)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1325,axiom,((~c1_1(a470)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.09/1.32 tff(1326,plain,
% 1.09/1.32 ((~hskp6) | (~c1_1(a470))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 1.09/1.32 tff(1327,plain,
% 1.09/1.32 ((~hskp6) | (~c1_1(a470))),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1326, 1323])).
% 1.09/1.32 tff(1328,plain,
% 1.09/1.32 (~c1_1(a470)),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1327, 1302])).
% 1.09/1.32 tff(1329,plain,
% 1.09/1.32 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1330,plain,
% 1.09/1.32 ((hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470) | c1_1(a470) | c2_1(a470)) <=> (hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1331,plain,
% 1.09/1.32 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470) | c1_1(a470) | c2_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470)))),
% 1.09/1.32 inference(monotonicity,[status(thm)],[1330])).
% 1.09/1.32 tff(1332,plain,
% 1.09/1.32 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470) | c1_1(a470) | c2_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470))),
% 1.09/1.32 inference(transitivity,[status(thm)],[1331, 1329])).
% 1.09/1.32 tff(1333,plain,
% 1.09/1.32 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470) | c1_1(a470) | c2_1(a470))),
% 1.09/1.32 inference(quant_inst,[status(thm)],[])).
% 1.09/1.32 tff(1334,plain,
% 1.09/1.32 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470)),
% 1.09/1.32 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 1.09/1.32 tff(1335,plain,
% 1.09/1.32 ($false),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1334, 75, 1295, 337, 1328, 1308, 242, 594, 1322, 1321])).
% 1.09/1.32 tff(1336,plain,((~hskp6) | hskp2 | (~c3_1(a465)) | c1_1(a465) | (~c2_1(a465)) | hskp12 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.09/1.32 tff(1337,plain,
% 1.09/1.32 (~hskp6),
% 1.09/1.32 inference(unit_resolution,[status(thm)],[1336, 1301, 337, 242, 1295, 21, 31])).
% 1.09/1.32 tff(1338,plain,
% 1.09/1.32 (^[U: $i] : refl((hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.09/1.32 inference(bind,[status(th)],[])).
% 1.09/1.32 tff(1339,plain,
% 1.09/1.32 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.09/1.32 inference(quant_intro,[status(thm)],[1338])).
% 1.09/1.32 tff(1340,plain,
% 1.09/1.32 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.09/1.32 inference(rewrite,[status(thm)],[])).
% 1.09/1.32 tff(1341,plain,
% 1.09/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp6) <=> ((hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp6))), rewrite(((hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp6) <=> (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp6) <=> (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.09/1.33 inference(bind,[status(th)],[])).
% 1.09/1.33 tff(1342,plain,
% 1.09/1.33 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp6) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.09/1.33 inference(quant_intro,[status(thm)],[1341])).
% 1.09/1.33 tff(1343,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.09/1.33 tff(1344,plain,
% 1.09/1.33 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 1.09/1.33 tff(1345,plain,
% 1.09/1.33 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1344, 1340])).
% 1.09/1.33 tff(1346,plain,(
% 1.09/1.33 ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.09/1.33 inference(skolemize,[status(sab)],[1345])).
% 1.09/1.33 tff(1347,plain,
% 1.09/1.33 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1346, 1339])).
% 1.09/1.33 tff(1348,plain,
% 1.09/1.33 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1349,plain,
% 1.09/1.33 ((hskp18 | hskp6 | (~ndr1_0) | c0_1(a465) | (~c3_1(a465)) | (~c2_1(a465))) <=> (hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1350,plain,
% 1.09/1.33 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c0_1(a465) | (~c3_1(a465)) | (~c2_1(a465)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465))))),
% 1.09/1.33 inference(monotonicity,[status(thm)],[1349])).
% 1.09/1.33 tff(1351,plain,
% 1.09/1.33 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c0_1(a465) | (~c3_1(a465)) | (~c2_1(a465)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.09/1.33 inference(transitivity,[status(thm)],[1350, 1348])).
% 1.09/1.33 tff(1352,plain,
% 1.09/1.33 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c0_1(a465) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.09/1.33 inference(quant_inst,[status(thm)],[])).
% 1.09/1.33 tff(1353,plain,
% 1.09/1.33 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 1.09/1.33 tff(1354,plain,
% 1.09/1.33 (hskp18 | hskp6 | (~c2_1(a465))),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1353, 75, 337, 243, 1347])).
% 1.09/1.33 tff(1355,plain,
% 1.09/1.33 (hskp18),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1354, 1337, 1301])).
% 1.09/1.33 tff(1356,plain,
% 1.09/1.33 (~c3_1(a494)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[284, 1355])).
% 1.09/1.33 tff(1357,plain,
% 1.09/1.33 (~c2_1(a494)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[290, 1355])).
% 1.09/1.33 tff(1358,plain,
% 1.09/1.33 (c0_1(a494)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[298, 1355])).
% 1.09/1.33 tff(1359,plain,
% 1.09/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1360,plain,
% 1.09/1.33 (((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465))) <=> (c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1361,plain,
% 1.09/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494))))),
% 1.09/1.33 inference(monotonicity,[status(thm)],[1360])).
% 1.09/1.33 tff(1362,plain,
% 1.09/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494)))),
% 1.09/1.33 inference(transitivity,[status(thm)],[1361, 1359])).
% 1.09/1.33 tff(1363,plain,
% 1.09/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))),
% 1.09/1.33 inference(quant_inst,[status(thm)],[])).
% 1.09/1.33 tff(1364,plain,
% 1.09/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 1.09/1.33 tff(1365,plain,
% 1.09/1.33 ($false),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1364, 75, 1358, 337, 1357, 1356, 243, 242, 386, 1301])).
% 1.09/1.33 tff(1366,plain,(hskp5 | (~c3_1(a465)) | c0_1(a465) | c1_1(a465) | hskp2 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.09/1.33 tff(1367,plain,
% 1.09/1.33 (hskp5),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1366, 1299, 1298, 1297, 1295, 21])).
% 1.09/1.33 tff(1368,plain,
% 1.09/1.33 (~c3_1(a467)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1091, 1367])).
% 1.09/1.33 tff(1369,plain,
% 1.09/1.33 (c0_1(a467)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[548, 1367])).
% 1.09/1.33 tff(1370,plain,
% 1.09/1.33 (~c1_1(a467)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[989, 1367])).
% 1.09/1.33 tff(1371,plain,
% 1.09/1.33 ($false),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[540, 1370, 1369, 21, 656, 29, 1368, 104, 655])).
% 1.09/1.33 tff(1372,plain,(hskp16 | hskp12 | c2_1(a471) | hskp2 | hskp31 | (~c2_1(a478)) | c0_1(a478) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.33 tff(1373,plain,
% 1.09/1.33 (c2_1(a471)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1372, 1293, 21, 1295, 218, 241, 233, 227])).
% 1.09/1.33 tff(1374,plain,
% 1.09/1.33 ($false),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[483, 1373, 1294])).
% 1.09/1.33 tff(1375,plain,(hskp12 | hskp2 | hskp31 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.09/1.33 tff(1376,plain,
% 1.09/1.33 (hskp12),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1375, 1286, 218, 217])).
% 1.09/1.33 tff(1377,plain,
% 1.09/1.33 (~c3_1(a481)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[421, 1376])).
% 1.09/1.33 tff(1378,plain,
% 1.09/1.33 (~c0_1(a481)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[427, 1376])).
% 1.09/1.33 tff(1379,plain,
% 1.09/1.33 (c1_1(a481)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[435, 1376])).
% 1.09/1.33 tff(1380,plain,
% 1.09/1.33 (c2_1(a481)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[442, 75, 1379, 1378, 1377, 10])).
% 1.09/1.33 tff(1381,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1382,plain,
% 1.09/1.33 (((~ndr1_0) | c2_1(a464) | c1_1(a464) | (~c0_1(a464)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1383,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a464) | c1_1(a464) | (~c0_1(a464)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.09/1.33 inference(monotonicity,[status(thm)],[1382])).
% 1.09/1.33 tff(1384,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a464) | c1_1(a464) | (~c0_1(a464)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.33 inference(transitivity,[status(thm)],[1383, 1381])).
% 1.09/1.33 tff(1385,plain,
% 1.09/1.33 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a464) | c1_1(a464) | (~c0_1(a464)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.33 inference(quant_inst,[status(thm)],[])).
% 1.09/1.33 tff(1386,plain,
% 1.09/1.33 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 1.09/1.33 tff(1387,plain,
% 1.09/1.33 (c1_1(a464)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1386, 75, 1379, 1378, 1280, 219, 369, 1380])).
% 1.09/1.33 tff(1388,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1389,plain,
% 1.09/1.33 ((hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a464) | (~c1_1(a464)) | (~c0_1(a464))) <=> (hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1390,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a464) | (~c1_1(a464)) | (~c0_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.09/1.33 inference(monotonicity,[status(thm)],[1389])).
% 1.09/1.33 tff(1391,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a464) | (~c1_1(a464)) | (~c0_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.09/1.33 inference(transitivity,[status(thm)],[1390, 1388])).
% 1.09/1.33 tff(1392,plain,
% 1.09/1.33 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a464) | (~c1_1(a464)) | (~c0_1(a464)))),
% 1.09/1.33 inference(quant_inst,[status(thm)],[])).
% 1.09/1.33 tff(1393,plain,
% 1.09/1.33 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 1.09/1.33 tff(1394,plain,
% 1.09/1.33 (hskp29),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1393, 75, 1379, 1377, 1280, 219, 970, 1387, 1380])).
% 1.09/1.33 tff(1395,plain,
% 1.09/1.33 (c2_1(a474)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[310, 1394])).
% 1.09/1.33 tff(1396,plain,
% 1.09/1.33 (c1_1(a474)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[318, 1394])).
% 1.09/1.33 tff(1397,plain,
% 1.09/1.33 (c0_1(a474)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[326, 1394])).
% 1.09/1.33 tff(1398,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1399,plain,
% 1.09/1.33 ((hskp31 | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c0_1(a464)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1400,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c0_1(a464)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.09/1.33 inference(monotonicity,[status(thm)],[1399])).
% 1.09/1.33 tff(1401,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c0_1(a464)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.33 inference(transitivity,[status(thm)],[1400, 1398])).
% 1.09/1.33 tff(1402,plain,
% 1.09/1.33 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c0_1(a464)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.09/1.33 inference(quant_inst,[status(thm)],[])).
% 1.09/1.33 tff(1403,plain,
% 1.09/1.33 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 1.09/1.33 tff(1404,plain,
% 1.09/1.33 (~c3_1(a464)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1403, 218, 75, 1397, 1396, 1395, 1280, 1212, 1387])).
% 1.09/1.33 tff(1405,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1406,plain,
% 1.09/1.33 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a464) | c2_1(a464) | (~c0_1(a464))) <=> (c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1407,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a464) | c2_1(a464) | (~c0_1(a464)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.09/1.33 inference(monotonicity,[status(thm)],[1406])).
% 1.09/1.33 tff(1408,plain,
% 1.09/1.33 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a464) | c2_1(a464) | (~c0_1(a464)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.09/1.33 inference(transitivity,[status(thm)],[1407, 1405])).
% 1.09/1.33 tff(1409,plain,
% 1.09/1.33 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a464) | c2_1(a464) | (~c0_1(a464)))),
% 1.09/1.33 inference(quant_inst,[status(thm)],[])).
% 1.09/1.33 tff(1410,plain,
% 1.09/1.33 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 1.09/1.33 tff(1411,plain,
% 1.09/1.33 ($false),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1410, 75, 1397, 1396, 1395, 1404, 1280, 219, 103])).
% 1.09/1.33 tff(1412,plain,(c2_1(a464) | hskp31 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.09/1.33 tff(1413,plain,
% 1.09/1.33 (c2_1(a464)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1412, 218, 217])).
% 1.09/1.33 tff(1414,plain,
% 1.09/1.33 (((~hskp2) | (~c2_1(a464))) <=> ((~hskp2) | (~c2_1(a464)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1415,plain,
% 1.09/1.33 (((~c2_1(a464)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a464)))),
% 1.09/1.33 inference(rewrite,[status(thm)],[])).
% 1.09/1.33 tff(1416,axiom,((~c2_1(a464)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.09/1.33 tff(1417,plain,
% 1.09/1.33 ((~hskp2) | (~c2_1(a464))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 1.09/1.33 tff(1418,plain,
% 1.09/1.33 ((~hskp2) | (~c2_1(a464))),
% 1.09/1.33 inference(modus_ponens,[status(thm)],[1417, 1414])).
% 1.09/1.33 tff(1419,plain,
% 1.09/1.33 (~hskp2),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1418, 1413])).
% 1.09/1.33 tff(1420,plain,
% 1.09/1.33 (hskp12),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1375, 1419, 218, 217])).
% 1.09/1.33 tff(1421,plain,
% 1.09/1.33 (~c3_1(a481)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[421, 1420])).
% 1.09/1.33 tff(1422,plain,
% 1.09/1.33 (~c0_1(a481)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[427, 1420])).
% 1.09/1.33 tff(1423,plain,
% 1.09/1.33 (c1_1(a481)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[435, 1420])).
% 1.09/1.33 tff(1424,plain,
% 1.09/1.33 (c2_1(a481)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[442, 75, 1423, 1422, 1421, 10])).
% 1.09/1.33 tff(1425,assumption,(c1_1(a481)), introduced(assumption)).
% 1.09/1.33 tff(1426,plain,
% 1.09/1.33 (c2_1(a481)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[442, 75, 1425, 942, 941, 10])).
% 1.09/1.33 tff(1427,assumption,(hskp7), introduced(assumption)).
% 1.09/1.33 tff(1428,plain,
% 1.09/1.33 (~c2_1(a471)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[483, 1427])).
% 1.09/1.33 tff(1429,plain,
% 1.09/1.33 (c0_1(a471)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[499, 1427])).
% 1.09/1.33 tff(1430,plain,
% 1.09/1.33 (c1_1(a471)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[934, 75, 1425, 1429, 942, 1428, 369, 1426])).
% 1.09/1.33 tff(1431,plain,
% 1.09/1.33 (c3_1(a471)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[491, 1427])).
% 1.09/1.33 tff(1432,plain,
% 1.09/1.33 (hskp29 | (~c1_1(a471))),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[976, 75, 1425, 1429, 941, 1428, 970, 1426])).
% 1.09/1.33 tff(1433,plain,
% 1.09/1.33 (hskp29),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1432, 1430])).
% 1.09/1.33 tff(1434,plain,
% 1.09/1.33 (c2_1(a474)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[310, 1433])).
% 1.09/1.33 tff(1435,plain,
% 1.09/1.33 (c1_1(a474)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[318, 1433])).
% 1.09/1.33 tff(1436,plain,
% 1.09/1.33 (c0_1(a474)),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[326, 1433])).
% 1.09/1.33 tff(1437,plain,
% 1.09/1.33 ($false),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1222, 218, 75, 1436, 1435, 1434, 1429, 1431, 1212, 1430])).
% 1.09/1.33 tff(1438,plain,((~hskp7) | hskp31 | (~c1_1(a481)) | c3_1(a481) | c0_1(a481)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.33 tff(1439,plain,
% 1.09/1.33 (~hskp7),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1438, 218, 1423, 1421, 1422])).
% 1.09/1.33 tff(1440,plain,
% 1.09/1.33 (hskp16),
% 1.09/1.33 inference(unit_resolution,[status(thm)],[1168, 1439])).
% 1.19/1.33 tff(1441,plain,
% 1.19/1.33 (~c2_1(a487)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[263, 1440])).
% 1.19/1.33 tff(1442,plain,
% 1.19/1.33 (~c1_1(a487)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[27, 1440])).
% 1.19/1.33 tff(1443,plain,
% 1.19/1.33 (c0_1(a487)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[271, 1440])).
% 1.19/1.33 tff(1444,plain,
% 1.19/1.33 ($false),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1164, 75, 1443, 1423, 1442, 1441, 1422, 369, 1424])).
% 1.19/1.33 tff(1445,plain,(hskp31 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.19/1.33 tff(1446,plain,
% 1.19/1.33 (hskp31),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1445, 216])).
% 1.19/1.33 tff(1447,plain,
% 1.19/1.33 (((~hskp31) | c0_1(a529)) <=> ((~hskp31) | c0_1(a529))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1448,axiom,((~hskp31) | c0_1(a529)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.19/1.33 tff(1449,plain,
% 1.19/1.33 ((~hskp31) | c0_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 1.19/1.33 tff(1450,plain,
% 1.19/1.33 ((~hskp31) | c0_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1449, 1447])).
% 1.19/1.33 tff(1451,plain,
% 1.19/1.33 ((~hskp31) | c0_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1450, 1447])).
% 1.19/1.33 tff(1452,plain,
% 1.19/1.33 ((~hskp31) | c0_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1451, 1447])).
% 1.19/1.33 tff(1453,plain,
% 1.19/1.33 ((~hskp31) | c0_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1452, 1447])).
% 1.19/1.33 tff(1454,plain,
% 1.19/1.33 (c0_1(a529)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1453, 1446])).
% 1.19/1.33 tff(1455,plain,
% 1.19/1.33 (((~hskp31) | c3_1(a529)) <=> ((~hskp31) | c3_1(a529))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1456,axiom,((~hskp31) | c3_1(a529)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.19/1.33 tff(1457,plain,
% 1.19/1.33 ((~hskp31) | c3_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 1.19/1.33 tff(1458,plain,
% 1.19/1.33 ((~hskp31) | c3_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1457, 1455])).
% 1.19/1.33 tff(1459,plain,
% 1.19/1.33 ((~hskp31) | c3_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1458, 1455])).
% 1.19/1.33 tff(1460,plain,
% 1.19/1.33 ((~hskp31) | c3_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1459, 1455])).
% 1.19/1.33 tff(1461,plain,
% 1.19/1.33 ((~hskp31) | c3_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1460, 1455])).
% 1.19/1.33 tff(1462,plain,
% 1.19/1.33 (c3_1(a529)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1461, 1446])).
% 1.19/1.33 tff(1463,plain,
% 1.19/1.33 (((~hskp31) | c1_1(a529)) <=> ((~hskp31) | c1_1(a529))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1464,axiom,((~hskp31) | c1_1(a529)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.19/1.33 tff(1465,plain,
% 1.19/1.33 ((~hskp31) | c1_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 1.19/1.33 tff(1466,plain,
% 1.19/1.33 ((~hskp31) | c1_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1465, 1463])).
% 1.19/1.33 tff(1467,plain,
% 1.19/1.33 ((~hskp31) | c1_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1466, 1463])).
% 1.19/1.33 tff(1468,plain,
% 1.19/1.33 ((~hskp31) | c1_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1467, 1463])).
% 1.19/1.33 tff(1469,plain,
% 1.19/1.33 ((~hskp31) | c1_1(a529)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1468, 1463])).
% 1.19/1.33 tff(1470,plain,
% 1.19/1.33 (c1_1(a529)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1469, 1446])).
% 1.19/1.33 tff(1471,plain,
% 1.19/1.33 (^[U: $i] : refl((hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 1.19/1.33 inference(bind,[status(th)],[])).
% 1.19/1.33 tff(1472,plain,
% 1.19/1.33 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.33 inference(quant_intro,[status(thm)],[1471])).
% 1.19/1.33 tff(1473,plain,
% 1.19/1.33 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1474,plain,
% 1.19/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) | hskp10) <=> ((hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) | hskp10) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.19/1.33 inference(bind,[status(th)],[])).
% 1.19/1.33 tff(1475,plain,
% 1.19/1.33 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) | hskp10) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.33 inference(quant_intro,[status(thm)],[1474])).
% 1.19/1.33 tff(1476,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.19/1.33 tff(1477,plain,
% 1.19/1.33 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 1.19/1.33 tff(1478,plain,
% 1.19/1.33 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1477, 1473])).
% 1.19/1.33 tff(1479,plain,(
% 1.19/1.33 ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.33 inference(skolemize,[status(sab)],[1478])).
% 1.19/1.33 tff(1480,plain,
% 1.19/1.33 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1479, 1472])).
% 1.19/1.33 tff(1481,plain,
% 1.19/1.33 (hskp31),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1445, 217])).
% 1.19/1.33 tff(1482,plain,
% 1.19/1.33 (c3_1(a529)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1461, 1481])).
% 1.19/1.33 tff(1483,plain,
% 1.19/1.33 (c1_1(a529)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1469, 1481])).
% 1.19/1.33 tff(1484,plain,
% 1.19/1.33 (c0_1(a529)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1453, 1481])).
% 1.19/1.33 tff(1485,assumption,(~hskp10), introduced(assumption)).
% 1.19/1.33 tff(1486,plain,
% 1.19/1.33 (hskp29),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[415, 1191, 21])).
% 1.19/1.33 tff(1487,plain,
% 1.19/1.33 (c2_1(a474)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[310, 1486])).
% 1.19/1.33 tff(1488,plain,
% 1.19/1.33 (c1_1(a474)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[318, 1486])).
% 1.19/1.33 tff(1489,plain,
% 1.19/1.33 (c0_1(a474)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[326, 1486])).
% 1.19/1.33 tff(1490,plain,
% 1.19/1.33 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1491,plain,
% 1.19/1.33 ((hskp14 | hskp10 | (~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1492,plain,
% 1.19/1.33 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.19/1.33 inference(monotonicity,[status(thm)],[1491])).
% 1.19/1.33 tff(1493,plain,
% 1.19/1.33 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.33 inference(transitivity,[status(thm)],[1492, 1490])).
% 1.19/1.33 tff(1494,plain,
% 1.19/1.33 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.19/1.33 inference(quant_inst,[status(thm)],[])).
% 1.19/1.33 tff(1495,plain,
% 1.19/1.33 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.19/1.33 tff(1496,plain,
% 1.19/1.33 (hskp14),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1495, 75, 1485, 1489, 1488, 1487, 1480])).
% 1.19/1.33 tff(1497,plain,
% 1.19/1.33 (((~hskp14) | (~c0_1(a483))) <=> ((~hskp14) | (~c0_1(a483)))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1498,plain,
% 1.19/1.33 (((~c0_1(a483)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a483)))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1499,axiom,((~c0_1(a483)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.19/1.33 tff(1500,plain,
% 1.19/1.33 ((~hskp14) | (~c0_1(a483))),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 1.19/1.33 tff(1501,plain,
% 1.19/1.33 ((~hskp14) | (~c0_1(a483))),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1500, 1497])).
% 1.19/1.33 tff(1502,plain,
% 1.19/1.33 (~c0_1(a483)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1501, 1496])).
% 1.19/1.33 tff(1503,plain,
% 1.19/1.33 (((~hskp14) | c2_1(a483)) <=> ((~hskp14) | c2_1(a483))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1504,axiom,((~hskp14) | c2_1(a483)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.19/1.33 tff(1505,plain,
% 1.19/1.33 ((~hskp14) | c2_1(a483)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 1.19/1.33 tff(1506,plain,
% 1.19/1.33 ((~hskp14) | c2_1(a483)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1505, 1503])).
% 1.19/1.33 tff(1507,plain,
% 1.19/1.33 ((~hskp14) | c2_1(a483)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1506, 1503])).
% 1.19/1.33 tff(1508,plain,
% 1.19/1.33 ((~hskp14) | c2_1(a483)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1507, 1503])).
% 1.19/1.33 tff(1509,plain,
% 1.19/1.33 ((~hskp14) | c2_1(a483)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1508, 1503])).
% 1.19/1.33 tff(1510,plain,
% 1.19/1.33 (c2_1(a483)),
% 1.19/1.33 inference(unit_resolution,[status(thm)],[1509, 1496])).
% 1.19/1.33 tff(1511,plain,
% 1.19/1.33 (((~hskp14) | c1_1(a483)) <=> ((~hskp14) | c1_1(a483))),
% 1.19/1.33 inference(rewrite,[status(thm)],[])).
% 1.19/1.33 tff(1512,axiom,((~hskp14) | c1_1(a483)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.19/1.33 tff(1513,plain,
% 1.19/1.33 ((~hskp14) | c1_1(a483)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.19/1.33 tff(1514,plain,
% 1.19/1.33 ((~hskp14) | c1_1(a483)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1513, 1511])).
% 1.19/1.33 tff(1515,plain,
% 1.19/1.33 ((~hskp14) | c1_1(a483)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1514, 1511])).
% 1.19/1.33 tff(1516,plain,
% 1.19/1.33 ((~hskp14) | c1_1(a483)),
% 1.19/1.33 inference(modus_ponens,[status(thm)],[1515, 1511])).
% 1.19/1.34 tff(1517,plain,
% 1.19/1.34 ((~hskp14) | c1_1(a483)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1516, 1511])).
% 1.19/1.34 tff(1518,plain,
% 1.19/1.34 (c1_1(a483)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1517, 1496])).
% 1.19/1.34 tff(1519,plain,
% 1.19/1.34 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1520,plain,
% 1.19/1.34 ((hskp16 | (~ndr1_0) | (~c1_1(a483)) | (~c3_1(a483)) | (~c2_1(a483)) | c0_1(a483) | (~c3_1(a483)) | (~c1_1(a483))) <=> (hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1521,plain,
% 1.19/1.34 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a483)) | (~c3_1(a483)) | (~c2_1(a483)) | c0_1(a483) | (~c3_1(a483)) | (~c1_1(a483)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483))))),
% 1.19/1.34 inference(monotonicity,[status(thm)],[1520])).
% 1.19/1.34 tff(1522,plain,
% 1.19/1.34 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a483)) | (~c3_1(a483)) | (~c2_1(a483)) | c0_1(a483) | (~c3_1(a483)) | (~c1_1(a483)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.19/1.34 inference(transitivity,[status(thm)],[1521, 1519])).
% 1.19/1.34 tff(1523,plain,
% 1.19/1.34 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a483)) | (~c3_1(a483)) | (~c2_1(a483)) | c0_1(a483) | (~c3_1(a483)) | (~c1_1(a483)))),
% 1.19/1.34 inference(quant_inst,[status(thm)],[])).
% 1.19/1.34 tff(1524,plain,
% 1.19/1.34 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 1.19/1.34 tff(1525,plain,
% 1.19/1.34 (~c3_1(a483)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1524, 75, 104, 1518, 1510, 1502, 207])).
% 1.19/1.34 tff(1526,plain,
% 1.19/1.34 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1527,plain,
% 1.19/1.34 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a483) | c3_1(a483) | (~c2_1(a483))) <=> (hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1528,plain,
% 1.19/1.34 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a483) | c3_1(a483) | (~c2_1(a483)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483))))),
% 1.19/1.34 inference(monotonicity,[status(thm)],[1527])).
% 1.19/1.34 tff(1529,plain,
% 1.19/1.34 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a483) | c3_1(a483) | (~c2_1(a483)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483)))),
% 1.19/1.34 inference(transitivity,[status(thm)],[1528, 1526])).
% 1.19/1.34 tff(1530,plain,
% 1.19/1.34 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a483) | c3_1(a483) | (~c2_1(a483)))),
% 1.19/1.34 inference(quant_inst,[status(thm)],[])).
% 1.19/1.34 tff(1531,plain,
% 1.19/1.34 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 1.19/1.34 tff(1532,plain,
% 1.19/1.34 (hskp7),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1531, 75, 104, 1510, 1502, 20, 1525])).
% 1.19/1.34 tff(1533,plain,
% 1.19/1.34 (c0_1(a471)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[499, 1532])).
% 1.19/1.34 tff(1534,plain,
% 1.19/1.34 (c3_1(a471)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[491, 1532])).
% 1.19/1.34 tff(1535,plain,
% 1.19/1.34 ($false),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1196, 1534, 1533, 217, 21, 242, 1173, 29])).
% 1.19/1.34 tff(1536,plain,((~c0_1(a465)) | hskp19 | hskp12 | c1_1(a465) | c2_1(a471) | hskp16 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.19/1.34 tff(1537,plain,
% 1.19/1.34 (~c0_1(a465)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1536, 1485, 21, 242, 29, 104, 217])).
% 1.19/1.34 tff(1538,assumption,(c1_1(a529)), introduced(assumption)).
% 1.19/1.34 tff(1539,assumption,(c3_1(a529)), introduced(assumption)).
% 1.19/1.34 tff(1540,assumption,(c0_1(a529)), introduced(assumption)).
% 1.19/1.34 tff(1541,plain,
% 1.19/1.34 (hskp2),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1366, 31, 243, 242, 337, 21])).
% 1.19/1.34 tff(1542,plain,
% 1.19/1.34 (hskp5 | c0_1(a464) | (~c3_1(a464))),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[573, 75, 21, 219, 41])).
% 1.19/1.34 tff(1543,plain,
% 1.19/1.34 (~c3_1(a464)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1542, 31, 220])).
% 1.19/1.34 tff(1544,plain,
% 1.19/1.34 ($false),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[602, 1543, 1541])).
% 1.19/1.34 tff(1545,plain,(hskp5 | c0_1(a464) | hskp12 | c2_1(a464) | c0_1(a465) | c1_1(a465) | (~c3_1(a465))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.34 tff(1546,plain,
% 1.19/1.34 (hskp5),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1545, 337, 21, 219, 243, 242, 220])).
% 1.19/1.34 tff(1547,plain,
% 1.19/1.34 (~c3_1(a467)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1091, 1546])).
% 1.19/1.34 tff(1548,plain,
% 1.19/1.34 (~c1_1(a467)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[989, 1546])).
% 1.19/1.34 tff(1549,plain,
% 1.19/1.34 (c0_1(a467)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[548, 1546])).
% 1.19/1.34 tff(1550,plain,
% 1.19/1.34 (c2_1(a467)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[519, 75, 104, 1549, 1548, 1547, 513])).
% 1.19/1.34 tff(1551,plain,
% 1.19/1.34 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.19/1.34 inference(bind,[status(th)],[])).
% 1.19/1.34 tff(1552,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.19/1.34 inference(quant_intro,[status(thm)],[1551])).
% 1.19/1.34 tff(1553,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1554,plain,
% 1.19/1.34 (^[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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.19/1.34 inference(bind,[status(th)],[])).
% 1.19/1.34 tff(1555,plain,
% 1.19/1.34 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.19/1.34 inference(quant_intro,[status(thm)],[1554])).
% 1.19/1.34 tff(1556,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.19/1.34 tff(1557,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 1.19/1.34 tff(1558,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1557, 1553])).
% 1.19/1.34 tff(1559,plain,(
% 1.19/1.34 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.19/1.34 inference(skolemize,[status(sab)],[1558])).
% 1.19/1.34 tff(1560,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1559, 1552])).
% 1.19/1.34 tff(1561,plain,
% 1.19/1.34 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.19/1.34 inference(bind,[status(th)],[])).
% 1.19/1.34 tff(1562,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.19/1.34 inference(quant_intro,[status(thm)],[1561])).
% 1.19/1.34 tff(1563,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1564,plain,
% 1.19/1.34 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.19/1.34 inference(bind,[status(th)],[])).
% 1.19/1.34 tff(1565,plain,
% 1.19/1.34 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.19/1.34 inference(quant_intro,[status(thm)],[1564])).
% 1.19/1.34 tff(1566,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.19/1.34 tff(1567,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 1.19/1.34 tff(1568,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1567, 1563])).
% 1.19/1.34 tff(1569,plain,(
% 1.19/1.34 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.19/1.34 inference(skolemize,[status(sab)],[1568])).
% 1.19/1.34 tff(1570,plain,
% 1.19/1.34 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1569, 1562])).
% 1.19/1.34 tff(1571,plain,
% 1.19/1.34 (~hskp7),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[499, 30])).
% 1.19/1.34 tff(1572,assumption,(~c3_1(a471)), introduced(assumption)).
% 1.19/1.34 tff(1573,plain,
% 1.19/1.34 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.19/1.34 inference(bind,[status(th)],[])).
% 1.19/1.34 tff(1574,plain,
% 1.19/1.34 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.19/1.34 inference(quant_intro,[status(thm)],[1573])).
% 1.19/1.34 tff(1575,plain,
% 1.19/1.34 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1576,plain,
% 1.19/1.34 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.19/1.34 inference(bind,[status(th)],[])).
% 1.19/1.34 tff(1577,plain,
% 1.19/1.34 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.19/1.34 inference(quant_intro,[status(thm)],[1576])).
% 1.19/1.34 tff(1578,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.19/1.34 tff(1579,plain,
% 1.19/1.34 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 1.19/1.34 tff(1580,plain,
% 1.19/1.34 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1579, 1575])).
% 1.19/1.34 tff(1581,plain,(
% 1.19/1.34 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.19/1.34 inference(skolemize,[status(sab)],[1580])).
% 1.19/1.34 tff(1582,plain,
% 1.19/1.34 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1581, 1574])).
% 1.19/1.34 tff(1583,plain,
% 1.19/1.34 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1584,plain,
% 1.19/1.34 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | c3_1(a471)) <=> (hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1585,plain,
% 1.19/1.34 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | c3_1(a471))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0)))),
% 1.19/1.34 inference(monotonicity,[status(thm)],[1584])).
% 1.19/1.34 tff(1586,plain,
% 1.19/1.34 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | c3_1(a471))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0))),
% 1.19/1.34 inference(transitivity,[status(thm)],[1585, 1583])).
% 1.19/1.34 tff(1587,plain,
% 1.19/1.34 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | c3_1(a471))),
% 1.19/1.34 inference(quant_inst,[status(thm)],[])).
% 1.19/1.34 tff(1588,plain,
% 1.19/1.34 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 1.19/1.34 tff(1589,plain,
% 1.19/1.34 (hskp8 | hskp7 | c0_1(a471) | c3_1(a471)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1588, 75, 29, 1582])).
% 1.19/1.34 tff(1590,plain,
% 1.19/1.34 (hskp8),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1589, 1572, 30, 1571])).
% 1.19/1.34 tff(1591,plain,
% 1.19/1.34 (((~hskp8) | (~c2_1(a472))) <=> ((~hskp8) | (~c2_1(a472)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1592,plain,
% 1.19/1.34 (((~c2_1(a472)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a472)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1593,axiom,((~c2_1(a472)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.19/1.34 tff(1594,plain,
% 1.19/1.34 ((~hskp8) | (~c2_1(a472))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 1.19/1.34 tff(1595,plain,
% 1.19/1.34 ((~hskp8) | (~c2_1(a472))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1594, 1591])).
% 1.19/1.34 tff(1596,plain,
% 1.19/1.34 (~c2_1(a472)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1595, 1590])).
% 1.19/1.34 tff(1597,plain,
% 1.19/1.34 (((~hskp8) | c3_1(a472)) <=> ((~hskp8) | c3_1(a472))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1598,axiom,((~hskp8) | c3_1(a472)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.19/1.34 tff(1599,plain,
% 1.19/1.34 ((~hskp8) | c3_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 1.19/1.34 tff(1600,plain,
% 1.19/1.34 ((~hskp8) | c3_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1599, 1597])).
% 1.19/1.34 tff(1601,plain,
% 1.19/1.34 ((~hskp8) | c3_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1600, 1597])).
% 1.19/1.34 tff(1602,plain,
% 1.19/1.34 ((~hskp8) | c3_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1601, 1597])).
% 1.19/1.34 tff(1603,plain,
% 1.19/1.34 ((~hskp8) | c3_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1602, 1597])).
% 1.19/1.34 tff(1604,plain,
% 1.19/1.34 (c3_1(a472)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1603, 1590])).
% 1.19/1.34 tff(1605,plain,
% 1.19/1.34 (((~hskp8) | c1_1(a472)) <=> ((~hskp8) | c1_1(a472))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1606,axiom,((~hskp8) | c1_1(a472)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.19/1.34 tff(1607,plain,
% 1.19/1.34 ((~hskp8) | c1_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1606, 1605])).
% 1.19/1.34 tff(1608,plain,
% 1.19/1.34 ((~hskp8) | c1_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1607, 1605])).
% 1.19/1.34 tff(1609,plain,
% 1.19/1.34 ((~hskp8) | c1_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1608, 1605])).
% 1.19/1.34 tff(1610,plain,
% 1.19/1.34 ((~hskp8) | c1_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1609, 1605])).
% 1.19/1.34 tff(1611,plain,
% 1.19/1.34 ((~hskp8) | c1_1(a472)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1610, 1605])).
% 1.19/1.34 tff(1612,plain,
% 1.19/1.34 (c1_1(a472)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1611, 1590])).
% 1.19/1.34 tff(1613,plain,
% 1.19/1.34 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1614,plain,
% 1.19/1.34 ((hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464))) <=> (hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1615,plain,
% 1.19/1.34 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472))))),
% 1.19/1.34 inference(monotonicity,[status(thm)],[1614])).
% 1.19/1.34 tff(1616,plain,
% 1.19/1.34 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.19/1.34 inference(transitivity,[status(thm)],[1615, 1613])).
% 1.19/1.34 tff(1617,plain,
% 1.19/1.34 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))),
% 1.19/1.34 inference(quant_inst,[status(thm)],[])).
% 1.19/1.34 tff(1618,plain,
% 1.19/1.34 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.19/1.34 tff(1619,plain,
% 1.19/1.34 (~c3_1(a464)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1618, 75, 1485, 1612, 1604, 1596, 220, 219, 1570])).
% 1.19/1.34 tff(1620,plain,
% 1.19/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1621,plain,
% 1.19/1.34 (((~ndr1_0) | c0_1(a471) | c3_1(a471) | (~c1_1(a471)) | c0_1(a471) | c2_1(a471) | (~c1_1(a471)) | c3_1(a471) | c0_1(a471) | c2_1(a471)) <=> (c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1622,plain,
% 1.19/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a471) | c3_1(a471) | (~c1_1(a471)) | c0_1(a471) | c2_1(a471) | (~c1_1(a471)) | c3_1(a471) | c0_1(a471) | c2_1(a471))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471))))),
% 1.19/1.34 inference(monotonicity,[status(thm)],[1621])).
% 1.19/1.34 tff(1623,plain,
% 1.19/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a471) | c3_1(a471) | (~c1_1(a471)) | c0_1(a471) | c2_1(a471) | (~c1_1(a471)) | c3_1(a471) | c0_1(a471) | c2_1(a471))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)))),
% 1.19/1.34 inference(transitivity,[status(thm)],[1622, 1620])).
% 1.19/1.34 tff(1624,plain,
% 1.19/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a471) | c3_1(a471) | (~c1_1(a471)) | c0_1(a471) | c2_1(a471) | (~c1_1(a471)) | c3_1(a471) | c0_1(a471) | c2_1(a471))),
% 1.19/1.34 inference(quant_inst,[status(thm)],[])).
% 1.19/1.34 tff(1625,plain,
% 1.19/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471))),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 1.19/1.34 tff(1626,plain,
% 1.19/1.34 (~c1_1(a471)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1625, 75, 30, 1572, 29, 10])).
% 1.19/1.34 tff(1627,plain,
% 1.19/1.34 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1628,plain,
% 1.19/1.34 ((hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a471) | c1_1(a471) | c2_1(a471)) <=> (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1629,plain,
% 1.19/1.34 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a471) | c1_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471)))),
% 1.19/1.34 inference(monotonicity,[status(thm)],[1628])).
% 1.19/1.34 tff(1630,plain,
% 1.19/1.34 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a471) | c1_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471))),
% 1.19/1.34 inference(transitivity,[status(thm)],[1629, 1627])).
% 1.19/1.34 tff(1631,plain,
% 1.19/1.34 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a471) | c1_1(a471) | c2_1(a471))),
% 1.19/1.34 inference(quant_inst,[status(thm)],[])).
% 1.19/1.34 tff(1632,plain,
% 1.19/1.34 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471)),
% 1.19/1.34 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 1.19/1.34 tff(1633,plain,
% 1.19/1.34 (~c0_1(a467)),
% 1.19/1.34 inference(unit_resolution,[status(thm)],[1632, 75, 104, 1572, 29, 248, 247, 513, 1626])).
% 1.19/1.34 tff(1634,plain,
% 1.19/1.34 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1635,plain,
% 1.19/1.34 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c2_1(a467))) <=> (hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.19/1.34 inference(rewrite,[status(thm)],[])).
% 1.19/1.34 tff(1636,plain,
% 1.19/1.34 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467))))),
% 1.19/1.34 inference(monotonicity,[status(thm)],[1635])).
% 1.19/1.34 tff(1637,plain,
% 1.19/1.34 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.19/1.34 inference(transitivity,[status(thm)],[1636, 1634])).
% 1.19/1.34 tff(1638,plain,
% 1.19/1.34 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c2_1(a467)))),
% 1.19/1.34 inference(quant_inst,[status(thm)],[])).
% 1.19/1.35 tff(1639,plain,
% 1.19/1.35 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467))),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.19/1.35 tff(1640,plain,
% 1.19/1.35 (c0_1(a467) | (~c2_1(a467))),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1639, 75, 104, 1571, 247, 20])).
% 1.19/1.35 tff(1641,plain,
% 1.19/1.35 (~c2_1(a467)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1640, 1633])).
% 1.19/1.35 tff(1642,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1643,plain,
% 1.19/1.35 ((hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465))) <=> (hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1644,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472))))),
% 1.19/1.35 inference(monotonicity,[status(thm)],[1643])).
% 1.19/1.35 tff(1645,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.19/1.35 inference(transitivity,[status(thm)],[1644, 1642])).
% 1.19/1.35 tff(1646,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))),
% 1.19/1.35 inference(quant_inst,[status(thm)],[])).
% 1.19/1.35 tff(1647,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472))),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 1.19/1.35 tff(1648,plain,
% 1.19/1.35 (c2_1(a465)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1647, 75, 1485, 1612, 1604, 337, 1596, 243, 1570])).
% 1.19/1.35 tff(1649,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1650,plain,
% 1.19/1.35 ((hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a467) | c1_1(a467) | c2_1(a467)) <=> (hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1651,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a467) | c1_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467)))),
% 1.19/1.35 inference(monotonicity,[status(thm)],[1650])).
% 1.19/1.35 tff(1652,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a467) | c1_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467))),
% 1.19/1.35 inference(transitivity,[status(thm)],[1651, 1649])).
% 1.19/1.35 tff(1653,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a467) | c1_1(a467) | c2_1(a467))),
% 1.19/1.35 inference(quant_inst,[status(thm)],[])).
% 1.19/1.35 tff(1654,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467)),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 1.19/1.35 tff(1655,plain,
% 1.19/1.35 (hskp2 | c1_1(a467) | (~c2_1(a465)) | c2_1(a467)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1654, 75, 337, 247, 242, 594])).
% 1.19/1.35 tff(1656,plain,
% 1.19/1.35 (hskp2),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1655, 1648, 248, 1641])).
% 1.19/1.35 tff(1657,plain,
% 1.19/1.35 ($false),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[602, 1656, 1619])).
% 1.19/1.35 tff(1658,plain,(c3_1(a471) | c1_1(a467) | (~c3_1(a465)) | c3_1(a467) | c1_1(a465) | hskp16 | hskp10 | c0_1(a464) | c2_1(a464) | c0_1(a465) | c2_1(a471) | c0_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.35 tff(1659,plain,
% 1.19/1.35 (c3_1(a471)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1658, 248, 337, 247, 242, 104, 1485, 220, 219, 243, 29, 30])).
% 1.19/1.35 tff(1660,plain,
% 1.19/1.35 (hskp5),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[82, 1659, 30])).
% 1.19/1.35 tff(1661,plain,
% 1.19/1.35 (c0_1(a467)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[548, 1660])).
% 1.19/1.35 tff(1662,plain,
% 1.19/1.35 ((~c0_1(a467)) | c2_1(a467)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[519, 75, 104, 248, 247, 513])).
% 1.19/1.35 tff(1663,plain,
% 1.19/1.35 (c2_1(a467)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1662, 1661])).
% 1.19/1.35 tff(1664,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1665,plain,
% 1.19/1.35 ((hskp7 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1666,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))))),
% 1.19/1.35 inference(monotonicity,[status(thm)],[1665])).
% 1.19/1.35 tff(1667,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.19/1.35 inference(transitivity,[status(thm)],[1666, 1664])).
% 1.19/1.35 tff(1668,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.19/1.35 inference(quant_inst,[status(thm)],[])).
% 1.19/1.35 tff(1669,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 1.19/1.35 tff(1670,plain,
% 1.19/1.35 ((~c2_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1669, 75, 1571, 1538, 1539, 247, 1560])).
% 1.19/1.35 tff(1671,plain,
% 1.19/1.35 (~c2_1(a529)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1670, 1663, 1661])).
% 1.19/1.35 tff(1672,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1673,plain,
% 1.19/1.35 ((hskp12 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1674,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))))),
% 1.19/1.35 inference(monotonicity,[status(thm)],[1673])).
% 1.19/1.35 tff(1675,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.19/1.35 inference(transitivity,[status(thm)],[1674, 1672])).
% 1.19/1.35 tff(1676,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.19/1.35 inference(quant_inst,[status(thm)],[])).
% 1.19/1.35 tff(1677,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 1.19/1.35 tff(1678,plain,
% 1.19/1.35 ($false),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1677, 75, 21, 1540, 1539, 1661, 248, 531, 1671, 1663])).
% 1.19/1.35 tff(1679,plain,(c1_1(a467) | hskp12 | (~c0_1(a529)) | (~c3_1(a529)) | (~c1_1(a529)) | c3_1(a467) | hskp16 | c0_1(a471) | c2_1(a471) | (~c3_1(a465)) | c1_1(a465) | hskp10 | c0_1(a464) | c2_1(a464) | c0_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.35 tff(1680,plain,
% 1.19/1.35 (c0_1(a471)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1679, 1547, 1540, 1539, 1538, 21, 104, 1548, 29, 337, 242, 1485, 220, 219, 243])).
% 1.19/1.35 tff(1681,plain,
% 1.19/1.35 (~c3_1(a471)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[540, 1680, 21, 1548, 29, 1547, 104, 1549])).
% 1.19/1.35 tff(1682,plain,
% 1.19/1.35 (~hskp7),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[491, 1681])).
% 1.19/1.35 tff(1683,plain,
% 1.19/1.35 (~c2_1(a529)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1669, 75, 1682, 1538, 1539, 1549, 1547, 1560, 1550])).
% 1.19/1.35 tff(1684,plain,
% 1.19/1.35 ($false),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1677, 75, 21, 1540, 1539, 1549, 1548, 531, 1683, 1550])).
% 1.19/1.35 tff(1685,plain,((~c3_1(a465)) | hskp12 | (~c0_1(a529)) | (~c3_1(a529)) | (~c1_1(a529)) | hskp16 | c2_1(a471) | c1_1(a465) | hskp10 | c0_1(a464) | c2_1(a464) | c0_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.35 tff(1686,plain,
% 1.19/1.35 (~c3_1(a465)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1685, 220, 1540, 1539, 1538, 104, 29, 242, 1485, 21, 219, 243])).
% 1.19/1.35 tff(1687,plain,
% 1.19/1.35 (~hskp3),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[403, 1686])).
% 1.19/1.35 tff(1688,plain,
% 1.19/1.35 (hskp29),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[415, 1687, 21])).
% 1.19/1.35 tff(1689,plain,
% 1.19/1.35 (c2_1(a474)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[310, 1688])).
% 1.19/1.35 tff(1690,plain,
% 1.19/1.35 (c1_1(a474)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[318, 1688])).
% 1.19/1.35 tff(1691,plain,
% 1.19/1.35 (c0_1(a474)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[326, 1688])).
% 1.19/1.35 tff(1692,plain,
% 1.19/1.35 (hskp14),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1495, 75, 1485, 1691, 1690, 1689, 1480])).
% 1.19/1.35 tff(1693,plain,
% 1.19/1.35 (~c0_1(a483)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1501, 1692])).
% 1.19/1.35 tff(1694,plain,
% 1.19/1.35 (c2_1(a483)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1509, 1692])).
% 1.19/1.35 tff(1695,plain,
% 1.19/1.35 (c1_1(a483)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1517, 1692])).
% 1.19/1.35 tff(1696,plain,
% 1.19/1.35 (~c3_1(a483)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1524, 75, 104, 1695, 1694, 1693, 207])).
% 1.19/1.35 tff(1697,plain,
% 1.19/1.35 (hskp7),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1531, 75, 104, 1694, 1693, 20, 1696])).
% 1.19/1.35 tff(1698,plain,
% 1.19/1.35 (c0_1(a471)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[499, 1697])).
% 1.19/1.35 tff(1699,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1700,plain,
% 1.19/1.35 (((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a483) | (~c1_1(a483)) | (~c2_1(a483))) <=> (c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1701,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a483) | (~c1_1(a483)) | (~c2_1(a483)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483))))),
% 1.19/1.35 inference(monotonicity,[status(thm)],[1700])).
% 1.19/1.35 tff(1702,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a483) | (~c1_1(a483)) | (~c2_1(a483)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.19/1.35 inference(transitivity,[status(thm)],[1701, 1699])).
% 1.19/1.35 tff(1703,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a483) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.19/1.35 inference(quant_inst,[status(thm)],[])).
% 1.19/1.35 tff(1704,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483))),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 1.19/1.35 tff(1705,plain,
% 1.19/1.35 (c1_1(a471) | (~c0_1(a471))),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1704, 75, 1695, 1694, 1693, 29, 369])).
% 1.19/1.35 tff(1706,plain,
% 1.19/1.35 (c1_1(a471)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1705, 1698])).
% 1.19/1.35 tff(1707,plain,
% 1.19/1.35 (c3_1(a471)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[491, 1697])).
% 1.19/1.35 tff(1708,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1709,plain,
% 1.19/1.35 ((hskp10 | (~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c3_1(a471)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464))) <=> (hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1710,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c3_1(a471)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471))))),
% 1.19/1.35 inference(monotonicity,[status(thm)],[1709])).
% 1.19/1.35 tff(1711,plain,
% 1.19/1.35 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c3_1(a471)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471)))),
% 1.19/1.35 inference(transitivity,[status(thm)],[1710, 1708])).
% 1.19/1.35 tff(1712,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c3_1(a471)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))),
% 1.19/1.35 inference(quant_inst,[status(thm)],[])).
% 1.19/1.35 tff(1713,plain,
% 1.19/1.35 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471))),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 1.19/1.35 tff(1714,plain,
% 1.19/1.35 ((~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471))),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1713, 75, 1485, 29, 220, 219, 1570])).
% 1.19/1.35 tff(1715,plain,
% 1.19/1.35 (~c3_1(a464)),
% 1.19/1.35 inference(unit_resolution,[status(thm)],[1714, 1707, 1706])).
% 1.19/1.35 tff(1716,plain,
% 1.19/1.35 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.19/1.35 inference(bind,[status(th)],[])).
% 1.19/1.35 tff(1717,plain,
% 1.19/1.35 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.35 inference(quant_intro,[status(thm)],[1716])).
% 1.19/1.35 tff(1718,plain,
% 1.19/1.35 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1719,plain,
% 1.19/1.35 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_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))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_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))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.19/1.35 inference(bind,[status(th)],[])).
% 1.19/1.35 tff(1720,plain,
% 1.19/1.35 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.35 inference(quant_intro,[status(thm)],[1719])).
% 1.19/1.35 tff(1721,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.19/1.35 tff(1722,plain,
% 1.19/1.35 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 1.19/1.35 tff(1723,plain,
% 1.19/1.35 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1722, 1718])).
% 1.19/1.35 tff(1724,plain,(
% 1.19/1.35 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.35 inference(skolemize,[status(sab)],[1723])).
% 1.19/1.35 tff(1725,plain,
% 1.19/1.35 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.35 inference(modus_ponens,[status(thm)],[1724, 1717])).
% 1.19/1.35 tff(1726,plain,
% 1.19/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1727,plain,
% 1.19/1.35 (((~ndr1_0) | c2_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a465) | c1_1(a465) | c0_1(a465)) <=> (c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.19/1.35 inference(rewrite,[status(thm)],[])).
% 1.19/1.35 tff(1728,plain,
% 1.19/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a465) | c1_1(a465) | c0_1(a465))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))))),
% 1.19/1.35 inference(monotonicity,[status(thm)],[1727])).
% 1.19/1.35 tff(1729,plain,
% 1.19/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a465) | c1_1(a465) | c0_1(a465))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.19/1.35 inference(transitivity,[status(thm)],[1728, 1726])).
% 1.19/1.35 tff(1730,plain,
% 1.19/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a465) | c1_1(a465) | c0_1(a465))),
% 1.19/1.35 inference(quant_inst,[status(thm)],[])).
% 1.19/1.36 tff(1731,plain,
% 1.19/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 1.19/1.36 tff(1732,plain,
% 1.19/1.36 (c3_1(a464) | (~c1_1(a464))),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1731, 75, 1686, 243, 242, 220, 219, 1725])).
% 1.19/1.36 tff(1733,plain,
% 1.19/1.36 (~c1_1(a464)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1732, 1715])).
% 1.19/1.36 tff(1734,plain,
% 1.19/1.36 (~hskp2),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[602, 1715])).
% 1.19/1.36 tff(1735,plain,
% 1.19/1.36 (hskp1),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1042, 1734, 220, 1733])).
% 1.19/1.36 tff(1736,plain,
% 1.19/1.36 (~c3_1(a463)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1048, 1735])).
% 1.19/1.36 tff(1737,plain,
% 1.19/1.36 (~c1_1(a463)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1054, 1735])).
% 1.19/1.36 tff(1738,plain,
% 1.19/1.36 (c2_1(a463)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1062, 1735])).
% 1.19/1.36 tff(1739,plain,
% 1.19/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1740,plain,
% 1.19/1.36 (((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a483) | c0_1(a483) | (~c1_1(a483))) <=> (c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1741,plain,
% 1.19/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a483) | c0_1(a483) | (~c1_1(a483)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483))))),
% 1.19/1.36 inference(monotonicity,[status(thm)],[1740])).
% 1.19/1.36 tff(1742,plain,
% 1.19/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a483) | c0_1(a483) | (~c1_1(a483)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483)))),
% 1.19/1.36 inference(transitivity,[status(thm)],[1741, 1739])).
% 1.19/1.36 tff(1743,plain,
% 1.19/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a483) | c0_1(a483) | (~c1_1(a483)))),
% 1.19/1.36 inference(quant_inst,[status(thm)],[])).
% 1.19/1.36 tff(1744,plain,
% 1.19/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 1.19/1.36 tff(1745,plain,
% 1.19/1.36 ($false),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1744, 75, 1695, 1698, 1738, 1693, 29, 1737, 1736, 454, 1706, 1696])).
% 1.19/1.36 tff(1746,plain,(c0_1(a464) | c2_1(a471) | c2_1(a464) | c0_1(a465) | c1_1(a465) | hskp10 | hskp16 | hskp12 | (~c0_1(a529)) | (~c3_1(a529)) | (~c1_1(a529))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.36 tff(1747,plain,
% 1.19/1.36 (c0_1(a464)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1746, 243, 219, 29, 242, 1485, 104, 21, 1540, 1539, 1538])).
% 1.19/1.36 tff(1748,plain,
% 1.19/1.36 (~hskp2),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1285, 1747])).
% 1.19/1.36 tff(1749,plain,
% 1.19/1.36 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.19/1.36 inference(bind,[status(th)],[])).
% 1.19/1.36 tff(1750,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(quant_intro,[status(thm)],[1749])).
% 1.19/1.36 tff(1751,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1752,plain,
% 1.19/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~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)) | hskp2) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~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)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.19/1.36 inference(bind,[status(th)],[])).
% 1.19/1.36 tff(1753,plain,
% 1.19/1.36 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(quant_intro,[status(thm)],[1752])).
% 1.19/1.36 tff(1754,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)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.19/1.36 tff(1755,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 1.19/1.36 tff(1756,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1755, 1751])).
% 1.19/1.36 tff(1757,plain,(
% 1.19/1.36 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(skolemize,[status(sab)],[1756])).
% 1.19/1.36 tff(1758,plain,
% 1.19/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1757, 1750])).
% 1.19/1.36 tff(1759,assumption,(hskp5), introduced(assumption)).
% 1.19/1.36 tff(1760,plain,
% 1.19/1.36 (~c3_1(a467)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1091, 1759])).
% 1.19/1.36 tff(1761,plain,
% 1.19/1.36 (~c1_1(a467)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[989, 1759])).
% 1.19/1.36 tff(1762,plain,
% 1.19/1.36 (c0_1(a467)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[548, 1759])).
% 1.19/1.36 tff(1763,plain,
% 1.19/1.36 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1764,plain,
% 1.19/1.36 ((hskp2 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467))) <=> (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1765,plain,
% 1.19/1.36 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467))))),
% 1.19/1.36 inference(monotonicity,[status(thm)],[1764])).
% 1.19/1.36 tff(1766,plain,
% 1.19/1.36 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)))),
% 1.19/1.36 inference(transitivity,[status(thm)],[1765, 1763])).
% 1.19/1.36 tff(1767,plain,
% 1.19/1.36 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))),
% 1.19/1.36 inference(quant_inst,[status(thm)],[])).
% 1.19/1.36 tff(1768,plain,
% 1.19/1.36 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 1.19/1.36 tff(1769,plain,
% 1.19/1.36 ($false),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1768, 75, 1295, 1540, 1538, 1539, 1762, 1761, 1760, 1758])).
% 1.19/1.36 tff(1770,plain,((~hskp5) | hskp2 | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.36 tff(1771,plain,
% 1.19/1.36 (~hskp5),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1770, 1748, 1540, 1538, 1539])).
% 1.19/1.36 tff(1772,plain,
% 1.19/1.36 (~c3_1(a465)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1366, 1771, 243, 242, 1748, 21])).
% 1.19/1.36 tff(1773,plain,
% 1.19/1.36 (~hskp3),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[403, 1772])).
% 1.19/1.36 tff(1774,plain,
% 1.19/1.36 (hskp29),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[415, 1773, 21])).
% 1.19/1.36 tff(1775,plain,
% 1.19/1.36 (c2_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[310, 1774])).
% 1.19/1.36 tff(1776,plain,
% 1.19/1.36 (c1_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[318, 1774])).
% 1.19/1.36 tff(1777,plain,
% 1.19/1.36 (c0_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[326, 1774])).
% 1.19/1.36 tff(1778,plain,
% 1.19/1.36 (hskp14),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1495, 75, 1485, 1777, 1776, 1775, 1480])).
% 1.19/1.36 tff(1779,plain,
% 1.19/1.36 (~c0_1(a483)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1501, 1778])).
% 1.19/1.36 tff(1780,plain,
% 1.19/1.36 (c2_1(a483)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1509, 1778])).
% 1.19/1.36 tff(1781,plain,
% 1.19/1.36 (c1_1(a483)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1517, 1778])).
% 1.19/1.36 tff(1782,plain,
% 1.19/1.36 (~c3_1(a483)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1524, 75, 104, 1781, 1780, 1779, 207])).
% 1.19/1.36 tff(1783,plain,
% 1.19/1.36 (hskp7),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1531, 75, 104, 1780, 1779, 20, 1782])).
% 1.19/1.36 tff(1784,plain,
% 1.19/1.36 (c0_1(a471)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[499, 1783])).
% 1.19/1.36 tff(1785,plain,
% 1.19/1.36 (c1_1(a471) | (~c0_1(a471))),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1704, 75, 1781, 1780, 1779, 29, 369])).
% 1.19/1.36 tff(1786,plain,
% 1.19/1.36 (c1_1(a471)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1785, 1784])).
% 1.19/1.36 tff(1787,plain,
% 1.19/1.36 ((hskp23 | hskp5 | hskp3) <=> (hskp23 | hskp5 | hskp3)),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1788,plain,
% 1.19/1.36 (((hskp5 | hskp3) | hskp23) <=> (hskp23 | hskp5 | hskp3)),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1789,plain,
% 1.19/1.36 ((hskp5 | hskp3) <=> (hskp5 | hskp3)),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1790,plain,
% 1.19/1.36 (((hskp5 | hskp3) | hskp23) <=> ((hskp5 | hskp3) | hskp23)),
% 1.19/1.36 inference(monotonicity,[status(thm)],[1789])).
% 1.19/1.36 tff(1791,plain,
% 1.19/1.36 (((hskp5 | hskp3) | hskp23) <=> (hskp23 | hskp5 | hskp3)),
% 1.19/1.36 inference(transitivity,[status(thm)],[1790, 1788])).
% 1.19/1.36 tff(1792,axiom,((hskp5 | hskp3) | hskp23), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.19/1.36 tff(1793,plain,
% 1.19/1.36 (hskp23 | hskp5 | hskp3),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 1.19/1.36 tff(1794,plain,
% 1.19/1.36 (hskp23 | hskp5 | hskp3),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1793, 1787])).
% 1.19/1.36 tff(1795,plain,
% 1.19/1.36 (hskp23 | hskp5 | hskp3),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1794, 1787])).
% 1.19/1.36 tff(1796,plain,
% 1.19/1.36 (hskp23 | hskp5 | hskp3),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1795, 1787])).
% 1.19/1.36 tff(1797,plain,
% 1.19/1.36 (hskp23 | hskp5 | hskp3),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1796, 1787])).
% 1.19/1.36 tff(1798,plain,
% 1.19/1.36 (hskp23),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1797, 1773, 1771])).
% 1.19/1.36 tff(1799,plain,
% 1.19/1.36 (((~hskp23) | (~c3_1(a521))) <=> ((~hskp23) | (~c3_1(a521)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1800,plain,
% 1.19/1.36 (((~c3_1(a521)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a521)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1801,axiom,((~c3_1(a521)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.19/1.36 tff(1802,plain,
% 1.19/1.36 ((~hskp23) | (~c3_1(a521))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 1.19/1.36 tff(1803,plain,
% 1.19/1.36 ((~hskp23) | (~c3_1(a521))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1802, 1799])).
% 1.19/1.36 tff(1804,plain,
% 1.19/1.36 (~c3_1(a521)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1803, 1798])).
% 1.19/1.36 tff(1805,plain,
% 1.19/1.36 (((~hskp23) | (~c2_1(a521))) <=> ((~hskp23) | (~c2_1(a521)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1806,plain,
% 1.19/1.36 (((~c2_1(a521)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a521)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1807,axiom,((~c2_1(a521)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.19/1.36 tff(1808,plain,
% 1.19/1.36 ((~hskp23) | (~c2_1(a521))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 1.19/1.36 tff(1809,plain,
% 1.19/1.36 ((~hskp23) | (~c2_1(a521))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1808, 1805])).
% 1.19/1.36 tff(1810,plain,
% 1.19/1.36 (~c2_1(a521)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1809, 1798])).
% 1.19/1.36 tff(1811,plain,
% 1.19/1.36 (((~hskp23) | (~c0_1(a521))) <=> ((~hskp23) | (~c0_1(a521)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1812,plain,
% 1.19/1.36 (((~c0_1(a521)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a521)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1813,axiom,((~c0_1(a521)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.19/1.36 tff(1814,plain,
% 1.19/1.36 ((~hskp23) | (~c0_1(a521))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 1.19/1.36 tff(1815,plain,
% 1.19/1.36 ((~hskp23) | (~c0_1(a521))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1814, 1811])).
% 1.19/1.36 tff(1816,plain,
% 1.19/1.36 (~c0_1(a521)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1815, 1798])).
% 1.19/1.36 tff(1817,plain,
% 1.19/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1818,plain,
% 1.19/1.36 (((~ndr1_0) | c0_1(a521) | c3_1(a521) | (~c1_1(a521)) | c0_1(a521) | c2_1(a521) | (~c1_1(a521)) | c3_1(a521) | c0_1(a521) | c2_1(a521)) <=> (c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1819,plain,
% 1.19/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a521) | c3_1(a521) | (~c1_1(a521)) | c0_1(a521) | c2_1(a521) | (~c1_1(a521)) | c3_1(a521) | c0_1(a521) | c2_1(a521))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521))))),
% 1.19/1.36 inference(monotonicity,[status(thm)],[1818])).
% 1.19/1.36 tff(1820,plain,
% 1.19/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a521) | c3_1(a521) | (~c1_1(a521)) | c0_1(a521) | c2_1(a521) | (~c1_1(a521)) | c3_1(a521) | c0_1(a521) | c2_1(a521))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521)))),
% 1.19/1.36 inference(transitivity,[status(thm)],[1819, 1817])).
% 1.19/1.36 tff(1821,plain,
% 1.19/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a521) | c3_1(a521) | (~c1_1(a521)) | c0_1(a521) | c2_1(a521) | (~c1_1(a521)) | c3_1(a521) | c0_1(a521) | c2_1(a521))),
% 1.19/1.36 inference(quant_inst,[status(thm)],[])).
% 1.19/1.36 tff(1822,plain,
% 1.19/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1821, 1820])).
% 1.19/1.36 tff(1823,plain,
% 1.19/1.36 (~c1_1(a521)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1822, 75, 1816, 1810, 1804, 10])).
% 1.19/1.36 tff(1824,plain,
% 1.19/1.36 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1825,plain,
% 1.19/1.36 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a521) | c1_1(a521) | c0_1(a521)) <=> (hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1826,plain,
% 1.19/1.36 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a521) | c1_1(a521) | c0_1(a521))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521)))),
% 1.19/1.36 inference(monotonicity,[status(thm)],[1825])).
% 1.19/1.36 tff(1827,plain,
% 1.19/1.36 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a521) | c1_1(a521) | c0_1(a521))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521))),
% 1.19/1.36 inference(transitivity,[status(thm)],[1826, 1824])).
% 1.19/1.36 tff(1828,plain,
% 1.19/1.36 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a521) | c1_1(a521) | c0_1(a521))),
% 1.19/1.36 inference(quant_inst,[status(thm)],[])).
% 1.19/1.36 tff(1829,plain,
% 1.19/1.36 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521)),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 1.19/1.36 tff(1830,plain,
% 1.19/1.36 (hskp1),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1829, 75, 1748, 1816, 1810, 1035, 1823])).
% 1.19/1.36 tff(1831,plain,
% 1.19/1.36 (~c3_1(a463)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1048, 1830])).
% 1.19/1.36 tff(1832,plain,
% 1.19/1.36 (~c1_1(a463)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1054, 1830])).
% 1.19/1.36 tff(1833,plain,
% 1.19/1.36 (c2_1(a463)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1062, 1830])).
% 1.19/1.36 tff(1834,plain,
% 1.19/1.36 ($false),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1744, 75, 1781, 1784, 1833, 1779, 29, 1832, 1831, 454, 1786, 1782])).
% 1.19/1.36 tff(1835,plain,(c0_1(a465) | c2_1(a471) | hskp16 | hskp10 | hskp12 | c1_1(a465) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529)) | c2_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.36 tff(1836,plain,
% 1.19/1.36 (c2_1(a464)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1835, 1537, 104, 1485, 21, 242, 1484, 1483, 1482, 29])).
% 1.19/1.36 tff(1837,plain,
% 1.19/1.36 (~hskp2),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1418, 1836])).
% 1.19/1.36 tff(1838,plain,
% 1.19/1.36 (~hskp5),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1770, 1837, 1484, 1483, 1482])).
% 1.19/1.36 tff(1839,plain,
% 1.19/1.36 (~c3_1(a465)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1366, 1838, 1537, 242, 1837, 21])).
% 1.19/1.36 tff(1840,plain,
% 1.19/1.36 (~hskp3),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[403, 1839])).
% 1.19/1.36 tff(1841,plain,
% 1.19/1.36 (hskp29),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[415, 1840, 21])).
% 1.19/1.36 tff(1842,plain,
% 1.19/1.36 (c2_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[310, 1841])).
% 1.19/1.36 tff(1843,plain,
% 1.19/1.36 (c1_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[318, 1841])).
% 1.19/1.36 tff(1844,plain,
% 1.19/1.36 (c0_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[326, 1841])).
% 1.19/1.36 tff(1845,plain,
% 1.19/1.36 (hskp14),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1495, 75, 1485, 1844, 1843, 1842, 1480])).
% 1.19/1.36 tff(1846,plain,
% 1.19/1.36 (~c0_1(a483)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1501, 1845])).
% 1.19/1.36 tff(1847,plain,
% 1.19/1.36 (c2_1(a483)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1509, 1845])).
% 1.19/1.36 tff(1848,plain,
% 1.19/1.36 (c1_1(a483)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1517, 1845])).
% 1.19/1.36 tff(1849,plain,
% 1.19/1.36 (~c3_1(a483)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1524, 75, 104, 1848, 1847, 1846, 207])).
% 1.19/1.36 tff(1850,plain,
% 1.19/1.36 (hskp7),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1531, 75, 104, 1847, 1846, 20, 1849])).
% 1.19/1.36 tff(1851,plain,
% 1.19/1.36 (c0_1(a471)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[499, 1850])).
% 1.19/1.36 tff(1852,plain,
% 1.19/1.36 (c1_1(a471) | (~c0_1(a471))),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1704, 75, 1848, 1847, 1846, 29, 369])).
% 1.19/1.36 tff(1853,plain,
% 1.19/1.36 (c1_1(a471)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1852, 1851])).
% 1.19/1.36 tff(1854,plain,
% 1.19/1.36 (hskp23),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1797, 1840, 1838])).
% 1.19/1.36 tff(1855,plain,
% 1.19/1.36 (~c3_1(a521)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1803, 1854])).
% 1.19/1.36 tff(1856,plain,
% 1.19/1.36 (~c2_1(a521)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1809, 1854])).
% 1.19/1.36 tff(1857,plain,
% 1.19/1.36 (~c0_1(a521)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1815, 1854])).
% 1.19/1.36 tff(1858,plain,
% 1.19/1.36 (~c1_1(a521)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1822, 75, 1857, 1856, 1855, 10])).
% 1.19/1.36 tff(1859,plain,
% 1.19/1.36 (hskp1),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1829, 75, 1837, 1857, 1856, 1035, 1858])).
% 1.19/1.36 tff(1860,plain,
% 1.19/1.36 (~c3_1(a463)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1048, 1859])).
% 1.19/1.36 tff(1861,plain,
% 1.19/1.36 (~c1_1(a463)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1054, 1859])).
% 1.19/1.36 tff(1862,plain,
% 1.19/1.36 (c2_1(a463)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1062, 1859])).
% 1.19/1.36 tff(1863,plain,
% 1.19/1.36 ($false),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1744, 75, 1848, 1851, 1862, 1846, 29, 1861, 1860, 454, 1853, 1849])).
% 1.19/1.36 tff(1864,plain,(hskp10 | c2_1(a471) | hskp16 | hskp12 | c1_1(a465) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.19/1.36 tff(1865,plain,
% 1.19/1.36 (hskp10),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1864, 242, 104, 21, 29, 217])).
% 1.19/1.36 tff(1866,plain,
% 1.19/1.36 (~c3_1(a478)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[226, 1865])).
% 1.19/1.36 tff(1867,plain,
% 1.19/1.36 (~c0_1(a478)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[232, 1865])).
% 1.19/1.36 tff(1868,plain,
% 1.19/1.36 (c2_1(a478)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[240, 1865])).
% 1.19/1.36 tff(1869,plain,
% 1.19/1.36 (hskp7),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[476, 75, 104, 1868, 1867, 1866, 20])).
% 1.19/1.36 tff(1870,plain,
% 1.19/1.36 (c0_1(a471)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[499, 1869])).
% 1.19/1.36 tff(1871,plain,
% 1.19/1.36 (c3_1(a471)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[491, 1869])).
% 1.19/1.36 tff(1872,plain,
% 1.19/1.36 (~c0_1(a465)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1196, 1871, 217, 21, 242, 1870, 29])).
% 1.19/1.36 tff(1873,plain,
% 1.19/1.36 (~hskp5),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1770, 1295, 1540, 1538, 1539])).
% 1.19/1.36 tff(1874,plain,
% 1.19/1.36 (hskp17),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[683, 1873, 501, 502])).
% 1.19/1.36 tff(1875,plain,
% 1.19/1.36 (~c0_1(a493)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[697, 1874])).
% 1.19/1.36 tff(1876,plain,
% 1.19/1.36 (c3_1(a493)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[705, 1874])).
% 1.19/1.36 tff(1877,plain,
% 1.19/1.36 (c2_1(a493)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[691, 1874])).
% 1.19/1.36 tff(1878,plain,
% 1.19/1.36 (~c3_1(a465)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1366, 1873, 243, 242, 1295, 21])).
% 1.19/1.36 tff(1879,plain,
% 1.19/1.36 (~hskp3),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[403, 1878])).
% 1.19/1.36 tff(1880,plain,
% 1.19/1.36 (hskp29),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[415, 1879, 21])).
% 1.19/1.36 tff(1881,plain,
% 1.19/1.36 (c2_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[310, 1880])).
% 1.19/1.36 tff(1882,plain,
% 1.19/1.36 (c1_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[318, 1880])).
% 1.19/1.36 tff(1883,plain,
% 1.19/1.36 (c0_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[326, 1880])).
% 1.19/1.36 tff(1884,plain,
% 1.19/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1885,plain,
% 1.19/1.36 (((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493))) <=> (c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1886,plain,
% 1.19/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.19/1.36 inference(monotonicity,[status(thm)],[1885])).
% 1.19/1.36 tff(1887,plain,
% 1.19/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.36 inference(transitivity,[status(thm)],[1886, 1884])).
% 1.19/1.36 tff(1888,plain,
% 1.19/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.19/1.36 inference(quant_inst,[status(thm)],[])).
% 1.19/1.36 tff(1889,plain,
% 1.19/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1888, 1887])).
% 1.19/1.36 tff(1890,plain,
% 1.19/1.36 ($false),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1889, 75, 1540, 1538, 1539, 1883, 1882, 1881, 1877, 1876, 1875, 844])).
% 1.19/1.36 tff(1891,plain,(hskp2 | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529)) | hskp12 | (~c0_1(a471)) | (~c3_1(a471)) | c2_1(a471) | c0_1(a465) | c1_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.36 tff(1892,plain,
% 1.19/1.36 (hskp2),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1891, 1870, 1483, 1482, 21, 1484, 1871, 29, 1872, 242])).
% 1.19/1.36 tff(1893,plain,
% 1.19/1.36 (~c0_1(a464)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1285, 1892])).
% 1.19/1.36 tff(1894,plain,
% 1.19/1.36 (~c2_1(a464)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1418, 1892])).
% 1.19/1.36 tff(1895,plain,
% 1.19/1.36 ($false),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1130, 1894, 1893, 242, 1868, 1872, 1867, 1866, 217])).
% 1.19/1.36 tff(1896,plain,(c1_1(a465) | hskp19 | hskp12 | c2_1(a471) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.19/1.36 tff(1897,plain,
% 1.19/1.36 (c1_1(a465)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1896, 216, 21, 29, 104])).
% 1.19/1.36 tff(1898,plain,
% 1.19/1.36 (~hskp3),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1230, 1897])).
% 1.19/1.36 tff(1899,plain,
% 1.19/1.36 (hskp29),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[415, 1898, 21])).
% 1.19/1.36 tff(1900,plain,
% 1.19/1.36 (c2_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[310, 1899])).
% 1.19/1.36 tff(1901,plain,
% 1.19/1.36 (c1_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[318, 1899])).
% 1.19/1.36 tff(1902,plain,
% 1.19/1.36 (c0_1(a474)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[326, 1899])).
% 1.19/1.36 tff(1903,assumption,(hskp17), introduced(assumption)).
% 1.19/1.36 tff(1904,plain,
% 1.19/1.36 (~c0_1(a493)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[697, 1903])).
% 1.19/1.36 tff(1905,plain,
% 1.19/1.36 (c3_1(a493)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[705, 1903])).
% 1.19/1.36 tff(1906,plain,
% 1.19/1.36 (c2_1(a493)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[691, 1903])).
% 1.19/1.36 tff(1907,assumption,(c2_1(a474)), introduced(assumption)).
% 1.19/1.36 tff(1908,assumption,(c1_1(a474)), introduced(assumption)).
% 1.19/1.36 tff(1909,assumption,(c0_1(a474)), introduced(assumption)).
% 1.19/1.36 tff(1910,plain,
% 1.19/1.36 ($false),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1889, 75, 1540, 1538, 1539, 1909, 1908, 1907, 1906, 1905, 1904, 844])).
% 1.19/1.36 tff(1911,plain,((~hskp17) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.36 tff(1912,plain,
% 1.19/1.36 (~hskp17),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1911, 1454, 1470, 1462, 1902, 1901, 1900])).
% 1.19/1.36 tff(1913,plain,
% 1.19/1.36 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1914,plain,
% 1.19/1.36 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529))) <=> (hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1915,plain,
% 1.19/1.36 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529))))),
% 1.19/1.36 inference(monotonicity,[status(thm)],[1914])).
% 1.19/1.36 tff(1916,plain,
% 1.19/1.36 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)))),
% 1.19/1.36 inference(transitivity,[status(thm)],[1915, 1913])).
% 1.19/1.36 tff(1917,plain,
% 1.19/1.36 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)))),
% 1.19/1.36 inference(quant_inst,[status(thm)],[])).
% 1.19/1.36 tff(1918,plain,
% 1.19/1.36 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529))),
% 1.19/1.36 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 1.19/1.36 tff(1919,plain,
% 1.19/1.36 (hskp17 | hskp5 | c2_1(a529)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1918, 75, 1540, 1539, 676])).
% 1.19/1.36 tff(1920,plain,
% 1.19/1.36 (c2_1(a529)),
% 1.19/1.36 inference(unit_resolution,[status(thm)],[1919, 31, 936])).
% 1.19/1.36 tff(1921,plain,
% 1.19/1.36 (^[U: $i] : refl((hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 1.19/1.36 inference(bind,[status(th)],[])).
% 1.19/1.36 tff(1922,plain,
% 1.19/1.36 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.36 inference(quant_intro,[status(thm)],[1921])).
% 1.19/1.36 tff(1923,plain,
% 1.19/1.36 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.36 inference(rewrite,[status(thm)],[])).
% 1.19/1.36 tff(1924,plain,
% 1.19/1.36 (^[U: $i] : 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)) | hskp8) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp17) <=> ((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp17))), rewrite(((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp17) <=> (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.19/1.37 inference(bind,[status(th)],[])).
% 1.19/1.37 tff(1925,plain,
% 1.19/1.37 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp17) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.37 inference(quant_intro,[status(thm)],[1924])).
% 1.19/1.37 tff(1926,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.19/1.37 tff(1927,plain,
% 1.19/1.37 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 1.19/1.37 tff(1928,plain,
% 1.19/1.37 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[1927, 1923])).
% 1.19/1.37 tff(1929,plain,(
% 1.19/1.37 ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.37 inference(skolemize,[status(sab)],[1928])).
% 1.19/1.37 tff(1930,plain,
% 1.19/1.37 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[1929, 1922])).
% 1.19/1.37 tff(1931,plain,
% 1.19/1.37 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1932,plain,
% 1.19/1.37 ((hskp17 | hskp8 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529))) <=> (hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1933,plain,
% 1.19/1.37 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[1932])).
% 1.19/1.37 tff(1934,plain,
% 1.19/1.37 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[1933, 1931])).
% 1.19/1.37 tff(1935,plain,
% 1.19/1.37 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(1936,plain,
% 1.19/1.37 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 1.19/1.37 tff(1937,plain,
% 1.19/1.37 (hskp17 | hskp8 | (~c2_1(a529))),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1936, 75, 1538, 1539, 1930])).
% 1.19/1.37 tff(1938,plain,
% 1.19/1.37 (hskp8),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1937, 1920, 936])).
% 1.19/1.37 tff(1939,plain,
% 1.19/1.37 (~c2_1(a472)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1595, 1938])).
% 1.19/1.37 tff(1940,plain,
% 1.19/1.37 (c3_1(a472)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1603, 1938])).
% 1.19/1.37 tff(1941,plain,
% 1.19/1.37 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1942,plain,
% 1.19/1.37 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a472) | (~c3_1(a472)) | (~c0_1(a472))) <=> (hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1943,plain,
% 1.19/1.37 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a472) | (~c3_1(a472)) | (~c0_1(a472)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[1942])).
% 1.19/1.37 tff(1944,plain,
% 1.19/1.37 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a472) | (~c3_1(a472)) | (~c0_1(a472)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[1943, 1941])).
% 1.19/1.37 tff(1945,plain,
% 1.19/1.37 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a472) | (~c3_1(a472)) | (~c0_1(a472)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(1946,plain,
% 1.19/1.37 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[1945, 1944])).
% 1.19/1.37 tff(1947,plain,
% 1.19/1.37 (~c0_1(a472)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1946, 75, 936, 31, 1940, 1939, 676])).
% 1.19/1.37 tff(1948,plain,
% 1.19/1.37 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1949,plain,
% 1.19/1.37 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a472) | c0_1(a472) | (~c3_1(a472))) <=> (hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1950,plain,
% 1.19/1.37 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a472) | c0_1(a472) | (~c3_1(a472)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[1949])).
% 1.19/1.37 tff(1951,plain,
% 1.19/1.37 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a472) | c0_1(a472) | (~c3_1(a472)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[1950, 1948])).
% 1.19/1.37 tff(1952,plain,
% 1.19/1.37 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a472) | c0_1(a472) | (~c3_1(a472)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(1953,plain,
% 1.19/1.37 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 1.19/1.37 tff(1954,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1953, 75, 21, 31, 1940, 1939, 41, 1947])).
% 1.19/1.37 tff(1955,plain,(hskp5 | hskp12 | hskp17 | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(1956,plain,
% 1.19/1.37 (hskp5),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1955, 1912, 21, 1470, 1462, 1454])).
% 1.19/1.37 tff(1957,plain,
% 1.19/1.37 (c0_1(a467)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[548, 1956])).
% 1.19/1.37 tff(1958,plain,
% 1.19/1.37 (~c1_1(a467)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[989, 1956])).
% 1.19/1.37 tff(1959,assumption,(hskp31), introduced(assumption)).
% 1.19/1.37 tff(1960,plain,
% 1.19/1.37 (c3_1(a529)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1461, 1959])).
% 1.19/1.37 tff(1961,plain,
% 1.19/1.37 (c0_1(a529)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1453, 1959])).
% 1.19/1.37 tff(1962,plain,
% 1.19/1.37 (c1_1(a529)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1469, 1959])).
% 1.19/1.37 tff(1963,plain,
% 1.19/1.37 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1964,plain,
% 1.19/1.37 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | c0_1(a471)) <=> (hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1965,plain,
% 1.19/1.37 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | c0_1(a471))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471)))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[1964])).
% 1.19/1.37 tff(1966,plain,
% 1.19/1.37 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | c0_1(a471))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471))),
% 1.19/1.37 inference(transitivity,[status(thm)],[1965, 1963])).
% 1.19/1.37 tff(1967,plain,
% 1.19/1.37 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | c0_1(a471))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(1968,plain,
% 1.19/1.37 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471)),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 1.19/1.37 tff(1969,plain,
% 1.19/1.37 (hskp2 | hskp1 | c0_1(a471) | c1_1(a471)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1968, 75, 29, 1035])).
% 1.19/1.37 tff(1970,plain,
% 1.19/1.37 (hskp1),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1969, 1626, 1295, 30])).
% 1.19/1.37 tff(1971,plain,
% 1.19/1.37 (~c3_1(a463)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1048, 1970])).
% 1.19/1.37 tff(1972,plain,
% 1.19/1.37 (~c1_1(a463)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1054, 1970])).
% 1.19/1.37 tff(1973,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1974,plain,
% 1.19/1.37 ((hskp16 | (~ndr1_0) | c1_1(a463) | c3_1(a463) | (~c0_1(a463)) | c3_1(a471) | c1_1(a471) | c2_1(a471)) <=> (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1975,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a463) | c3_1(a463) | (~c0_1(a463)) | c3_1(a471) | c1_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471)))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[1974])).
% 1.19/1.37 tff(1976,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a463) | c3_1(a463) | (~c0_1(a463)) | c3_1(a471) | c1_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471))),
% 1.19/1.37 inference(transitivity,[status(thm)],[1975, 1973])).
% 1.19/1.37 tff(1977,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a463) | c3_1(a463) | (~c0_1(a463)) | c3_1(a471) | c1_1(a471) | c2_1(a471))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(1978,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471)),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 1.19/1.37 tff(1979,plain,
% 1.19/1.37 (~c0_1(a463)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1978, 75, 104, 1572, 29, 1972, 1971, 513, 1626])).
% 1.19/1.37 tff(1980,plain,
% 1.19/1.37 (c2_1(a463)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1062, 1970])).
% 1.19/1.37 tff(1981,plain,
% 1.19/1.37 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1982,plain,
% 1.19/1.37 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a463) | c3_1(a463) | (~c2_1(a463))) <=> (hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(1983,plain,
% 1.19/1.37 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a463) | c3_1(a463) | (~c2_1(a463)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[1982])).
% 1.19/1.37 tff(1984,plain,
% 1.19/1.37 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a463) | c3_1(a463) | (~c2_1(a463)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[1983, 1981])).
% 1.19/1.37 tff(1985,plain,
% 1.19/1.37 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a463) | c3_1(a463) | (~c2_1(a463)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(1986,plain,
% 1.19/1.37 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[1985, 1984])).
% 1.19/1.37 tff(1987,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1986, 75, 104, 1571, 1980, 1971, 20, 1979])).
% 1.19/1.37 tff(1988,plain,(c3_1(a471) | hskp16 | c2_1(a471) | hskp2 | c0_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(1989,plain,
% 1.19/1.37 (c3_1(a471)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1988, 1295, 29, 30, 104])).
% 1.19/1.37 tff(1990,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[82, 1989, 1873, 30])).
% 1.19/1.37 tff(1991,plain,(hskp2 | c0_1(a471) | hskp12 | c2_1(a471) | hskp16 | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(1992,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1991, 1962, 1961, 21, 29, 104, 30, 1295, 1960])).
% 1.19/1.37 tff(1993,plain,((~hskp31) | hskp12 | c2_1(a471) | hskp16 | c0_1(a471) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(1994,plain,
% 1.19/1.37 (hskp2),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1993, 30, 29, 104, 1446, 21])).
% 1.19/1.37 tff(1995,plain,
% 1.19/1.37 (~c2_1(a464)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1418, 1994])).
% 1.19/1.37 tff(1996,plain,
% 1.19/1.37 (~c0_1(a464)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1285, 1994])).
% 1.19/1.37 tff(1997,plain,
% 1.19/1.37 (c3_1(a464)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[602, 1994])).
% 1.19/1.37 tff(1998,plain,
% 1.19/1.37 (hskp5),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[573, 75, 21, 1997, 1996, 1995, 41])).
% 1.19/1.37 tff(1999,plain,
% 1.19/1.37 (~c3_1(a467)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1091, 1998])).
% 1.19/1.37 tff(2000,plain,
% 1.19/1.37 (~c1_1(a467)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[989, 1998])).
% 1.19/1.37 tff(2001,plain,
% 1.19/1.37 (c0_1(a467)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[548, 1998])).
% 1.19/1.37 tff(2002,plain,
% 1.19/1.37 (c2_1(a467)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[519, 75, 104, 2001, 2000, 1999, 513])).
% 1.19/1.37 tff(2003,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(2004,plain,
% 1.19/1.37 ((hskp7 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c2_1(a474)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(2005,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c2_1(a474)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[2004])).
% 1.19/1.37 tff(2006,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c2_1(a474)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[2005, 2003])).
% 1.19/1.37 tff(2007,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c2_1(a474)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(2008,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 1.19/1.37 tff(2009,plain,
% 1.19/1.37 (~c3_1(a474)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[2008, 75, 1571, 1901, 1900, 2001, 1999, 1560, 2002])).
% 1.19/1.37 tff(2010,assumption,(c2_1(a467)), introduced(assumption)).
% 1.19/1.37 tff(2011,assumption,(hskp30), introduced(assumption)).
% 1.19/1.37 tff(2012,plain,
% 1.19/1.37 (c3_1(a488)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[173, 2011])).
% 1.19/1.37 tff(2013,plain,
% 1.19/1.37 (c2_1(a488)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[181, 2011])).
% 1.19/1.37 tff(2014,plain,
% 1.19/1.37 (c1_1(a488)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[189, 2011])).
% 1.19/1.37 tff(2015,assumption,(~hskp7), introduced(assumption)).
% 1.19/1.37 tff(2016,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(2017,plain,
% 1.19/1.37 ((hskp7 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(2018,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[2017])).
% 1.19/1.37 tff(2019,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[2018, 2016])).
% 1.19/1.37 tff(2020,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(2021,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 1.19/1.37 tff(2022,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[2021, 75, 2015, 2014, 2013, 2012, 503, 247, 1560, 2010])).
% 1.19/1.37 tff(2023,plain,((~hskp30) | hskp7 | (~c0_1(a467)) | c3_1(a467) | (~c2_1(a467))), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(2024,plain,
% 1.19/1.37 (~hskp30),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[2023, 2002, 2001, 1999, 1571])).
% 1.19/1.37 tff(2025,plain,
% 1.19/1.37 (hskp30 | c3_1(a474)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1249, 75, 21, 1902, 1901, 158])).
% 1.19/1.37 tff(2026,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[2025, 2024, 2009])).
% 1.19/1.37 tff(2027,plain,(c0_1(a471) | hskp12 | hskp16 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(2028,plain,
% 1.19/1.37 (c0_1(a471)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[2027, 104, 21, 29])).
% 1.19/1.37 tff(2029,plain,
% 1.19/1.37 (~c3_1(a467)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1091, 1956])).
% 1.19/1.37 tff(2030,plain,
% 1.19/1.37 (~c3_1(a471)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[540, 2029, 21, 2028, 29, 1958, 104, 1957])).
% 1.19/1.37 tff(2031,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(2032,plain,
% 1.19/1.37 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a471) | c2_1(a471) | (~c0_1(a471))) <=> (c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(2033,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a471) | c2_1(a471) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.19/1.37 inference(monotonicity,[status(thm)],[2032])).
% 1.19/1.37 tff(2034,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a471) | c2_1(a471) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.37 inference(transitivity,[status(thm)],[2033, 2031])).
% 1.19/1.37 tff(2035,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a471) | c2_1(a471) | (~c0_1(a471)))),
% 1.19/1.37 inference(quant_inst,[status(thm)],[])).
% 1.19/1.37 tff(2036,plain,
% 1.19/1.37 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.19/1.37 inference(modus_ponens,[status(thm)],[2035, 2034])).
% 1.19/1.37 tff(2037,plain,
% 1.19/1.37 ($false),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[2036, 75, 1902, 1901, 1900, 2028, 2030, 29, 103])).
% 1.19/1.37 tff(2038,plain,(hskp16 | c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.19/1.37 tff(2039,plain,
% 1.19/1.37 (hskp16),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[2038, 29, 21])).
% 1.19/1.37 tff(2040,plain,
% 1.19/1.37 (~c2_1(a487)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[263, 2039])).
% 1.19/1.37 tff(2041,plain,
% 1.19/1.37 (~c1_1(a487)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[27, 2039])).
% 1.19/1.37 tff(2042,plain,
% 1.19/1.37 (hskp5 | c0_1(a472)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1953, 75, 21, 1604, 1596, 41])).
% 1.19/1.37 tff(2043,plain,
% 1.19/1.37 (c0_1(a472)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[2042, 31])).
% 1.19/1.37 tff(2044,plain,
% 1.19/1.37 (hskp17 | hskp5 | (~c0_1(a472))),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[1946, 75, 1604, 1596, 676])).
% 1.19/1.37 tff(2045,plain,
% 1.19/1.37 (hskp17),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[2044, 2043, 31])).
% 1.19/1.37 tff(2046,plain,
% 1.19/1.37 (~c0_1(a493)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[697, 2045])).
% 1.19/1.37 tff(2047,plain,
% 1.19/1.37 (c0_1(a487)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[271, 2039])).
% 1.19/1.37 tff(2048,plain,
% 1.19/1.37 (c3_1(a493)),
% 1.19/1.37 inference(unit_resolution,[status(thm)],[705, 2045])).
% 1.19/1.37 tff(2049,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(2050,plain,
% 1.19/1.37 ((hskp5 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a493) | (~c3_1(a493)) | (~c1_1(a493))) <=> (hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493)))),
% 1.19/1.37 inference(rewrite,[status(thm)],[])).
% 1.19/1.37 tff(2051,plain,
% 1.19/1.37 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a493) | (~c3_1(a493)) | (~c1_1(a493)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[2050])).
% 1.19/1.38 tff(2052,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a493) | (~c3_1(a493)) | (~c1_1(a493)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[2051, 2049])).
% 1.19/1.38 tff(2053,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a493) | (~c3_1(a493)) | (~c1_1(a493)))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(2054,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 1.19/1.38 tff(2055,plain,
% 1.19/1.38 (~c1_1(a493)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2054, 75, 31, 2048, 2047, 2046, 2041, 2040, 93])).
% 1.19/1.38 tff(2056,plain,
% 1.19/1.38 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(2057,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[2056])).
% 1.19/1.38 tff(2058,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2059,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)) | 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)) | 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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp6))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(2060,plain,
% 1.19/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[2059])).
% 1.19/1.38 tff(2061,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.19/1.38 tff(2062,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2061, 2060])).
% 1.19/1.38 tff(2063,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2062, 2058])).
% 1.19/1.38 tff(2064,plain,(
% 1.19/1.38 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.19/1.38 inference(skolemize,[status(sab)],[2063])).
% 1.19/1.38 tff(2065,plain,
% 1.19/1.38 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2064, 2057])).
% 1.19/1.38 tff(2066,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2067,plain,
% 1.19/1.38 ((hskp6 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a471) | c0_1(a471) | c2_1(a471)) <=> (hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2068,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a471) | c0_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[2067])).
% 1.19/1.38 tff(2069,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a471) | c0_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[2068, 2066])).
% 1.19/1.38 tff(2070,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a471) | c0_1(a471) | c2_1(a471))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(2071,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2070, 2069])).
% 1.19/1.38 tff(2072,plain,
% 1.19/1.38 (hskp6 | (~c0_1(a472))),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2071, 75, 1612, 1604, 30, 1572, 29, 2065])).
% 1.19/1.38 tff(2073,plain,
% 1.19/1.38 (hskp6),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2072, 2043])).
% 1.19/1.38 tff(2074,plain,
% 1.19/1.38 (~c2_1(a470)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1307, 2073])).
% 1.19/1.38 tff(2075,plain,
% 1.19/1.38 (~c0_1(a470)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1313, 2073])).
% 1.19/1.38 tff(2076,plain,
% 1.19/1.38 (~c3_1(a470)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1320, 75, 21, 31, 2075, 2074, 41])).
% 1.19/1.38 tff(2077,plain,
% 1.19/1.38 (~c1_1(a470)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1327, 2073])).
% 1.19/1.38 tff(2078,plain,
% 1.19/1.38 (c2_1(a493)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[691, 2045])).
% 1.19/1.38 tff(2079,plain,
% 1.19/1.38 (hskp8),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1589, 83, 30, 1571])).
% 1.19/1.38 tff(2080,plain,
% 1.19/1.38 (~c2_1(a472)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1595, 2079])).
% 1.19/1.38 tff(2081,plain,
% 1.19/1.38 (c3_1(a472)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1603, 2079])).
% 1.19/1.38 tff(2082,plain,
% 1.19/1.38 (c0_1(a472)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1953, 75, 21, 31, 2081, 2080, 41])).
% 1.19/1.38 tff(2083,plain,
% 1.19/1.38 (hskp17 | (~c0_1(a472))),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1946, 75, 31, 2081, 2080, 676])).
% 1.19/1.38 tff(2084,plain,
% 1.19/1.38 (hskp17),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2083, 2082])).
% 1.19/1.38 tff(2085,plain,
% 1.19/1.38 (~c0_1(a493)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[697, 2084])).
% 1.19/1.38 tff(2086,plain,
% 1.19/1.38 (c3_1(a493)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[705, 2084])).
% 1.19/1.38 tff(2087,plain,
% 1.19/1.38 (~c1_1(a493)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2054, 75, 31, 2086, 2047, 2085, 2041, 2040, 93])).
% 1.19/1.38 tff(2088,plain,
% 1.19/1.38 (c1_1(a472)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1611, 2079])).
% 1.19/1.38 tff(2089,plain,
% 1.19/1.38 (hskp6 | (~c0_1(a472))),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2071, 75, 2088, 2081, 30, 83, 29, 2065])).
% 1.19/1.38 tff(2090,plain,
% 1.19/1.38 (hskp6),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2089, 2082])).
% 1.19/1.38 tff(2091,plain,
% 1.19/1.38 (~c2_1(a470)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1307, 2090])).
% 1.19/1.38 tff(2092,plain,
% 1.19/1.38 (~c0_1(a470)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1313, 2090])).
% 1.19/1.38 tff(2093,plain,
% 1.19/1.38 (~c3_1(a470)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1320, 75, 21, 31, 2092, 2091, 41])).
% 1.19/1.38 tff(2094,plain,
% 1.19/1.38 (~c1_1(a470)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1327, 2090])).
% 1.19/1.38 tff(2095,plain,
% 1.19/1.38 (c2_1(a493)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[691, 2084])).
% 1.19/1.38 tff(2096,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2097,plain,
% 1.19/1.38 ((hskp2 | (~ndr1_0) | c1_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a470) | c1_1(a470) | c2_1(a470)) <=> (hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2098,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a470) | c1_1(a470) | c2_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493)))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[2097])).
% 1.19/1.38 tff(2099,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a470) | c1_1(a470) | c2_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493))),
% 1.19/1.38 inference(transitivity,[status(thm)],[2098, 2096])).
% 1.19/1.38 tff(2100,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a470) | c1_1(a470) | c2_1(a470))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(2101,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493)),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 1.19/1.38 tff(2102,plain,
% 1.19/1.38 (hskp2),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2101, 75, 2095, 2086, 2094, 2091, 594, 2093, 2087])).
% 1.19/1.38 tff(2103,plain,
% 1.19/1.38 (c3_1(a464)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[602, 2102])).
% 1.19/1.38 tff(2104,plain,
% 1.19/1.38 (~c0_1(a464)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1285, 2102])).
% 1.19/1.38 tff(2105,plain,
% 1.19/1.38 ($false),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1542, 2104, 2103, 31])).
% 1.19/1.38 tff(2106,plain,(hskp5 | hskp12 | c2_1(a464) | c0_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.38 tff(2107,plain,
% 1.19/1.38 (hskp5),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2106, 219, 21, 30, 29])).
% 1.19/1.38 tff(2108,plain,
% 1.19/1.38 (~c3_1(a467)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[1091, 2107])).
% 1.19/1.38 tff(2109,plain,
% 1.19/1.38 (c0_1(a467)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[548, 2107])).
% 1.19/1.38 tff(2110,plain,
% 1.19/1.38 (~c1_1(a467)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[989, 2107])).
% 1.19/1.38 tff(2111,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2112,plain,
% 1.19/1.38 ((hskp2 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467))) <=> (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2113,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[2112])).
% 1.19/1.38 tff(2114,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[2113, 2111])).
% 1.19/1.38 tff(2115,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(2116,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 1.19/1.38 tff(2117,plain,
% 1.19/1.38 (~c0_1(a472)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2116, 75, 1295, 1612, 1604, 503, 248, 247, 1758])).
% 1.19/1.38 tff(2118,plain,
% 1.19/1.38 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(2119,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[2118])).
% 1.19/1.38 tff(2120,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2121,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((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | 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)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | 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)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.19/1.38 inference(bind,[status(th)],[])).
% 1.19/1.38 tff(2122,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_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)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.38 inference(quant_intro,[status(thm)],[2121])).
% 1.19/1.38 tff(2123,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 1.19/1.38 tff(2124,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 1.19/1.38 tff(2125,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2124, 2120])).
% 1.19/1.38 tff(2126,plain,(
% 1.19/1.38 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.38 inference(skolemize,[status(sab)],[2125])).
% 1.19/1.38 tff(2127,plain,
% 1.19/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2126, 2119])).
% 1.19/1.38 tff(2128,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2129,plain,
% 1.19/1.38 (((~ndr1_0) | c1_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c0_1(a472) | (~c3_1(a472)) | (~c1_1(a472)) | c3_1(a471) | c1_1(a471) | c0_1(a471)) <=> (c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2130,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c0_1(a472) | (~c3_1(a472)) | (~c1_1(a472)) | c3_1(a471) | c1_1(a471) | c0_1(a471))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[2129])).
% 1.19/1.38 tff(2131,plain,
% 1.19/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c0_1(a472) | (~c3_1(a472)) | (~c1_1(a472)) | c3_1(a471) | c1_1(a471) | c0_1(a471))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[2130, 2128])).
% 1.19/1.38 tff(2132,plain,
% 1.19/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c0_1(a472) | (~c3_1(a472)) | (~c1_1(a472)) | c3_1(a471) | c1_1(a471) | c0_1(a471))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(2133,plain,
% 1.19/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2132, 2131])).
% 1.19/1.38 tff(2134,plain,
% 1.19/1.38 (~c3_1(a487)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2133, 75, 351, 1612, 1604, 30, 1572, 350, 2127, 1626, 2117])).
% 1.19/1.38 tff(2135,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2136,plain,
% 1.19/1.38 ((hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a472) | c2_1(a472) | (~c3_1(a472))) <=> (hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)))),
% 1.19/1.38 inference(rewrite,[status(thm)],[])).
% 1.19/1.38 tff(2137,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a472) | c2_1(a472) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487))))),
% 1.19/1.38 inference(monotonicity,[status(thm)],[2136])).
% 1.19/1.38 tff(2138,plain,
% 1.19/1.38 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a472) | c2_1(a472) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)))),
% 1.19/1.38 inference(transitivity,[status(thm)],[2137, 2135])).
% 1.19/1.38 tff(2139,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a472) | c2_1(a472) | (~c3_1(a472)))),
% 1.19/1.38 inference(quant_inst,[status(thm)],[])).
% 1.19/1.38 tff(2140,plain,
% 1.19/1.38 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487))),
% 1.19/1.38 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 1.19/1.38 tff(2141,plain,
% 1.19/1.38 (hskp29),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[2140, 75, 351, 1604, 350, 349, 1596, 348, 2117])).
% 1.19/1.38 tff(2142,plain,
% 1.19/1.38 (c2_1(a474)),
% 1.19/1.38 inference(unit_resolution,[status(thm)],[310, 2141])).
% 1.19/1.38 tff(2143,plain,
% 1.19/1.39 (c1_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[318, 2141])).
% 1.19/1.39 tff(2144,plain,
% 1.19/1.39 (c0_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[326, 2141])).
% 1.19/1.39 tff(2145,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2146,plain,
% 1.19/1.39 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a487) | c2_1(a487) | (~c0_1(a487))) <=> (c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2147,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a487) | c2_1(a487) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[2146])).
% 1.19/1.39 tff(2148,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a487) | c2_1(a487) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[2147, 2145])).
% 1.19/1.39 tff(2149,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a487) | c2_1(a487) | (~c0_1(a487)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(2150,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 1.19/1.39 tff(2151,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2150, 75, 2144, 2143, 2142, 351, 349, 103, 2134])).
% 1.19/1.39 tff(2152,plain,(c3_1(a471) | (~c0_1(a487)) | c2_1(a487) | c1_1(a487) | c0_1(a471) | c2_1(a471) | hskp2 | (~c0_1(a467)) | c1_1(a467) | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2153,plain,
% 1.19/1.39 (c3_1(a471)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2152, 1295, 2040, 2041, 30, 29, 2047, 503, 248, 247])).
% 1.19/1.39 tff(2154,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2155,plain,
% 1.19/1.39 ((hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a471) | c2_1(a471) | (~c3_1(a471))) <=> (hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2156,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a471) | c2_1(a471) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[2155])).
% 1.19/1.39 tff(2157,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a471) | c2_1(a471) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[2156, 2154])).
% 1.19/1.39 tff(2158,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a471) | c2_1(a471) | (~c3_1(a471)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(2159,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 1.19/1.39 tff(2160,plain,
% 1.19/1.39 (hskp29 | (~c3_1(a471))),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2159, 75, 2047, 30, 2041, 2040, 29, 348])).
% 1.19/1.39 tff(2161,plain,
% 1.19/1.39 (hskp29),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2160, 2153])).
% 1.19/1.39 tff(2162,plain,
% 1.19/1.39 (c2_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[310, 2161])).
% 1.19/1.39 tff(2163,plain,
% 1.19/1.39 (c1_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[318, 2161])).
% 1.19/1.39 tff(2164,plain,
% 1.19/1.39 (c0_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[326, 2161])).
% 1.19/1.39 tff(2165,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2166,plain,
% 1.19/1.39 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c2_1(a467) | (~c0_1(a467))) <=> (c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2167,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c2_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[2166])).
% 1.19/1.39 tff(2168,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c2_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[2167, 2165])).
% 1.19/1.39 tff(2169,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c2_1(a467) | (~c0_1(a467)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(2170,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 1.19/1.39 tff(2171,plain,
% 1.19/1.39 (c2_1(a467)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2170, 75, 2164, 2163, 2162, 503, 247, 103])).
% 1.19/1.39 tff(2172,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2173,plain,
% 1.19/1.39 ((hskp2 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467))) <=> (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2174,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[2173])).
% 1.19/1.39 tff(2175,plain,
% 1.19/1.39 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[2174, 2172])).
% 1.19/1.39 tff(2176,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(2177,plain,
% 1.19/1.39 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[2176, 2175])).
% 1.19/1.39 tff(2178,plain,
% 1.19/1.39 (~c3_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2177, 75, 1295, 2164, 2163, 503, 248, 247, 1758])).
% 1.19/1.39 tff(2179,plain,
% 1.19/1.39 (hskp30 | c3_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1249, 75, 21, 2164, 2163, 158])).
% 1.19/1.39 tff(2180,plain,
% 1.19/1.39 (hskp30),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2179, 2178])).
% 1.19/1.39 tff(2181,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2023, 2180, 2171, 503, 247, 1571])).
% 1.19/1.39 tff(2182,plain,(hskp2 | (~c0_1(a467)) | c3_1(a467) | hskp12 | c1_1(a467) | c0_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2183,plain,
% 1.19/1.39 (hskp2),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2182, 2109, 2108, 21, 2110, 30, 29])).
% 1.19/1.39 tff(2184,plain,
% 1.19/1.39 (~c0_1(a464)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1285, 2183])).
% 1.19/1.39 tff(2185,plain,
% 1.19/1.39 (c3_1(a464)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[602, 2183])).
% 1.19/1.39 tff(2186,plain,
% 1.19/1.39 (hskp29),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1148, 75, 2047, 2185, 2041, 2040, 2184, 219, 348])).
% 1.19/1.39 tff(2187,plain,
% 1.19/1.39 (c2_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[310, 2186])).
% 1.19/1.39 tff(2188,plain,
% 1.19/1.39 (c1_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[318, 2186])).
% 1.19/1.39 tff(2189,plain,
% 1.19/1.39 (c0_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[326, 2186])).
% 1.19/1.39 tff(2190,plain,
% 1.19/1.39 (c2_1(a467)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2170, 75, 2189, 2188, 2187, 2109, 2108, 103])).
% 1.19/1.39 tff(2191,plain,
% 1.19/1.39 (~hskp30),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2023, 2190, 2109, 2108, 1571])).
% 1.19/1.39 tff(2192,plain,
% 1.19/1.39 ((~c2_1(a467)) | (~c3_1(a474))),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2008, 75, 1571, 2188, 2187, 2109, 2108, 1560])).
% 1.19/1.39 tff(2193,plain,
% 1.19/1.39 (~c3_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2192, 2190])).
% 1.19/1.39 tff(2194,plain,
% 1.19/1.39 (hskp30 | c3_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1249, 75, 21, 2189, 2188, 158])).
% 1.19/1.39 tff(2195,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2194, 2193, 2191])).
% 1.19/1.39 tff(2196,plain,(c2_1(a464) | hskp12 | c0_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2197,plain,
% 1.19/1.39 (c2_1(a464)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2196, 30, 21, 29])).
% 1.19/1.39 tff(2198,plain,
% 1.19/1.39 (~hskp2),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1418, 2197])).
% 1.19/1.39 tff(2199,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2101, 75, 2198, 2078, 2048, 2077, 2074, 594, 2076, 2055])).
% 1.19/1.39 tff(2200,plain,(hskp5 | hskp12 | c0_1(a471) | c3_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2201,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2200, 83, 31, 30, 21, 29])).
% 1.19/1.39 tff(2202,plain,(hskp5 | c0_1(a471) | hskp12 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2203,plain,
% 1.19/1.39 (hskp5),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2202, 30, 21, 29])).
% 1.19/1.39 tff(2204,plain,
% 1.19/1.39 (~c3_1(a467)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1091, 2203])).
% 1.19/1.39 tff(2205,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2182, 1761, 1762, 2198, 21, 247, 30, 29])).
% 1.19/1.39 tff(2206,plain,((~hskp5) | hskp12 | c3_1(a467) | c0_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2207,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2206, 2204, 2203, 21, 30, 29])).
% 1.19/1.39 tff(2208,plain,(c0_1(a471) | hskp12 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2209,plain,
% 1.19/1.39 (c0_1(a471)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2208, 29, 21])).
% 1.19/1.39 tff(2210,assumption,(~hskp29), introduced(assumption)).
% 1.19/1.39 tff(2211,plain,
% 1.19/1.39 (hskp3),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[415, 2210, 21])).
% 1.19/1.39 tff(2212,plain,
% 1.19/1.39 (~c0_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1136, 2211])).
% 1.19/1.39 tff(2213,plain,
% 1.19/1.39 (c3_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[403, 2211])).
% 1.19/1.39 tff(2214,plain,
% 1.19/1.39 (c2_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[357, 75, 2210, 2047, 2213, 2041, 2040, 2212, 348])).
% 1.19/1.39 tff(2215,plain,
% 1.19/1.39 (~c1_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1230, 2211])).
% 1.19/1.39 tff(2216,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2217,plain,
% 1.19/1.39 (((~ndr1_0) | c2_1(a471) | c3_1(a471) | (~c0_1(a471)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465))) <=> (c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2218,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a471) | c3_1(a471) | (~c0_1(a471)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[2217])).
% 1.19/1.39 tff(2219,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a471) | c3_1(a471) | (~c0_1(a471)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[2218, 2216])).
% 1.19/1.39 tff(2220,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a471) | c3_1(a471) | (~c0_1(a471)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(2221,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 1.19/1.39 tff(2222,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2221, 75, 2209, 1572, 2213, 29, 2212, 2215, 386, 2214])).
% 1.19/1.39 tff(2223,plain,(hskp29 | c3_1(a471) | c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2224,plain,
% 1.19/1.39 (hskp29),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2223, 1572, 29, 21])).
% 1.19/1.39 tff(2225,plain,
% 1.19/1.39 (c2_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[310, 2224])).
% 1.19/1.39 tff(2226,plain,
% 1.19/1.39 (c0_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[326, 2224])).
% 1.19/1.39 tff(2227,plain,
% 1.19/1.39 (c1_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[318, 2224])).
% 1.19/1.39 tff(2228,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2036, 75, 1909, 1908, 1907, 501, 1572, 29, 103])).
% 1.19/1.39 tff(2229,plain,(c3_1(a471) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a471)) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2230,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2229, 2227, 2226, 1572, 2225, 2209, 29])).
% 1.19/1.39 tff(2231,plain,(c3_1(a471) | c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2232,plain,
% 1.19/1.39 (c3_1(a471)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2231, 29, 21])).
% 1.19/1.39 tff(2233,plain,
% 1.19/1.39 (hskp29),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[415, 1138, 21])).
% 1.19/1.39 tff(2234,plain,
% 1.19/1.39 (c2_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[310, 2233])).
% 1.19/1.39 tff(2235,plain,
% 1.19/1.39 (c1_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[318, 2233])).
% 1.19/1.39 tff(2236,plain,
% 1.19/1.39 (c0_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[326, 2233])).
% 1.19/1.39 tff(2237,plain,
% 1.19/1.39 (c3_1(a471)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2229, 2236, 2235, 2234, 2209, 29])).
% 1.19/1.39 tff(2238,plain,
% 1.19/1.39 (hskp17),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[683, 2237, 2209, 31])).
% 1.19/1.39 tff(2239,plain,
% 1.19/1.39 (~c0_1(a493)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[697, 2238])).
% 1.19/1.39 tff(2240,plain,
% 1.19/1.39 (c3_1(a493)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[705, 2238])).
% 1.19/1.39 tff(2241,plain,
% 1.19/1.39 (c2_1(a493)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[691, 2238])).
% 1.19/1.39 tff(2242,plain,
% 1.19/1.39 (~c3_1(a474)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1109, 75, 2236, 2235, 2234, 2241, 2240, 2239, 844])).
% 1.19/1.39 tff(2243,plain,
% 1.19/1.39 (hskp23),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1797, 1138, 31])).
% 1.19/1.39 tff(2244,plain,
% 1.19/1.39 (~c3_1(a521)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1803, 2243])).
% 1.19/1.39 tff(2245,plain,
% 1.19/1.39 (~c2_1(a521)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1809, 2243])).
% 1.19/1.39 tff(2246,plain,
% 1.19/1.39 (~c0_1(a521)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1815, 2243])).
% 1.19/1.39 tff(2247,plain,
% 1.19/1.39 (~c1_1(a521)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1822, 75, 2246, 2245, 2244, 10])).
% 1.19/1.39 tff(2248,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2249,plain,
% 1.19/1.39 (((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a521) | c1_1(a521) | c2_1(a521)) <=> (c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(rewrite,[status(thm)],[])).
% 1.19/1.39 tff(2250,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a521) | c1_1(a521) | c2_1(a521))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.19/1.39 inference(monotonicity,[status(thm)],[2249])).
% 1.19/1.39 tff(2251,plain,
% 1.19/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a521) | c1_1(a521) | c2_1(a521))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.19/1.39 inference(transitivity,[status(thm)],[2250, 2248])).
% 1.19/1.39 tff(2252,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a521) | c1_1(a521) | c2_1(a521))),
% 1.19/1.39 inference(quant_inst,[status(thm)],[])).
% 1.19/1.39 tff(2253,plain,
% 1.19/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.19/1.39 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 1.19/1.39 tff(2254,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2253, 75, 2236, 2235, 2241, 2240, 2245, 2244, 2239, 748, 2247, 2242])).
% 1.19/1.39 tff(2255,plain,(hskp3 | hskp5 | c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2256,plain,
% 1.19/1.39 (hskp3),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2255, 31, 29, 21])).
% 1.19/1.39 tff(2257,plain,
% 1.19/1.39 (c3_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[403, 2256])).
% 1.19/1.39 tff(2258,plain,
% 1.19/1.39 (~c0_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1136, 2256])).
% 1.19/1.39 tff(2259,plain,
% 1.19/1.39 (~c1_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1230, 2256])).
% 1.19/1.39 tff(2260,assumption,(hskp3), introduced(assumption)).
% 1.19/1.39 tff(2261,plain,
% 1.19/1.39 (~c1_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1230, 2260])).
% 1.19/1.39 tff(2262,plain,
% 1.19/1.39 (c3_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[403, 2260])).
% 1.19/1.39 tff(2263,plain,
% 1.19/1.39 (~c0_1(a465)),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1136, 2260])).
% 1.19/1.39 tff(2264,plain,
% 1.19/1.39 ($false),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[1366, 2263, 2262, 2261, 31, 1295, 21])).
% 1.19/1.39 tff(2265,plain,((~hskp3) | hskp5 | hskp2 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.19/1.39 tff(2266,plain,
% 1.19/1.39 (hskp2),
% 1.19/1.39 inference(unit_resolution,[status(thm)],[2265, 2256, 31, 21])).
% 1.25/1.39 tff(2267,plain,
% 1.25/1.39 (~c0_1(a464)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1285, 2266])).
% 1.25/1.39 tff(2268,plain,
% 1.25/1.39 (~c2_1(a464)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1418, 2266])).
% 1.25/1.39 tff(2269,plain,
% 1.25/1.39 ($false),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1545, 2268, 2267, 21, 2259, 31, 2258, 2257])).
% 1.25/1.39 tff(2270,plain,(hskp5 | hskp12 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.25/1.39 tff(2271,plain,
% 1.25/1.39 (hskp5),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[2270, 29, 21])).
% 1.25/1.39 tff(2272,plain,
% 1.25/1.39 (~c1_1(a467)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[989, 2271])).
% 1.25/1.39 tff(2273,plain,
% 1.25/1.39 (c0_1(a467)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[548, 2271])).
% 1.25/1.39 tff(2274,plain,
% 1.25/1.39 ((~c2_1(a467)) | (~c3_1(a471))),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[537, 75, 21, 2209, 2273, 29, 2272, 531])).
% 1.25/1.39 tff(2275,plain,
% 1.25/1.39 (~c2_1(a467)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[2274, 2232])).
% 1.25/1.39 tff(2276,plain,
% 1.25/1.39 (~c3_1(a467)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1091, 2271])).
% 1.25/1.39 tff(2277,assumption,(~c2_1(a467)), introduced(assumption)).
% 1.25/1.39 tff(2278,plain,
% 1.25/1.39 (c2_1(a465)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[357, 75, 2210, 351, 2213, 350, 349, 2212, 348])).
% 1.25/1.39 tff(2279,plain,
% 1.25/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467))),
% 1.25/1.39 inference(rewrite,[status(thm)],[])).
% 1.25/1.39 tff(2280,plain,
% 1.25/1.39 (((~ndr1_0) | c2_1(a467) | c3_1(a467) | (~c0_1(a467)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465))) <=> (c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467))),
% 1.25/1.39 inference(rewrite,[status(thm)],[])).
% 1.25/1.39 tff(2281,plain,
% 1.25/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a467) | c3_1(a467) | (~c0_1(a467)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467)))),
% 1.25/1.39 inference(monotonicity,[status(thm)],[2280])).
% 1.25/1.39 tff(2282,plain,
% 1.25/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a467) | c3_1(a467) | (~c0_1(a467)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467))),
% 1.25/1.39 inference(transitivity,[status(thm)],[2281, 2279])).
% 1.25/1.39 tff(2283,plain,
% 1.25/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a467) | c3_1(a467) | (~c0_1(a467)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))),
% 1.25/1.39 inference(quant_inst,[status(thm)],[])).
% 1.25/1.39 tff(2284,plain,
% 1.25/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467)),
% 1.25/1.39 inference(modus_ponens,[status(thm)],[2283, 2282])).
% 1.25/1.39 tff(2285,plain,
% 1.25/1.39 ($false),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[2284, 75, 503, 2213, 247, 2212, 2215, 386, 2278, 2277])).
% 1.25/1.39 tff(2286,plain,(hskp29 | (~c0_1(a467)) | c3_1(a467) | c2_1(a467) | (~c0_1(a487)) | c1_1(a487) | c2_1(a487) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.25/1.39 tff(2287,plain,
% 1.25/1.39 (hskp29),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[2286, 2273, 2276, 2275, 2047, 2041, 2040, 21])).
% 1.25/1.39 tff(2288,plain,
% 1.25/1.39 (c2_1(a474)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[310, 2287])).
% 1.25/1.39 tff(2289,plain,
% 1.25/1.39 (c1_1(a474)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[318, 2287])).
% 1.25/1.39 tff(2290,plain,
% 1.25/1.39 (c0_1(a474)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[326, 2287])).
% 1.25/1.39 tff(2291,plain,
% 1.25/1.39 ($false),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[2170, 75, 2290, 2289, 2288, 2273, 2276, 103, 2275])).
% 1.25/1.39 tff(2292,plain,(c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.25/1.39 tff(2293,plain,
% 1.25/1.39 (c2_1(a471)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[2292, 21])).
% 1.25/1.39 tff(2294,plain,
% 1.25/1.39 (~hskp7),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[483, 2293])).
% 1.25/1.39 tff(2295,plain,
% 1.25/1.39 (hskp2),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[2265, 2260, 31, 21])).
% 1.25/1.39 tff(2296,plain,
% 1.25/1.39 (~c0_1(a464)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1285, 2295])).
% 1.25/1.39 tff(2297,plain,
% 1.25/1.39 (~c2_1(a464)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1418, 2295])).
% 1.25/1.39 tff(2298,plain,
% 1.25/1.39 ($false),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1545, 2297, 2296, 21, 2261, 31, 2263, 2262])).
% 1.25/1.39 tff(2299,plain,((~hskp3) | hskp12 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.25/1.39 tff(2300,plain,
% 1.25/1.39 (~hskp3),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[2299, 31, 21])).
% 1.25/1.39 tff(2301,plain,
% 1.25/1.39 (hskp29),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[415, 2300, 21])).
% 1.25/1.39 tff(2302,plain,
% 1.25/1.39 (c2_1(a474)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[310, 2301])).
% 1.25/1.39 tff(2303,plain,
% 1.25/1.39 (c1_1(a474)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[318, 2301])).
% 1.25/1.39 tff(2304,plain,
% 1.25/1.39 (c0_1(a474)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[326, 2301])).
% 1.25/1.39 tff(2305,plain,
% 1.25/1.39 (hskp23),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1797, 2300, 31])).
% 1.25/1.39 tff(2306,plain,
% 1.25/1.39 (~c3_1(a521)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1803, 2305])).
% 1.25/1.39 tff(2307,plain,
% 1.25/1.39 (~c2_1(a521)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1809, 2305])).
% 1.25/1.39 tff(2308,plain,
% 1.25/1.39 (~c0_1(a521)),
% 1.25/1.39 inference(unit_resolution,[status(thm)],[1815, 2305])).
% 1.25/1.39 tff(2309,plain,
% 1.25/1.39 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0))),
% 1.25/1.39 inference(rewrite,[status(thm)],[])).
% 1.25/1.39 tff(2310,plain,
% 1.25/1.39 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a521) | c0_1(a521) | c3_1(a521)) <=> (hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0))),
% 1.25/1.39 inference(rewrite,[status(thm)],[])).
% 1.25/1.39 tff(2311,plain,
% 1.25/1.39 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a521) | c0_1(a521) | c3_1(a521))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0)))),
% 1.25/1.39 inference(monotonicity,[status(thm)],[2310])).
% 1.25/1.39 tff(2312,plain,
% 1.25/1.39 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a521) | c0_1(a521) | c3_1(a521))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0))),
% 1.25/1.39 inference(transitivity,[status(thm)],[2311, 2309])).
% 1.25/1.39 tff(2313,plain,
% 1.25/1.39 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a521) | c0_1(a521) | c3_1(a521))),
% 1.25/1.39 inference(quant_inst,[status(thm)],[])).
% 1.25/1.39 tff(2314,plain,
% 1.25/1.39 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0)),
% 1.25/1.39 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 1.25/1.39 tff(2315,plain,
% 1.25/1.40 (hskp8),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2314, 75, 2294, 2308, 2307, 2306, 1582])).
% 1.25/1.40 tff(2316,plain,
% 1.25/1.40 (~c2_1(a472)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1595, 2315])).
% 1.25/1.40 tff(2317,plain,
% 1.25/1.40 (c3_1(a472)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1603, 2315])).
% 1.25/1.40 tff(2318,plain,
% 1.25/1.40 (c0_1(a472)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1953, 75, 21, 31, 2317, 2316, 41])).
% 1.25/1.40 tff(2319,plain,
% 1.25/1.40 (c1_1(a472)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1611, 2315])).
% 1.25/1.40 tff(2320,plain,
% 1.25/1.40 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2321,plain,
% 1.25/1.40 ((hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2322,plain,
% 1.25/1.40 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[2321])).
% 1.25/1.40 tff(2323,plain,
% 1.25/1.40 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.25/1.40 inference(transitivity,[status(thm)],[2322, 2320])).
% 1.25/1.40 tff(2324,plain,
% 1.25/1.40 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(2325,plain,
% 1.25/1.40 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 1.25/1.40 tff(2326,plain,
% 1.25/1.40 (hskp31 | (~c0_1(a472))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2325, 75, 2304, 2303, 2302, 2319, 2317, 1212])).
% 1.25/1.40 tff(2327,plain,
% 1.25/1.40 (hskp31),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2326, 2318])).
% 1.25/1.40 tff(2328,plain,
% 1.25/1.40 (c3_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1461, 2327])).
% 1.25/1.40 tff(2329,plain,
% 1.25/1.40 (hskp17 | (~c0_1(a472))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1946, 75, 31, 2317, 2316, 676])).
% 1.25/1.40 tff(2330,plain,
% 1.25/1.40 (hskp17),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2329, 2318])).
% 1.25/1.40 tff(2331,plain,
% 1.25/1.40 (c0_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1453, 2327])).
% 1.25/1.40 tff(2332,plain,
% 1.25/1.40 (c1_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1469, 2327])).
% 1.25/1.40 tff(2333,plain,
% 1.25/1.40 ($false),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1911, 2332, 2331, 2330, 2328, 2304, 2303, 2302])).
% 1.25/1.40 tff(2334,plain,(hskp5 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.25/1.40 tff(2335,plain,
% 1.25/1.40 (hskp5),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2334, 21])).
% 1.25/1.40 tff(2336,plain,
% 1.25/1.40 (~c3_1(a467)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1091, 2335])).
% 1.25/1.40 tff(2337,plain,
% 1.25/1.40 (c0_1(a467)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[548, 2335])).
% 1.25/1.40 tff(2338,plain,
% 1.25/1.40 (c2_1(a467)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2170, 75, 327, 319, 311, 2337, 2336, 103])).
% 1.25/1.40 tff(2339,plain,
% 1.25/1.40 (~hskp30),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2023, 2338, 2337, 2336, 2294])).
% 1.25/1.40 tff(2340,plain,
% 1.25/1.40 ((~c2_1(a467)) | (~c3_1(a474))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2008, 75, 2294, 319, 311, 2337, 2336, 1560])).
% 1.25/1.40 tff(2341,plain,
% 1.25/1.40 (~c3_1(a474)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2340, 2338])).
% 1.25/1.40 tff(2342,plain,
% 1.25/1.40 (hskp30 | c3_1(a474)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1249, 75, 21, 327, 319, 158])).
% 1.25/1.40 tff(2343,plain,
% 1.25/1.40 ($false),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2342, 2341, 2339])).
% 1.25/1.40 tff(2344,plain,((~hskp29) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.25/1.40 tff(2345,plain,
% 1.25/1.40 (~hskp29),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2344, 21])).
% 1.25/1.40 tff(2346,plain,
% 1.25/1.40 (c2_1(a467)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2286, 2210, 2336, 349, 351, 350, 2337, 21])).
% 1.25/1.40 tff(2347,plain,
% 1.25/1.40 (~c1_1(a467)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[989, 2335])).
% 1.25/1.40 tff(2348,plain,
% 1.25/1.40 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2349,plain,
% 1.25/1.40 ((hskp12 | (~ndr1_0) | c2_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2350,plain,
% 1.25/1.40 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[2349])).
% 1.25/1.40 tff(2351,plain,
% 1.25/1.40 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.25/1.40 inference(transitivity,[status(thm)],[2350, 2348])).
% 1.25/1.40 tff(2352,plain,
% 1.25/1.40 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(2353,plain,
% 1.25/1.40 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2352, 2351])).
% 1.25/1.40 tff(2354,plain,
% 1.25/1.40 ((~c2_1(a467)) | (~c3_1(a487))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2353, 75, 21, 351, 2337, 349, 2347, 531])).
% 1.25/1.40 tff(2355,plain,
% 1.25/1.40 (~c3_1(a487)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2354, 2346])).
% 1.25/1.40 tff(2356,plain,
% 1.25/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2357,plain,
% 1.25/1.40 (((~ndr1_0) | c2_1(a487) | c3_1(a487) | (~c0_1(a487)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465))) <=> (c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2358,plain,
% 1.25/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a487) | c3_1(a487) | (~c0_1(a487)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[2357])).
% 1.25/1.40 tff(2359,plain,
% 1.25/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a487) | c3_1(a487) | (~c0_1(a487)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487)))),
% 1.25/1.40 inference(transitivity,[status(thm)],[2358, 2356])).
% 1.25/1.40 tff(2360,plain,
% 1.25/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a487) | c3_1(a487) | (~c0_1(a487)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(2361,plain,
% 1.25/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2360, 2359])).
% 1.25/1.40 tff(2362,plain,
% 1.25/1.40 ($false),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2361, 75, 351, 2213, 349, 2212, 2215, 386, 2278, 2355])).
% 1.25/1.40 tff(2363,plain,(hskp29 | (~c0_1(a487)) | c2_1(a487) | c1_1(a487) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.25/1.40 tff(2364,plain,
% 1.25/1.40 ($false),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2363, 264, 272, 2345, 28, 21])).
% 1.25/1.40 tff(2365,plain,((~hskp16) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.25/1.40 tff(2366,plain,
% 1.25/1.40 (~hskp16),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2365, 21])).
% 1.25/1.40 tff(2367,plain,
% 1.25/1.40 (hskp16 | c2_1(a467)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[519, 75, 2337, 2347, 2336, 513])).
% 1.25/1.40 tff(2368,plain,
% 1.25/1.40 (c2_1(a467)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2367, 2366])).
% 1.25/1.40 tff(2369,plain,
% 1.25/1.40 (~hskp30),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2023, 2368, 2337, 2336, 2294])).
% 1.25/1.40 tff(2370,plain,
% 1.25/1.40 (^[U: $i] : refl((hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.25/1.40 inference(bind,[status(th)],[])).
% 1.25/1.40 tff(2371,plain,
% 1.25/1.40 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.25/1.40 inference(quant_intro,[status(thm)],[2370])).
% 1.25/1.40 tff(2372,plain,
% 1.25/1.40 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2373,plain,
% 1.25/1.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp21) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp21) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.25/1.40 inference(bind,[status(th)],[])).
% 1.25/1.40 tff(2374,plain,
% 1.25/1.40 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp21) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.25/1.40 inference(quant_intro,[status(thm)],[2373])).
% 1.25/1.40 tff(2375,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.25/1.40 tff(2376,plain,
% 1.25/1.40 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 1.25/1.40 tff(2377,plain,
% 1.25/1.40 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2376, 2372])).
% 1.25/1.40 tff(2378,plain,(
% 1.25/1.40 ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.25/1.40 inference(skolemize,[status(sab)],[2377])).
% 1.25/1.40 tff(2379,plain,
% 1.25/1.40 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2378, 2371])).
% 1.25/1.40 tff(2380,plain,
% 1.25/1.40 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2381,plain,
% 1.25/1.40 ((hskp30 | hskp21 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c2_1(a467))) <=> (hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2382,plain,
% 1.25/1.40 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[2381])).
% 1.25/1.40 tff(2383,plain,
% 1.25/1.40 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.25/1.40 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.25/1.40 tff(2384,plain,
% 1.25/1.40 ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c2_1(a467)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(2385,plain,
% 1.25/1.40 ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.25/1.40 tff(2386,plain,
% 1.25/1.40 (hskp30 | hskp21 | (~c2_1(a467))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2385, 75, 2347, 2336, 2379])).
% 1.25/1.40 tff(2387,plain,
% 1.25/1.40 (hskp21),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2386, 2369, 2368])).
% 1.25/1.40 tff(2388,plain,
% 1.25/1.40 (((~hskp21) | (~c0_1(a507))) <=> ((~hskp21) | (~c0_1(a507)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2389,plain,
% 1.25/1.40 (((~c0_1(a507)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a507)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2390,axiom,((~c0_1(a507)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.25/1.40 tff(2391,plain,
% 1.25/1.40 ((~hskp21) | (~c0_1(a507))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 1.25/1.40 tff(2392,plain,
% 1.25/1.40 ((~hskp21) | (~c0_1(a507))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2391, 2388])).
% 1.25/1.40 tff(2393,plain,
% 1.25/1.40 (~c0_1(a507)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2392, 2387])).
% 1.25/1.40 tff(2394,plain,
% 1.25/1.40 (((~hskp21) | c2_1(a507)) <=> ((~hskp21) | c2_1(a507))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2395,axiom,((~hskp21) | c2_1(a507)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.25/1.40 tff(2396,plain,
% 1.25/1.40 ((~hskp21) | c2_1(a507)),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2395, 2394])).
% 1.25/1.40 tff(2397,plain,
% 1.25/1.40 ((~hskp21) | c2_1(a507)),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2396, 2394])).
% 1.25/1.40 tff(2398,plain,
% 1.25/1.40 ((~hskp21) | c2_1(a507)),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2397, 2394])).
% 1.25/1.40 tff(2399,plain,
% 1.25/1.40 ((~hskp21) | c2_1(a507)),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2398, 2394])).
% 1.25/1.40 tff(2400,plain,
% 1.25/1.40 ((~hskp21) | c2_1(a507)),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2399, 2394])).
% 1.25/1.40 tff(2401,plain,
% 1.25/1.40 (c2_1(a507)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2400, 2387])).
% 1.25/1.40 tff(2402,plain,
% 1.25/1.40 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2403,plain,
% 1.25/1.40 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a507) | c3_1(a507) | (~c2_1(a507))) <=> (hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2404,plain,
% 1.25/1.40 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a507) | c3_1(a507) | (~c2_1(a507)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[2403])).
% 1.25/1.40 tff(2405,plain,
% 1.25/1.40 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a507) | c3_1(a507) | (~c2_1(a507)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507)))),
% 1.25/1.40 inference(transitivity,[status(thm)],[2404, 2402])).
% 1.25/1.40 tff(2406,plain,
% 1.25/1.40 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a507) | c3_1(a507) | (~c2_1(a507)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(2407,plain,
% 1.25/1.40 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 1.25/1.40 tff(2408,plain,
% 1.25/1.40 (c3_1(a507)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2407, 75, 2366, 2294, 2401, 2393, 20])).
% 1.25/1.40 tff(2409,plain,
% 1.25/1.40 (~hskp19),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[215, 2366, 21])).
% 1.25/1.40 tff(2410,plain,
% 1.25/1.40 (hskp31),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1445, 2409])).
% 1.25/1.40 tff(2411,plain,
% 1.25/1.40 (c3_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1461, 2410])).
% 1.25/1.40 tff(2412,plain,
% 1.25/1.40 (c1_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1469, 2410])).
% 1.25/1.40 tff(2413,plain,
% 1.25/1.40 (c0_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1453, 2410])).
% 1.25/1.40 tff(2414,plain,
% 1.25/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2415,plain,
% 1.25/1.40 (((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c2_1(a529)) | (~c0_1(a529)) | c0_1(a507) | (~c3_1(a507)) | (~c2_1(a507))) <=> (c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2416,plain,
% 1.25/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c2_1(a529)) | (~c0_1(a529)) | c0_1(a507) | (~c3_1(a507)) | (~c2_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[2415])).
% 1.25/1.40 tff(2417,plain,
% 1.25/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c2_1(a529)) | (~c0_1(a529)) | c0_1(a507) | (~c3_1(a507)) | (~c2_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507)))),
% 1.25/1.40 inference(transitivity,[status(thm)],[2416, 2414])).
% 1.25/1.40 tff(2418,plain,
% 1.25/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c2_1(a529)) | (~c0_1(a529)) | c0_1(a507) | (~c3_1(a507)) | (~c2_1(a507)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(2419,plain,
% 1.25/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2418, 2417])).
% 1.25/1.40 tff(2420,plain,
% 1.25/1.40 (~c2_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2419, 75, 2413, 2412, 2411, 2401, 2393, 844, 2408])).
% 1.25/1.40 tff(2421,plain,
% 1.25/1.40 ($false),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1677, 75, 21, 2413, 2411, 2337, 2347, 531, 2368, 2420])).
% 1.25/1.40 tff(2422,plain,(hskp12), inference(lemma,lemma(discharge,[]))).
% 1.25/1.40 tff(2423,plain,
% 1.25/1.40 (~c3_1(a481)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[421, 2422])).
% 1.25/1.40 tff(2424,plain,
% 1.25/1.40 (~c0_1(a481)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[427, 2422])).
% 1.25/1.40 tff(2425,plain,
% 1.25/1.40 (c1_1(a481)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[435, 2422])).
% 1.25/1.40 tff(2426,plain,
% 1.25/1.40 (c2_1(a481)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[442, 75, 2425, 2424, 2423, 10])).
% 1.25/1.40 tff(2427,plain,
% 1.25/1.40 ($false),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1164, 75, 272, 2425, 28, 264, 2424, 369, 2426])).
% 1.25/1.40 tff(2428,plain,(~hskp16), inference(lemma,lemma(discharge,[]))).
% 1.25/1.40 tff(2429,plain,
% 1.25/1.40 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2430,plain,
% 1.25/1.40 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c2_1(a481))) <=> (hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2431,plain,
% 1.25/1.40 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[2430])).
% 1.25/1.40 tff(2432,plain,
% 1.25/1.40 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481)))),
% 1.25/1.40 inference(transitivity,[status(thm)],[2431, 2429])).
% 1.25/1.40 tff(2433,plain,
% 1.25/1.40 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c2_1(a481)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(2434,plain,
% 1.25/1.40 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.25/1.40 tff(2435,plain,
% 1.25/1.40 (hskp16 | hskp7),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2434, 75, 2424, 2423, 20, 2426])).
% 1.25/1.40 tff(2436,plain,
% 1.25/1.40 (hskp7),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2435, 2428])).
% 1.25/1.40 tff(2437,plain,
% 1.25/1.40 (~c2_1(a471)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[483, 2436])).
% 1.25/1.40 tff(2438,plain,
% 1.25/1.40 (c0_1(a471)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[499, 2436])).
% 1.25/1.40 tff(2439,plain,
% 1.25/1.40 (c1_1(a471)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[934, 75, 2425, 2438, 2424, 2437, 369, 2426])).
% 1.25/1.40 tff(2440,plain,
% 1.25/1.40 (hskp29 | (~c1_1(a471))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[976, 75, 2425, 2438, 2423, 2437, 970, 2426])).
% 1.25/1.40 tff(2441,plain,
% 1.25/1.40 (hskp29),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2440, 2439])).
% 1.25/1.40 tff(2442,plain,
% 1.25/1.40 (c2_1(a474)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[310, 2441])).
% 1.25/1.40 tff(2443,plain,
% 1.25/1.40 (c0_1(a474)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[326, 2441])).
% 1.25/1.40 tff(2444,plain,
% 1.25/1.40 (hskp31),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1438, 2436, 2425, 2423, 2424])).
% 1.25/1.40 tff(2445,plain,
% 1.25/1.40 (c1_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1469, 2444])).
% 1.25/1.40 tff(2446,plain,
% 1.25/1.40 (c3_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1461, 2444])).
% 1.25/1.40 tff(2447,plain,
% 1.25/1.40 (c0_1(a529)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1453, 2444])).
% 1.25/1.40 tff(2448,plain,
% 1.25/1.40 (c1_1(a474)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[318, 2441])).
% 1.25/1.40 tff(2449,plain,
% 1.25/1.40 (~hskp17),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1911, 2448, 2447, 2446, 2445, 2443, 2442])).
% 1.25/1.40 tff(2450,plain,
% 1.25/1.40 (^[U: $i] : refl((hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.25/1.40 inference(bind,[status(th)],[])).
% 1.25/1.40 tff(2451,plain,
% 1.25/1.40 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.25/1.40 inference(quant_intro,[status(thm)],[2450])).
% 1.25/1.40 tff(2452,plain,
% 1.25/1.40 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2453,plain,
% 1.25/1.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp17) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp17) <=> (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.25/1.40 inference(bind,[status(th)],[])).
% 1.25/1.40 tff(2454,plain,
% 1.25/1.40 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp17) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.25/1.40 inference(quant_intro,[status(thm)],[2453])).
% 1.25/1.40 tff(2455,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.25/1.40 tff(2456,plain,
% 1.25/1.40 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 1.25/1.40 tff(2457,plain,
% 1.25/1.40 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2456, 2452])).
% 1.25/1.40 tff(2458,plain,(
% 1.25/1.40 ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.25/1.40 inference(skolemize,[status(sab)],[2457])).
% 1.25/1.40 tff(2459,plain,
% 1.25/1.40 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[2458, 2451])).
% 1.25/1.40 tff(2460,plain,
% 1.25/1.40 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2461,plain,
% 1.25/1.40 ((hskp18 | hskp17 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(2462,plain,
% 1.25/1.40 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[2461])).
% 1.25/1.40 tff(2463,plain,
% 1.25/1.40 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.25/1.40 inference(transitivity,[status(thm)],[2462, 2460])).
% 1.25/1.40 tff(2464,plain,
% 1.25/1.40 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.25/1.41 inference(quant_inst,[status(thm)],[])).
% 1.25/1.41 tff(2465,plain,
% 1.25/1.41 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[2464, 2463])).
% 1.25/1.41 tff(2466,plain,
% 1.25/1.41 (hskp18 | hskp17 | (~c2_1(a481))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[2465, 75, 2425, 2423, 2459])).
% 1.25/1.41 tff(2467,plain,
% 1.25/1.41 (hskp18),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[2466, 2449, 2426])).
% 1.25/1.41 tff(2468,plain,
% 1.25/1.41 (~c3_1(a494)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[284, 2467])).
% 1.25/1.41 tff(2469,plain,
% 1.25/1.41 (c0_1(a494)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[298, 2467])).
% 1.25/1.41 tff(2470,plain,
% 1.25/1.41 (~c2_1(a494)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[290, 2467])).
% 1.25/1.41 tff(2471,plain,
% 1.25/1.41 ($false),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[335, 2470, 2469, 2441, 2468])).
% 1.25/1.41 % SZS output end Proof
% 1.25/1.41 % E exiting
%------------------------------------------------------------------------------