%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN509-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:24 AM UTC 2025
% Result : Unsatisfiable 0.68s 0.86s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN509-1 : TPTP v9.0.0. Released v2.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:38:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.68/0.86 % SZS status Unsatisfiable
% 0.68/0.86 % SZS output start Proof
% 0.68/0.86 tff(c3_1_type, type, (
% 0.68/0.86 c3_1: $i > $o)).
% 0.68/0.86 tff(a463_type, type, (
% 0.68/0.86 a463: $i)).
% 0.68/0.86 tff(c2_1_type, type, (
% 0.68/0.86 c2_1: $i > $o)).
% 0.68/0.86 tff(a445_type, type, (
% 0.68/0.86 a445: $i)).
% 0.68/0.86 tff(c1_1_type, type, (
% 0.68/0.86 c1_1: $i > $o)).
% 0.68/0.86 tff(c0_1_type, type, (
% 0.68/0.86 c0_1: $i > $o)).
% 0.68/0.86 tff(ndr1_0_type, type, (
% 0.68/0.86 ndr1_0: $o)).
% 0.68/0.86 tff(a435_type, type, (
% 0.68/0.86 a435: $i)).
% 0.68/0.86 tff(hskp3_type, type, (
% 0.68/0.86 hskp3: $o)).
% 0.68/0.86 tff(hskp9_type, type, (
% 0.68/0.86 hskp9: $o)).
% 0.68/0.86 tff(a444_type, type, (
% 0.68/0.86 a444: $i)).
% 0.68/0.86 tff(hskp8_type, type, (
% 0.68/0.86 hskp8: $o)).
% 0.68/0.86 tff(a486_type, type, (
% 0.68/0.86 a486: $i)).
% 0.68/0.86 tff(hskp24_type, type, (
% 0.68/0.86 hskp24: $o)).
% 0.68/0.86 tff(a454_type, type, (
% 0.68/0.86 a454: $i)).
% 0.68/0.86 tff(hskp15_type, type, (
% 0.68/0.86 hskp15: $o)).
% 0.68/0.86 tff(a452_type, type, (
% 0.68/0.86 a452: $i)).
% 0.68/0.86 tff(hskp14_type, type, (
% 0.68/0.86 hskp14: $o)).
% 0.68/0.86 tff(a448_type, type, (
% 0.68/0.86 a448: $i)).
% 0.68/0.86 tff(hskp10_type, type, (
% 0.68/0.86 hskp10: $o)).
% 0.68/0.86 tff(a447_type, type, (
% 0.68/0.86 a447: $i)).
% 0.68/0.86 tff(a433_type, type, (
% 0.68/0.86 a433: $i)).
% 0.68/0.86 tff(hskp1_type, type, (
% 0.68/0.86 hskp1: $o)).
% 0.68/0.86 tff(a456_type, type, (
% 0.68/0.86 a456: $i)).
% 0.68/0.86 tff(hskp30_type, type, (
% 0.68/0.86 hskp30: $o)).
% 0.68/0.86 tff(a450_type, type, (
% 0.68/0.86 a450: $i)).
% 0.68/0.86 tff(hskp12_type, type, (
% 0.68/0.86 hskp12: $o)).
% 0.68/0.86 tff(a442_type, type, (
% 0.68/0.86 a442: $i)).
% 0.68/0.86 tff(hskp6_type, type, (
% 0.68/0.86 hskp6: $o)).
% 0.68/0.86 tff(a457_type, type, (
% 0.68/0.86 a457: $i)).
% 0.68/0.86 tff(hskp16_type, type, (
% 0.68/0.86 hskp16: $o)).
% 0.68/0.86 tff(a432_type, type, (
% 0.68/0.86 a432: $i)).
% 0.68/0.86 tff(hskp0_type, type, (
% 0.68/0.86 hskp0: $o)).
% 0.68/0.86 tff(a492_type, type, (
% 0.68/0.86 a492: $i)).
% 0.68/0.86 tff(hskp26_type, type, (
% 0.68/0.86 hskp26: $o)).
% 0.68/0.86 tff(hskp29_type, type, (
% 0.68/0.86 hskp29: $o)).
% 0.68/0.86 tff(a434_type, type, (
% 0.68/0.86 a434: $i)).
% 0.68/0.86 tff(hskp2_type, type, (
% 0.68/0.86 hskp2: $o)).
% 0.68/0.86 tff(a489_type, type, (
% 0.68/0.86 a489: $i)).
% 0.68/0.86 tff(hskp25_type, type, (
% 0.68/0.86 hskp25: $o)).
% 0.68/0.86 tff(a443_type, type, (
% 0.68/0.86 a443: $i)).
% 0.68/0.86 tff(hskp7_type, type, (
% 0.68/0.86 hskp7: $o)).
% 0.68/0.86 tff(hskp23_type, type, (
% 0.68/0.86 hskp23: $o)).
% 0.68/0.86 tff(a437_type, type, (
% 0.68/0.86 a437: $i)).
% 0.68/0.86 tff(hskp28_type, type, (
% 0.68/0.86 hskp28: $o)).
% 0.68/0.86 tff(a449_type, type, (
% 0.68/0.86 a449: $i)).
% 0.68/0.86 tff(hskp11_type, type, (
% 0.68/0.86 hskp11: $o)).
% 0.68/0.86 tff(a467_type, type, (
% 0.68/0.86 a467: $i)).
% 0.68/0.86 tff(hskp19_type, type, (
% 0.68/0.86 hskp19: $o)).
% 0.68/0.86 tff(a484_type, type, (
% 0.68/0.86 a484: $i)).
% 0.68/0.86 tff(hskp17_type, type, (
% 0.68/0.86 hskp17: $o)).
% 0.68/0.86 tff(1,plain,
% 0.68/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(2,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[1])).
% 0.68/0.86 tff(3,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(4,plain,
% 0.68/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(5,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[4])).
% 0.68/0.86 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.68/0.86 tff(7,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.68/0.86 tff(8,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.68/0.86 tff(9,plain,(
% 0.68/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.68/0.86 inference(skolemize,[status(sab)],[8])).
% 0.68/0.86 tff(10,plain,
% 0.68/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.68/0.86 tff(11,plain,
% 0.68/0.86 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(12,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[11])).
% 0.68/0.86 tff(13,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(14,plain,
% 0.68/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(15,plain,
% 0.68/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[14])).
% 0.68/0.86 tff(16,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 0.68/0.86 tff(17,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.68/0.86 tff(18,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.68/0.86 tff(19,plain,(
% 0.68/0.86 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.68/0.86 inference(skolemize,[status(sab)],[18])).
% 0.68/0.86 tff(20,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.68/0.86 tff(21,plain,
% 0.68/0.86 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(22,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[21])).
% 0.68/0.86 tff(23,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(24,plain,
% 0.68/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(25,plain,
% 0.68/0.87 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[24])).
% 0.68/0.87 tff(26,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.68/0.87 tff(27,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.68/0.87 tff(28,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.68/0.87 tff(29,plain,(
% 0.68/0.87 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.68/0.87 inference(skolemize,[status(sab)],[28])).
% 0.68/0.87 tff(30,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.68/0.87 tff(31,assumption,(~hskp9), introduced(assumption)).
% 0.68/0.87 tff(32,assumption,(~hskp8), introduced(assumption)).
% 0.68/0.87 tff(33,assumption,(hskp3), introduced(assumption)).
% 0.68/0.87 tff(34,plain,
% 0.68/0.87 (((~hskp3) | (~c3_1(a435))) <=> ((~hskp3) | (~c3_1(a435)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(35,plain,
% 0.68/0.87 (((~c3_1(a435)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a435)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(36,axiom,((~c3_1(a435)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.68/0.87 tff(37,plain,
% 0.68/0.87 ((~hskp3) | (~c3_1(a435))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.68/0.87 tff(38,plain,
% 0.68/0.87 ((~hskp3) | (~c3_1(a435))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.68/0.87 tff(39,plain,
% 0.68/0.87 (~c3_1(a435)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.68/0.87 tff(40,assumption,(~c0_1(a445)), introduced(assumption)).
% 0.68/0.87 tff(41,plain,
% 0.68/0.87 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(42,plain,
% 0.68/0.87 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[41])).
% 0.68/0.87 tff(43,plain,
% 0.68/0.87 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(44,plain,
% 0.68/0.87 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(45,plain,
% 0.68/0.87 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[44])).
% 0.68/0.87 tff(46,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.68/0.87 tff(47,plain,
% 0.68/0.87 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.68/0.87 tff(48,plain,
% 0.68/0.87 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.68/0.87 tff(49,plain,(
% 0.68/0.87 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.68/0.87 inference(skolemize,[status(sab)],[48])).
% 0.68/0.87 tff(50,plain,
% 0.68/0.87 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.68/0.87 tff(51,assumption,(~c3_1(a445)), introduced(assumption)).
% 0.68/0.87 tff(52,assumption,(~c1_1(a445)), introduced(assumption)).
% 0.68/0.87 tff(53,assumption,(~hskp14), introduced(assumption)).
% 0.68/0.87 tff(54,assumption,(~hskp10), introduced(assumption)).
% 0.68/0.87 tff(55,plain,
% 0.68/0.87 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(56,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[55])).
% 0.68/0.87 tff(57,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(58,plain,
% 0.68/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(59,plain,
% 0.68/0.87 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[58])).
% 0.68/0.87 tff(60,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.68/0.87 tff(61,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.68/0.87 tff(62,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.68/0.87 tff(63,plain,(
% 0.68/0.87 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(skolemize,[status(sab)],[62])).
% 0.68/0.87 tff(64,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.68/0.87 tff(65,plain,
% 0.68/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(66,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[65])).
% 0.68/0.87 tff(67,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(68,plain,
% 0.68/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_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) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(69,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[68])).
% 0.68/0.87 tff(70,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.68/0.87 tff(71,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.68/0.87 tff(72,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.68/0.87 tff(73,plain,(
% 0.68/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.68/0.87 inference(skolemize,[status(sab)],[72])).
% 0.68/0.87 tff(74,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.68/0.87 tff(75,plain,
% 0.68/0.87 ((hskp10 | hskp8 | hskp1) <=> (hskp10 | hskp8 | hskp1)),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(76,plain,
% 0.68/0.87 (((hskp10 | hskp8) | hskp1) <=> (hskp10 | hskp8 | hskp1)),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(77,axiom,((hskp10 | hskp8) | hskp1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.68/0.87 tff(78,plain,
% 0.68/0.87 (hskp10 | hskp8 | hskp1),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.68/0.87 tff(79,plain,
% 0.68/0.87 (hskp10 | hskp8 | hskp1),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.68/0.87 tff(80,plain,
% 0.68/0.87 (hskp10 | hskp8 | hskp1),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.68/0.87 tff(81,plain,
% 0.68/0.87 (hskp10 | hskp8 | hskp1),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[80, 75])).
% 0.68/0.87 tff(82,plain,
% 0.68/0.87 (hskp10 | hskp8 | hskp1),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.68/0.87 tff(83,plain,
% 0.68/0.87 (hskp1),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[82, 32, 54])).
% 0.68/0.87 tff(84,plain,
% 0.68/0.87 (((~hskp1) | (~c2_1(a433))) <=> ((~hskp1) | (~c2_1(a433)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(85,plain,
% 0.68/0.87 (((~c2_1(a433)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a433)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(86,axiom,((~c2_1(a433)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.68/0.87 tff(87,plain,
% 0.68/0.87 ((~hskp1) | (~c2_1(a433))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.68/0.87 tff(88,plain,
% 0.68/0.87 ((~hskp1) | (~c2_1(a433))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.68/0.87 tff(89,plain,
% 0.68/0.87 (~c2_1(a433)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[88, 83])).
% 0.68/0.87 tff(90,plain,
% 0.68/0.87 (((~hskp1) | (~c1_1(a433))) <=> ((~hskp1) | (~c1_1(a433)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(91,plain,
% 0.68/0.87 (((~c1_1(a433)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a433)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(92,axiom,((~c1_1(a433)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.68/0.87 tff(93,plain,
% 0.68/0.87 ((~hskp1) | (~c1_1(a433))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.68/0.87 tff(94,plain,
% 0.68/0.87 ((~hskp1) | (~c1_1(a433))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[93, 90])).
% 0.68/0.87 tff(95,plain,
% 0.68/0.87 (~c1_1(a433)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[94, 83])).
% 0.68/0.87 tff(96,plain,
% 0.68/0.87 (((~hskp1) | (~c0_1(a433))) <=> ((~hskp1) | (~c0_1(a433)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(97,plain,
% 0.68/0.87 (((~c0_1(a433)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a433)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(98,axiom,((~c0_1(a433)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.68/0.87 tff(99,plain,
% 0.68/0.87 ((~hskp1) | (~c0_1(a433))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.68/0.87 tff(100,plain,
% 0.68/0.87 ((~hskp1) | (~c0_1(a433))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.68/0.87 tff(101,plain,
% 0.68/0.87 (~c0_1(a433)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[100, 83])).
% 0.68/0.87 tff(102,assumption,(~hskp30), introduced(assumption)).
% 0.68/0.87 tff(103,plain,
% 0.68/0.87 ((hskp30 | hskp24 | hskp14) <=> (hskp30 | hskp24 | hskp14)),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(104,plain,
% 0.68/0.87 (((hskp30 | hskp14) | hskp24) <=> (hskp30 | hskp24 | hskp14)),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(105,plain,
% 0.68/0.87 ((hskp30 | hskp14) <=> (hskp30 | hskp14)),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(106,plain,
% 0.68/0.87 (((hskp30 | hskp14) | hskp24) <=> ((hskp30 | hskp14) | hskp24)),
% 0.68/0.87 inference(monotonicity,[status(thm)],[105])).
% 0.68/0.87 tff(107,plain,
% 0.68/0.87 (((hskp30 | hskp14) | hskp24) <=> (hskp30 | hskp24 | hskp14)),
% 0.68/0.87 inference(transitivity,[status(thm)],[106, 104])).
% 0.68/0.87 tff(108,axiom,((hskp30 | hskp14) | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.68/0.87 tff(109,plain,
% 0.68/0.87 (hskp30 | hskp24 | hskp14),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.68/0.87 tff(110,plain,
% 0.68/0.87 (hskp30 | hskp24 | hskp14),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[109, 103])).
% 0.68/0.87 tff(111,plain,
% 0.68/0.87 (hskp30 | hskp24 | hskp14),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.68/0.87 tff(112,plain,
% 0.68/0.87 (hskp30 | hskp24 | hskp14),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[111, 103])).
% 0.68/0.87 tff(113,plain,
% 0.68/0.87 (hskp30 | hskp24 | hskp14),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[112, 103])).
% 0.68/0.87 tff(114,plain,
% 0.68/0.87 (hskp24),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[113, 102, 53])).
% 0.68/0.87 tff(115,plain,
% 0.68/0.87 (((~hskp24) | (~c0_1(a486))) <=> ((~hskp24) | (~c0_1(a486)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(116,plain,
% 0.68/0.87 (((~c0_1(a486)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a486)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(117,axiom,((~c0_1(a486)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.68/0.87 tff(118,plain,
% 0.68/0.87 ((~hskp24) | (~c0_1(a486))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.68/0.87 tff(119,plain,
% 0.68/0.87 ((~hskp24) | (~c0_1(a486))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[118, 115])).
% 0.68/0.87 tff(120,plain,
% 0.68/0.87 (~c0_1(a486)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[119, 114])).
% 0.68/0.87 tff(121,plain,
% 0.68/0.87 (((~hskp24) | c2_1(a486)) <=> ((~hskp24) | c2_1(a486))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(122,axiom,((~hskp24) | c2_1(a486)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.68/0.87 tff(123,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.68/0.87 tff(124,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[123, 121])).
% 0.68/0.87 tff(125,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.68/0.87 tff(126,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.68/0.87 tff(127,plain,
% 0.68/0.87 ((~hskp24) | c2_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[126, 121])).
% 0.68/0.87 tff(128,plain,
% 0.68/0.87 (c2_1(a486)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[127, 114])).
% 0.68/0.87 tff(129,plain,
% 0.68/0.87 (((~hskp24) | c1_1(a486)) <=> ((~hskp24) | c1_1(a486))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(130,axiom,((~hskp24) | c1_1(a486)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.68/0.87 tff(131,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.68/0.87 tff(132,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[131, 129])).
% 0.68/0.87 tff(133,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[132, 129])).
% 0.68/0.87 tff(134,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.68/0.87 tff(135,plain,
% 0.68/0.87 ((~hskp24) | c1_1(a486)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[134, 129])).
% 0.68/0.87 tff(136,plain,
% 0.68/0.87 (c1_1(a486)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[135, 114])).
% 0.68/0.87 tff(137,plain,
% 0.68/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(138,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[137])).
% 0.68/0.87 tff(139,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(140,plain,
% 0.68/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(141,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[140])).
% 0.68/0.87 tff(142,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.68/0.87 tff(143,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.68/0.87 tff(144,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.68/0.87 tff(145,plain,(
% 0.68/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.87 inference(skolemize,[status(sab)],[144])).
% 0.68/0.87 tff(146,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.68/0.87 tff(147,plain,
% 0.68/0.87 (^[U: $i] : refl((hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(148,plain,
% 0.68/0.87 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[147])).
% 0.68/0.87 tff(149,plain,
% 0.68/0.87 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(150,plain,
% 0.68/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp12) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp12))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp12) <=> (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(151,plain,
% 0.68/0.87 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp12) <=> ![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[150])).
% 0.68/0.87 tff(152,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.68/0.87 tff(153,plain,
% 0.68/0.87 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.68/0.87 tff(154,plain,
% 0.68/0.87 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.68/0.87 tff(155,plain,(
% 0.68/0.87 ![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.68/0.87 inference(skolemize,[status(sab)],[154])).
% 0.68/0.87 tff(156,plain,
% 0.68/0.87 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.68/0.87 tff(157,plain,
% 0.68/0.87 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(158,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[157])).
% 0.68/0.87 tff(159,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(160,plain,
% 0.68/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(161,plain,
% 0.68/0.87 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[160])).
% 0.68/0.87 tff(162,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.68/0.87 tff(163,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.68/0.87 tff(164,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.68/0.87 tff(165,plain,(
% 0.68/0.87 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.87 inference(skolemize,[status(sab)],[164])).
% 0.68/0.87 tff(166,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.68/0.87 tff(167,plain,
% 0.68/0.87 (^[U: $i] : refl((hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(168,plain,
% 0.68/0.87 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[167])).
% 0.68/0.87 tff(169,plain,
% 0.68/0.87 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(170,plain,
% 0.68/0.87 (^[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)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp16) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp16))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp16) <=> (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp16) <=> (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(171,plain,
% 0.68/0.87 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp16) <=> ![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.68/0.88 inference(quant_intro,[status(thm)],[170])).
% 0.68/0.88 tff(172,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.68/0.88 tff(173,plain,
% 0.68/0.88 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.68/0.88 tff(174,plain,
% 0.68/0.88 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.68/0.88 tff(175,plain,(
% 0.68/0.88 ![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.68/0.88 inference(skolemize,[status(sab)],[174])).
% 0.68/0.88 tff(176,plain,
% 0.68/0.88 (![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.68/0.88 tff(177,assumption,(c1_1(a486)), introduced(assumption)).
% 0.68/0.88 tff(178,assumption,(~c0_1(a486)), introduced(assumption)).
% 0.68/0.88 tff(179,assumption,(c2_1(a486)), introduced(assumption)).
% 0.68/0.88 tff(180,assumption,(~hskp0), introduced(assumption)).
% 0.68/0.88 tff(181,assumption,(~c3_1(a486)), introduced(assumption)).
% 0.68/0.88 tff(182,assumption,(~ndr1_0), introduced(assumption)).
% 0.68/0.88 tff(183,plain,
% 0.68/0.88 ((ndr1_0 | (~hskp14)) <=> (ndr1_0 | (~hskp14))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(184,plain,
% 0.68/0.88 (((~hskp14) | ndr1_0) <=> (ndr1_0 | (~hskp14))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(185,axiom,((~hskp14) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 0.68/0.88 tff(186,plain,
% 0.68/0.88 (ndr1_0 | (~hskp14)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.68/0.88 tff(187,plain,
% 0.68/0.88 (ndr1_0 | (~hskp14)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[186, 183])).
% 0.68/0.88 tff(188,plain,
% 0.68/0.88 (~hskp14),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[187, 182])).
% 0.68/0.88 tff(189,plain,
% 0.68/0.88 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(190,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.68/0.88 tff(191,plain,
% 0.68/0.88 ((~hskp30) | ndr1_0),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.68/0.88 tff(192,plain,
% 0.68/0.88 ((~hskp30) | ndr1_0),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[191, 189])).
% 0.68/0.88 tff(193,plain,
% 0.68/0.88 ((~hskp30) | ndr1_0),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[192, 189])).
% 0.68/0.88 tff(194,plain,
% 0.68/0.88 ((~hskp30) | ndr1_0),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.68/0.88 tff(195,plain,
% 0.68/0.88 ((~hskp30) | ndr1_0),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[194, 189])).
% 0.68/0.88 tff(196,plain,
% 0.68/0.88 (~hskp30),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[195, 182])).
% 0.68/0.88 tff(197,plain,
% 0.68/0.88 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(198,plain,
% 0.68/0.88 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(199,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 0.68/0.88 tff(200,plain,
% 0.68/0.88 (ndr1_0 | (~hskp24)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.68/0.88 tff(201,plain,
% 0.68/0.88 (ndr1_0 | (~hskp24)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[200, 197])).
% 0.68/0.88 tff(202,plain,
% 0.68/0.88 (~hskp24),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[201, 182])).
% 0.68/0.88 tff(203,plain,
% 0.68/0.88 ($false),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[113, 202, 196, 188])).
% 0.68/0.88 tff(204,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.68/0.88 tff(205,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(206,plain,
% 0.68/0.88 (((~ndr1_0) | c3_1(a445) | c1_1(a445) | (~c2_1(a445)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486))) <=> (c0_1(a486) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(207,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a445) | c1_1(a445) | (~c2_1(a445)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[206])).
% 0.68/0.88 tff(208,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a445) | c1_1(a445) | (~c2_1(a445)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[207, 205])).
% 0.68/0.88 tff(209,plain,
% 0.68/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a445) | c1_1(a445) | (~c2_1(a445)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(210,plain,
% 0.68/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.68/0.88 tff(211,plain,
% 0.68/0.88 ((~c2_1(a445)) | c3_1(a486)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[210, 204, 177, 179, 178, 52, 51, 10])).
% 0.68/0.88 tff(212,plain,
% 0.68/0.88 (~c2_1(a445)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[211, 181])).
% 0.68/0.88 tff(213,plain,
% 0.68/0.88 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.68/0.88 inference(bind,[status(th)],[])).
% 0.68/0.88 tff(214,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.68/0.88 inference(quant_intro,[status(thm)],[213])).
% 0.68/0.88 tff(215,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(216,plain,
% 0.68/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.68/0.88 inference(bind,[status(th)],[])).
% 0.68/0.88 tff(217,plain,
% 0.68/0.88 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.68/0.88 inference(quant_intro,[status(thm)],[216])).
% 0.68/0.88 tff(218,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.68/0.88 tff(219,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.68/0.88 tff(220,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.68/0.88 tff(221,plain,(
% 0.68/0.88 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.68/0.88 inference(skolemize,[status(sab)],[220])).
% 0.68/0.88 tff(222,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.68/0.88 tff(223,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | c2_1(a445) | c3_1(a486) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | c2_1(a445) | c3_1(a486) | (~c2_1(a486)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(224,plain,
% 0.68/0.88 ((hskp0 | (~ndr1_0) | c3_1(a486) | c0_1(a486) | (~c2_1(a486)) | c2_1(a445) | c1_1(a445) | c0_1(a445)) <=> (hskp0 | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | c2_1(a445) | c3_1(a486) | (~c2_1(a486)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(225,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a486) | c0_1(a486) | (~c2_1(a486)) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | c2_1(a445) | c3_1(a486) | (~c2_1(a486))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[224])).
% 0.68/0.88 tff(226,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a486) | c0_1(a486) | (~c2_1(a486)) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | c2_1(a445) | c3_1(a486) | (~c2_1(a486)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[225, 223])).
% 0.68/0.88 tff(227,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a486) | c0_1(a486) | (~c2_1(a486)) | c2_1(a445) | c1_1(a445) | c0_1(a445))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(228,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | c2_1(a445) | c3_1(a486) | (~c2_1(a486))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.68/0.88 tff(229,plain,
% 0.68/0.88 ($false),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[228, 204, 180, 179, 178, 40, 52, 222, 181, 212])).
% 0.68/0.88 tff(230,plain,(c3_1(a486) | hskp0 | (~c2_1(a486)) | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~c1_1(a486)) | c3_1(a445)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.88 tff(231,plain,
% 0.68/0.88 (c3_1(a486)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[230, 180, 179, 178, 40, 52, 177, 51])).
% 0.68/0.88 tff(232,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a486) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c2_1(a486)) | (~c3_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a486) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c2_1(a486)) | (~c3_1(a486)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(233,plain,
% 0.68/0.88 ((hskp14 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a445) | c3_1(a445) | (~c2_1(a445))) <=> (hskp14 | c0_1(a486) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c2_1(a486)) | (~c3_1(a486)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(234,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a445) | c3_1(a445) | (~c2_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a486) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c2_1(a486)) | (~c3_1(a486))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[233])).
% 0.68/0.88 tff(235,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a445) | c3_1(a445) | (~c2_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a486) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c2_1(a486)) | (~c3_1(a486)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[234, 232])).
% 0.68/0.88 tff(236,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a445) | c3_1(a445) | (~c2_1(a445)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(237,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a486) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c2_1(a486)) | (~c3_1(a486))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.68/0.88 tff(238,plain,
% 0.68/0.88 (c3_1(a445) | (~c2_1(a445)) | (~c3_1(a486))),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[237, 204, 53, 179, 178, 40, 64])).
% 0.68/0.88 tff(239,plain,
% 0.68/0.88 (~c2_1(a445)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[238, 231, 51])).
% 0.68/0.88 tff(240,plain,
% 0.68/0.88 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.68/0.88 inference(bind,[status(th)],[])).
% 0.68/0.88 tff(241,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.88 inference(quant_intro,[status(thm)],[240])).
% 0.68/0.88 tff(242,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(243,plain,
% 0.68/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.68/0.88 inference(bind,[status(th)],[])).
% 0.68/0.88 tff(244,plain,
% 0.68/0.88 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.88 inference(quant_intro,[status(thm)],[243])).
% 0.68/0.88 tff(245,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.68/0.88 tff(246,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.68/0.88 tff(247,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.68/0.88 tff(248,plain,(
% 0.68/0.88 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.88 inference(skolemize,[status(sab)],[247])).
% 0.68/0.88 tff(249,plain,
% 0.68/0.88 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.68/0.88 tff(250,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | c0_1(a486) | (~ndr1_0) | (~c1_1(a486)) | (~c2_1(a486)) | (~c3_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a486) | (~ndr1_0) | (~c1_1(a486)) | (~c2_1(a486)) | (~c3_1(a486)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(251,plain,
% 0.68/0.88 ((hskp8 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486))) <=> (hskp8 | c0_1(a486) | (~ndr1_0) | (~c1_1(a486)) | (~c2_1(a486)) | (~c3_1(a486)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(252,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | c0_1(a486) | (~ndr1_0) | (~c1_1(a486)) | (~c2_1(a486)) | (~c3_1(a486))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[251])).
% 0.68/0.88 tff(253,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a486) | (~ndr1_0) | (~c1_1(a486)) | (~c2_1(a486)) | (~c3_1(a486)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[252, 250])).
% 0.68/0.88 tff(254,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(255,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a486) | (~ndr1_0) | (~c1_1(a486)) | (~c2_1(a486)) | (~c3_1(a486))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.68/0.88 tff(256,plain,
% 0.68/0.88 (hskp8 | (~c3_1(a486))),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[255, 204, 177, 179, 178, 249])).
% 0.68/0.88 tff(257,plain,
% 0.68/0.88 (hskp8),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[256, 231])).
% 0.68/0.88 tff(258,plain,
% 0.68/0.88 (((~hskp8) | (~c3_1(a444))) <=> ((~hskp8) | (~c3_1(a444)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(259,plain,
% 0.68/0.88 (((~c3_1(a444)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a444)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(260,axiom,((~c3_1(a444)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.68/0.88 tff(261,plain,
% 0.68/0.88 ((~hskp8) | (~c3_1(a444))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.68/0.88 tff(262,plain,
% 0.68/0.88 ((~hskp8) | (~c3_1(a444))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[261, 258])).
% 0.68/0.88 tff(263,plain,
% 0.68/0.88 (~c3_1(a444)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[262, 257])).
% 0.68/0.88 tff(264,plain,
% 0.68/0.88 (((~hskp8) | (~c0_1(a444))) <=> ((~hskp8) | (~c0_1(a444)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(265,plain,
% 0.68/0.88 (((~c0_1(a444)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a444)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(266,axiom,((~c0_1(a444)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.68/0.88 tff(267,plain,
% 0.68/0.88 ((~hskp8) | (~c0_1(a444))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.68/0.88 tff(268,plain,
% 0.68/0.88 ((~hskp8) | (~c0_1(a444))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[267, 264])).
% 0.68/0.88 tff(269,plain,
% 0.68/0.88 (~c0_1(a444)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[268, 257])).
% 0.68/0.88 tff(270,plain,
% 0.68/0.88 (((~hskp8) | c2_1(a444)) <=> ((~hskp8) | c2_1(a444))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(271,axiom,((~hskp8) | c2_1(a444)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.68/0.88 tff(272,plain,
% 0.68/0.88 ((~hskp8) | c2_1(a444)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.68/0.88 tff(273,plain,
% 0.68/0.88 ((~hskp8) | c2_1(a444)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[272, 270])).
% 0.68/0.88 tff(274,plain,
% 0.68/0.88 ((~hskp8) | c2_1(a444)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[273, 270])).
% 0.68/0.88 tff(275,plain,
% 0.68/0.88 ((~hskp8) | c2_1(a444)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.68/0.88 tff(276,plain,
% 0.68/0.88 ((~hskp8) | c2_1(a444)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[275, 270])).
% 0.68/0.88 tff(277,plain,
% 0.68/0.88 (c2_1(a444)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[276, 257])).
% 0.68/0.88 tff(278,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c2_1(a445))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c2_1(a445))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(279,plain,
% 0.68/0.88 ((hskp0 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c2_1(a445) | c1_1(a445) | c0_1(a445)) <=> (hskp0 | c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c2_1(a445))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(280,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c2_1(a445)))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[279])).
% 0.68/0.88 tff(281,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c2_1(a445))),
% 0.68/0.88 inference(transitivity,[status(thm)],[280, 278])).
% 0.68/0.88 tff(282,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c2_1(a445) | c1_1(a445) | c0_1(a445))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(283,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c2_1(a445)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.68/0.88 tff(284,plain,
% 0.68/0.88 ($false),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[283, 204, 180, 277, 40, 52, 269, 263, 222, 239])).
% 0.68/0.88 tff(285,plain,(hskp0 | c0_1(a445) | c1_1(a445) | c3_1(a445) | hskp14 | (~c2_1(a486)) | c0_1(a486) | (~c1_1(a486))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.88 tff(286,plain,
% 0.68/0.88 (hskp0),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[285, 51, 52, 40, 53, 128, 120, 136])).
% 0.68/0.89 tff(287,plain,
% 0.68/0.89 (((~hskp0) | (~c2_1(a432))) <=> ((~hskp0) | (~c2_1(a432)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(288,plain,
% 0.68/0.89 (((~c2_1(a432)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a432)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(289,axiom,((~c2_1(a432)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.68/0.89 tff(290,plain,
% 0.68/0.89 ((~hskp0) | (~c2_1(a432))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.68/0.89 tff(291,plain,
% 0.68/0.89 ((~hskp0) | (~c2_1(a432))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[290, 287])).
% 0.68/0.89 tff(292,plain,
% 0.68/0.89 (~c2_1(a432)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[291, 286])).
% 0.68/0.89 tff(293,plain,
% 0.68/0.89 (((~hskp0) | (~c0_1(a432))) <=> ((~hskp0) | (~c0_1(a432)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(294,plain,
% 0.68/0.89 (((~c0_1(a432)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a432)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(295,axiom,((~c0_1(a432)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.68/0.89 tff(296,plain,
% 0.68/0.89 ((~hskp0) | (~c0_1(a432))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.68/0.89 tff(297,plain,
% 0.68/0.89 ((~hskp0) | (~c0_1(a432))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[296, 293])).
% 0.68/0.89 tff(298,plain,
% 0.68/0.89 (~c0_1(a432)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[297, 286])).
% 0.68/0.89 tff(299,plain,
% 0.68/0.89 (((~hskp0) | c3_1(a432)) <=> ((~hskp0) | c3_1(a432))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(300,axiom,((~hskp0) | c3_1(a432)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.68/0.89 tff(301,plain,
% 0.68/0.89 ((~hskp0) | c3_1(a432)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.68/0.89 tff(302,plain,
% 0.68/0.89 ((~hskp0) | c3_1(a432)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[301, 299])).
% 0.68/0.89 tff(303,plain,
% 0.68/0.89 ((~hskp0) | c3_1(a432)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[302, 299])).
% 0.68/0.89 tff(304,plain,
% 0.68/0.89 ((~hskp0) | c3_1(a432)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.68/0.89 tff(305,plain,
% 0.68/0.89 ((~hskp0) | c3_1(a432)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[304, 299])).
% 0.68/0.89 tff(306,plain,
% 0.68/0.89 (c3_1(a432)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[305, 286])).
% 0.68/0.89 tff(307,plain,
% 0.68/0.89 (((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)))) <=> ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp16 | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(308,plain,
% 0.68/0.89 ((hskp30 | hskp16 | (~ndr1_0) | c2_1(a432) | c0_1(a432) | (~c3_1(a432))) <=> (hskp30 | hskp16 | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(309,plain,
% 0.68/0.89 (((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | (~ndr1_0) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[308])).
% 0.68/0.89 tff(310,plain,
% 0.68/0.89 (((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | (~ndr1_0) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp16 | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[309, 307])).
% 0.68/0.89 tff(311,plain,
% 0.68/0.89 ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | (~ndr1_0) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(312,plain,
% 0.68/0.89 ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp16 | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.68/0.89 tff(313,plain,
% 0.68/0.89 (hskp16),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[312, 102, 204, 306, 298, 292, 176])).
% 0.68/0.89 tff(314,plain,
% 0.68/0.89 (((~hskp16) | (~c2_1(a457))) <=> ((~hskp16) | (~c2_1(a457)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(315,plain,
% 0.68/0.89 (((~c2_1(a457)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a457)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(316,axiom,((~c2_1(a457)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.68/0.89 tff(317,plain,
% 0.68/0.89 ((~hskp16) | (~c2_1(a457))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.68/0.89 tff(318,plain,
% 0.68/0.89 ((~hskp16) | (~c2_1(a457))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[317, 314])).
% 0.68/0.89 tff(319,plain,
% 0.68/0.89 (~c2_1(a457)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[318, 313])).
% 0.68/0.89 tff(320,plain,
% 0.68/0.89 (((~hskp16) | c3_1(a457)) <=> ((~hskp16) | c3_1(a457))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(321,axiom,((~hskp16) | c3_1(a457)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.68/0.89 tff(322,plain,
% 0.68/0.89 ((~hskp16) | c3_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.68/0.89 tff(323,plain,
% 0.68/0.89 ((~hskp16) | c3_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[322, 320])).
% 0.68/0.89 tff(324,plain,
% 0.68/0.89 ((~hskp16) | c3_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[323, 320])).
% 0.68/0.89 tff(325,plain,
% 0.68/0.89 ((~hskp16) | c3_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.68/0.89 tff(326,plain,
% 0.68/0.89 ((~hskp16) | c3_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[325, 320])).
% 0.68/0.89 tff(327,plain,
% 0.68/0.89 (c3_1(a457)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[326, 313])).
% 0.68/0.89 tff(328,plain,
% 0.68/0.89 (((~hskp16) | c1_1(a457)) <=> ((~hskp16) | c1_1(a457))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(329,axiom,((~hskp16) | c1_1(a457)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.68/0.89 tff(330,plain,
% 0.68/0.89 ((~hskp16) | c1_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.68/0.89 tff(331,plain,
% 0.68/0.89 ((~hskp16) | c1_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[330, 328])).
% 0.68/0.89 tff(332,plain,
% 0.68/0.89 ((~hskp16) | c1_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[331, 328])).
% 0.68/0.89 tff(333,plain,
% 0.68/0.89 ((~hskp16) | c1_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[332, 328])).
% 0.68/0.89 tff(334,plain,
% 0.68/0.89 ((~hskp16) | c1_1(a457)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[333, 328])).
% 0.68/0.89 tff(335,plain,
% 0.68/0.89 (c1_1(a457)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[334, 313])).
% 0.68/0.89 tff(336,plain,
% 0.68/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | c0_1(a486) | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a486) | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(337,plain,
% 0.68/0.89 ((hskp6 | (~ndr1_0) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486))) <=> (hskp6 | c0_1(a486) | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(338,plain,
% 0.68/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | c0_1(a486) | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[337])).
% 0.68/0.89 tff(339,plain,
% 0.68/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a486) | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[338, 336])).
% 0.68/0.89 tff(340,plain,
% 0.68/0.89 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(341,plain,
% 0.68/0.89 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a486) | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.68/0.89 tff(342,plain,
% 0.68/0.89 (hskp6),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[341, 204, 136, 128, 335, 327, 120, 319, 166])).
% 0.68/0.89 tff(343,plain,
% 0.68/0.89 (((~hskp6) | (~c3_1(a442))) <=> ((~hskp6) | (~c3_1(a442)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(344,plain,
% 0.68/0.89 (((~c3_1(a442)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a442)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(345,axiom,((~c3_1(a442)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.68/0.89 tff(346,plain,
% 0.68/0.89 ((~hskp6) | (~c3_1(a442))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.68/0.89 tff(347,plain,
% 0.68/0.89 ((~hskp6) | (~c3_1(a442))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[346, 343])).
% 0.68/0.89 tff(348,plain,
% 0.68/0.89 (~c3_1(a442)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[347, 342])).
% 0.68/0.89 tff(349,plain,
% 0.68/0.89 (((~hskp6) | c2_1(a442)) <=> ((~hskp6) | c2_1(a442))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(350,axiom,((~hskp6) | c2_1(a442)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.68/0.89 tff(351,plain,
% 0.68/0.89 ((~hskp6) | c2_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.68/0.89 tff(352,plain,
% 0.68/0.89 ((~hskp6) | c2_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[351, 349])).
% 0.68/0.89 tff(353,plain,
% 0.68/0.89 ((~hskp6) | c2_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[352, 349])).
% 0.68/0.89 tff(354,plain,
% 0.68/0.89 ((~hskp6) | c2_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[353, 349])).
% 0.68/0.89 tff(355,plain,
% 0.68/0.89 ((~hskp6) | c2_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[354, 349])).
% 0.68/0.89 tff(356,plain,
% 0.68/0.89 (c2_1(a442)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[355, 342])).
% 0.68/0.89 tff(357,plain,
% 0.68/0.89 (((~hskp6) | c0_1(a442)) <=> ((~hskp6) | c0_1(a442))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(358,axiom,((~hskp6) | c0_1(a442)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.68/0.89 tff(359,plain,
% 0.68/0.89 ((~hskp6) | c0_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.68/0.89 tff(360,plain,
% 0.68/0.89 ((~hskp6) | c0_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[359, 357])).
% 0.68/0.89 tff(361,plain,
% 0.68/0.89 ((~hskp6) | c0_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[360, 357])).
% 0.68/0.89 tff(362,plain,
% 0.68/0.89 ((~hskp6) | c0_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[361, 357])).
% 0.68/0.89 tff(363,plain,
% 0.68/0.89 ((~hskp6) | c0_1(a442)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[362, 357])).
% 0.68/0.89 tff(364,plain,
% 0.68/0.89 (c0_1(a442)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[363, 342])).
% 0.68/0.89 tff(365,plain,
% 0.68/0.89 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | c3_1(a442) | (~ndr1_0) | (~c0_1(a442)) | (~c2_1(a442)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp12 | c3_1(a442) | (~ndr1_0) | (~c0_1(a442)) | (~c2_1(a442)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(366,plain,
% 0.68/0.89 ((hskp14 | hskp12 | (~ndr1_0) | c3_1(a442) | (~c2_1(a442)) | (~c0_1(a442))) <=> (hskp14 | hskp12 | c3_1(a442) | (~ndr1_0) | (~c0_1(a442)) | (~c2_1(a442)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(367,plain,
% 0.68/0.89 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c3_1(a442) | (~c2_1(a442)) | (~c0_1(a442)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | c3_1(a442) | (~ndr1_0) | (~c0_1(a442)) | (~c2_1(a442))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[366])).
% 0.68/0.89 tff(368,plain,
% 0.68/0.89 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c3_1(a442) | (~c2_1(a442)) | (~c0_1(a442)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp12 | c3_1(a442) | (~ndr1_0) | (~c0_1(a442)) | (~c2_1(a442)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[367, 365])).
% 0.68/0.89 tff(369,plain,
% 0.68/0.89 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c3_1(a442) | (~c2_1(a442)) | (~c0_1(a442)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(370,plain,
% 0.68/0.89 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp12 | c3_1(a442) | (~ndr1_0) | (~c0_1(a442)) | (~c2_1(a442))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.68/0.89 tff(371,plain,
% 0.68/0.89 (hskp12),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[370, 204, 53, 364, 356, 348, 156])).
% 0.68/0.89 tff(372,plain,
% 0.68/0.89 (((~hskp12) | (~c0_1(a450))) <=> ((~hskp12) | (~c0_1(a450)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(373,plain,
% 0.68/0.89 (((~c0_1(a450)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a450)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(374,axiom,((~c0_1(a450)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.68/0.89 tff(375,plain,
% 0.68/0.89 ((~hskp12) | (~c0_1(a450))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.68/0.89 tff(376,plain,
% 0.68/0.89 ((~hskp12) | (~c0_1(a450))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[375, 372])).
% 0.68/0.89 tff(377,plain,
% 0.68/0.89 (~c0_1(a450)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[376, 371])).
% 0.68/0.89 tff(378,plain,
% 0.68/0.89 (^[U: $i] : refl((hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.68/0.89 inference(bind,[status(th)],[])).
% 0.68/0.89 tff(379,plain,
% 0.68/0.89 (![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.89 inference(quant_intro,[status(thm)],[378])).
% 0.68/0.89 tff(380,plain,
% 0.68/0.89 (![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(381,plain,
% 0.68/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp26) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp26))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp26) <=> (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp26) <=> (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.68/0.89 inference(bind,[status(th)],[])).
% 0.68/0.89 tff(382,plain,
% 0.68/0.89 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp26) <=> ![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.89 inference(quant_intro,[status(thm)],[381])).
% 0.68/0.89 tff(383,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.68/0.89 tff(384,plain,
% 0.68/0.89 (![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.68/0.89 tff(385,plain,
% 0.68/0.89 (![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[384, 380])).
% 0.68/0.89 tff(386,plain,(
% 0.68/0.89 ![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.89 inference(skolemize,[status(sab)],[385])).
% 0.68/0.89 tff(387,plain,
% 0.68/0.89 (![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[386, 379])).
% 0.68/0.89 tff(388,plain,
% 0.68/0.89 (((~![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp26 | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)))) <=> ((~![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp26 | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(389,plain,
% 0.68/0.89 ((hskp30 | hskp26 | (~ndr1_0) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457))) <=> (hskp30 | hskp26 | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(390,plain,
% 0.68/0.89 (((~![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp26 | (~ndr1_0) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)))) <=> ((~![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp26 | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[389])).
% 0.68/0.89 tff(391,plain,
% 0.68/0.89 (((~![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp26 | (~ndr1_0) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)))) <=> ((~![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp26 | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[390, 388])).
% 0.68/0.89 tff(392,plain,
% 0.68/0.89 ((~![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp30 | hskp26 | (~ndr1_0) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(393,plain,
% 0.68/0.89 ((~![U: $i] : (hskp30 | hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp30 | hskp26 | c2_1(a457) | (~ndr1_0) | (~c3_1(a457)) | (~c1_1(a457))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.68/0.89 tff(394,plain,
% 0.68/0.89 (hskp26),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[393, 102, 204, 335, 327, 319, 387])).
% 0.68/0.89 tff(395,plain,
% 0.68/0.89 (((~hskp26) | (~c3_1(a492))) <=> ((~hskp26) | (~c3_1(a492)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(396,plain,
% 0.68/0.89 (((~c3_1(a492)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a492)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(397,axiom,((~c3_1(a492)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.68/0.89 tff(398,plain,
% 0.68/0.89 ((~hskp26) | (~c3_1(a492))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.68/0.89 tff(399,plain,
% 0.68/0.89 ((~hskp26) | (~c3_1(a492))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[398, 395])).
% 0.68/0.89 tff(400,plain,
% 0.68/0.89 (~c3_1(a492)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[399, 394])).
% 0.68/0.89 tff(401,plain,
% 0.68/0.89 (((~hskp12) | c3_1(a450)) <=> ((~hskp12) | c3_1(a450))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(402,axiom,((~hskp12) | c3_1(a450)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.68/0.89 tff(403,plain,
% 0.68/0.89 ((~hskp12) | c3_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.68/0.89 tff(404,plain,
% 0.68/0.89 ((~hskp12) | c3_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[403, 401])).
% 0.68/0.89 tff(405,plain,
% 0.68/0.89 ((~hskp12) | c3_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[404, 401])).
% 0.68/0.89 tff(406,plain,
% 0.68/0.89 ((~hskp12) | c3_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[405, 401])).
% 0.68/0.89 tff(407,plain,
% 0.68/0.89 ((~hskp12) | c3_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[406, 401])).
% 0.68/0.89 tff(408,plain,
% 0.68/0.89 (c3_1(a450)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[407, 371])).
% 0.68/0.89 tff(409,plain,
% 0.68/0.89 (((~hskp12) | c1_1(a450)) <=> ((~hskp12) | c1_1(a450))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(410,axiom,((~hskp12) | c1_1(a450)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.68/0.89 tff(411,plain,
% 0.68/0.89 ((~hskp12) | c1_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.68/0.89 tff(412,plain,
% 0.68/0.89 ((~hskp12) | c1_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[411, 409])).
% 0.68/0.89 tff(413,plain,
% 0.68/0.89 ((~hskp12) | c1_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[412, 409])).
% 0.68/0.89 tff(414,plain,
% 0.68/0.89 ((~hskp12) | c1_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[413, 409])).
% 0.68/0.89 tff(415,plain,
% 0.68/0.89 ((~hskp12) | c1_1(a450)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[414, 409])).
% 0.68/0.89 tff(416,plain,
% 0.68/0.89 (c1_1(a450)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[415, 371])).
% 0.68/0.89 tff(417,plain,
% 0.68/0.89 (((~hskp26) | c2_1(a492)) <=> ((~hskp26) | c2_1(a492))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(418,axiom,((~hskp26) | c2_1(a492)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.68/0.89 tff(419,plain,
% 0.68/0.89 ((~hskp26) | c2_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.68/0.89 tff(420,plain,
% 0.68/0.89 ((~hskp26) | c2_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[419, 417])).
% 0.68/0.89 tff(421,plain,
% 0.68/0.89 ((~hskp26) | c2_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[420, 417])).
% 0.68/0.89 tff(422,plain,
% 0.68/0.89 ((~hskp26) | c2_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[421, 417])).
% 0.68/0.89 tff(423,plain,
% 0.68/0.89 ((~hskp26) | c2_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[422, 417])).
% 0.68/0.89 tff(424,plain,
% 0.68/0.89 (c2_1(a492)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[423, 394])).
% 0.68/0.89 tff(425,plain,
% 0.68/0.89 (((~hskp26) | c1_1(a492)) <=> ((~hskp26) | c1_1(a492))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(426,axiom,((~hskp26) | c1_1(a492)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.68/0.89 tff(427,plain,
% 0.68/0.89 ((~hskp26) | c1_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.68/0.89 tff(428,plain,
% 0.68/0.89 ((~hskp26) | c1_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[427, 425])).
% 0.68/0.89 tff(429,plain,
% 0.68/0.89 ((~hskp26) | c1_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[428, 425])).
% 0.68/0.89 tff(430,plain,
% 0.68/0.89 ((~hskp26) | c1_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[429, 425])).
% 0.68/0.89 tff(431,plain,
% 0.68/0.89 ((~hskp26) | c1_1(a492)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[430, 425])).
% 0.68/0.89 tff(432,plain,
% 0.68/0.89 (c1_1(a492)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[431, 394])).
% 0.68/0.89 tff(433,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a492) | c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c1_1(a492)) | (~c2_1(a492)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a492) | c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c1_1(a492)) | (~c2_1(a492)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(434,plain,
% 0.68/0.89 (((~ndr1_0) | c3_1(a492) | (~c2_1(a492)) | (~c1_1(a492)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445))) <=> (c3_1(a492) | c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c1_1(a492)) | (~c2_1(a492)))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(435,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a492) | (~c2_1(a492)) | (~c1_1(a492)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a492) | c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c1_1(a492)) | (~c2_1(a492))))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[434])).
% 0.68/0.89 tff(436,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a492) | (~c2_1(a492)) | (~c1_1(a492)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a492) | c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c1_1(a492)) | (~c2_1(a492)))),
% 0.68/0.89 inference(transitivity,[status(thm)],[435, 433])).
% 0.68/0.89 tff(437,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a492) | (~c2_1(a492)) | (~c1_1(a492)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445)))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(438,plain,
% 0.68/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a492) | c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c1_1(a492)) | (~c2_1(a492))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.68/0.89 tff(439,plain,
% 0.68/0.89 (~c2_1(a445)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[438, 204, 432, 424, 416, 408, 400, 377, 40, 52, 146])).
% 0.68/0.89 tff(440,plain,
% 0.68/0.89 (^[U: $i] : refl((hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 0.68/0.89 inference(bind,[status(th)],[])).
% 0.68/0.89 tff(441,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.68/0.89 inference(quant_intro,[status(thm)],[440])).
% 0.68/0.89 tff(442,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(443,plain,
% 0.68/0.89 (^[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) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp29) | hskp10) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp10))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp10) <=> (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp29) | hskp10) <=> (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 0.68/0.89 inference(bind,[status(th)],[])).
% 0.68/0.89 tff(444,plain,
% 0.68/0.89 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp29) | hskp10) <=> ![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.68/0.89 inference(quant_intro,[status(thm)],[443])).
% 0.68/0.89 tff(445,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp29) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.68/0.89 tff(446,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.68/0.89 tff(447,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[446, 442])).
% 0.68/0.89 tff(448,plain,(
% 0.68/0.89 ![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.68/0.89 inference(skolemize,[status(sab)],[447])).
% 0.68/0.89 tff(449,plain,
% 0.68/0.89 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[448, 441])).
% 0.68/0.89 tff(450,plain,
% 0.68/0.89 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | c0_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp29 | hskp10 | c0_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(451,plain,
% 0.68/0.89 ((hskp29 | hskp10 | (~ndr1_0) | c3_1(a445) | c2_1(a445) | c0_1(a445)) <=> (hskp29 | hskp10 | c0_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(452,plain,
% 0.68/0.89 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a445) | c2_1(a445) | c0_1(a445))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | c0_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445)))),
% 0.68/0.89 inference(monotonicity,[status(thm)],[451])).
% 0.68/0.89 tff(453,plain,
% 0.68/0.89 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a445) | c2_1(a445) | c0_1(a445))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp29 | hskp10 | c0_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445))),
% 0.68/0.89 inference(transitivity,[status(thm)],[452, 450])).
% 0.68/0.89 tff(454,plain,
% 0.68/0.89 ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a445) | c2_1(a445) | c0_1(a445))),
% 0.68/0.89 inference(quant_inst,[status(thm)],[])).
% 0.68/0.89 tff(455,plain,
% 0.68/0.89 ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp29 | hskp10 | c0_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.68/0.89 tff(456,plain,
% 0.68/0.89 (hskp29 | c3_1(a445) | c2_1(a445)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[455, 204, 54, 40, 449])).
% 0.68/0.89 tff(457,plain,
% 0.68/0.89 (hskp29),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[456, 439, 51])).
% 0.68/0.89 tff(458,plain,
% 0.68/0.89 (((~hskp29) | c3_1(a447)) <=> ((~hskp29) | c3_1(a447))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(459,axiom,((~hskp29) | c3_1(a447)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.68/0.89 tff(460,plain,
% 0.68/0.89 ((~hskp29) | c3_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.68/0.89 tff(461,plain,
% 0.68/0.89 ((~hskp29) | c3_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[460, 458])).
% 0.68/0.89 tff(462,plain,
% 0.68/0.89 ((~hskp29) | c3_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[461, 458])).
% 0.68/0.89 tff(463,plain,
% 0.68/0.89 ((~hskp29) | c3_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[462, 458])).
% 0.68/0.89 tff(464,plain,
% 0.68/0.89 ((~hskp29) | c3_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[463, 458])).
% 0.68/0.89 tff(465,plain,
% 0.68/0.89 (c3_1(a447)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[464, 457])).
% 0.68/0.89 tff(466,plain,
% 0.68/0.89 (((~hskp29) | c2_1(a447)) <=> ((~hskp29) | c2_1(a447))),
% 0.68/0.89 inference(rewrite,[status(thm)],[])).
% 0.68/0.89 tff(467,axiom,((~hskp29) | c2_1(a447)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.68/0.89 tff(468,plain,
% 0.68/0.89 ((~hskp29) | c2_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.68/0.89 tff(469,plain,
% 0.68/0.89 ((~hskp29) | c2_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[468, 466])).
% 0.68/0.89 tff(470,plain,
% 0.68/0.89 ((~hskp29) | c2_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[469, 466])).
% 0.68/0.89 tff(471,plain,
% 0.68/0.89 ((~hskp29) | c2_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[470, 466])).
% 0.68/0.89 tff(472,plain,
% 0.68/0.89 ((~hskp29) | c2_1(a447)),
% 0.68/0.89 inference(modus_ponens,[status(thm)],[471, 466])).
% 0.68/0.89 tff(473,plain,
% 0.68/0.89 (c2_1(a447)),
% 0.68/0.89 inference(unit_resolution,[status(thm)],[472, 457])).
% 0.68/0.89 tff(474,plain,
% 0.68/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(475,plain,
% 0.68/0.90 (((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c0_1(a447)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a445) | c1_1(a445) | c0_1(a445)) <=> (c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(476,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c0_1(a447)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[475])).
% 0.68/0.90 tff(477,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c0_1(a447)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[476, 474])).
% 0.68/0.90 tff(478,plain,
% 0.68/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c0_1(a447)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a445) | c1_1(a445) | c0_1(a445))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(479,plain,
% 0.68/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.68/0.90 tff(480,plain,
% 0.68/0.90 (~c0_1(a447)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[479, 204, 473, 465, 40, 52, 51, 74, 439])).
% 0.68/0.90 tff(481,plain,
% 0.68/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.68/0.90 inference(bind,[status(th)],[])).
% 0.68/0.90 tff(482,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.90 inference(quant_intro,[status(thm)],[481])).
% 0.68/0.90 tff(483,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(484,plain,
% 0.68/0.90 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.68/0.90 inference(bind,[status(th)],[])).
% 0.68/0.90 tff(485,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.90 inference(quant_intro,[status(thm)],[484])).
% 0.68/0.90 tff(486,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.68/0.90 tff(487,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.68/0.90 tff(488,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[487, 483])).
% 0.68/0.90 tff(489,plain,(
% 0.68/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.90 inference(skolemize,[status(sab)],[488])).
% 0.68/0.90 tff(490,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[489, 482])).
% 0.68/0.90 tff(491,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a486) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a486) | (~c1_1(a486)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a486) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a486) | (~c1_1(a486)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(492,plain,
% 0.68/0.90 (((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432))) <=> (c0_1(a486) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a486) | (~c1_1(a486)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(493,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a486) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a486) | (~c1_1(a486)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[492])).
% 0.68/0.90 tff(494,plain,
% 0.68/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a486) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a486) | (~c1_1(a486)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[493, 491])).
% 0.68/0.90 tff(495,plain,
% 0.68/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(496,plain,
% 0.68/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a486) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a486) | (~c1_1(a486)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.68/0.90 tff(497,plain,
% 0.68/0.90 (c3_1(a486)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[496, 204, 473, 465, 136, 306, 120, 298, 292, 490, 480])).
% 0.68/0.90 tff(498,plain,
% 0.68/0.90 (((~hskp29) | c1_1(a447)) <=> ((~hskp29) | c1_1(a447))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(499,axiom,((~hskp29) | c1_1(a447)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.68/0.90 tff(500,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a447)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.68/0.90 tff(501,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a447)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[500, 498])).
% 0.68/0.90 tff(502,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a447)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[501, 498])).
% 0.68/0.90 tff(503,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a447)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.68/0.90 tff(504,plain,
% 0.68/0.90 ((~hskp29) | c1_1(a447)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[503, 498])).
% 0.68/0.90 tff(505,plain,
% 0.68/0.90 (c1_1(a447)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[504, 457])).
% 0.68/0.90 tff(506,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | c0_1(a486) | (~ndr1_0) | (~c2_1(a486)) | (~c3_1(a486)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a486) | (~ndr1_0) | (~c2_1(a486)) | (~c3_1(a486)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(507,plain,
% 0.68/0.90 ((hskp8 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a447) | (~c1_1(a447)) | (~c2_1(a447))) <=> (hskp8 | c0_1(a486) | (~ndr1_0) | (~c2_1(a486)) | (~c3_1(a486)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(508,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a447) | (~c1_1(a447)) | (~c2_1(a447)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | c0_1(a486) | (~ndr1_0) | (~c2_1(a486)) | (~c3_1(a486)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[507])).
% 0.68/0.90 tff(509,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a447) | (~c1_1(a447)) | (~c2_1(a447)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a486) | (~ndr1_0) | (~c2_1(a486)) | (~c3_1(a486)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[508, 506])).
% 0.68/0.90 tff(510,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a447) | (~c1_1(a447)) | (~c2_1(a447)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(511,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a486) | (~ndr1_0) | (~c2_1(a486)) | (~c3_1(a486)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.68/0.90 tff(512,plain,
% 0.68/0.90 (hskp8),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[511, 204, 505, 473, 128, 120, 249, 497, 480])).
% 0.68/0.90 tff(513,plain,
% 0.68/0.90 (~c3_1(a444)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[262, 512])).
% 0.68/0.90 tff(514,plain,
% 0.68/0.90 (~c0_1(a444)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[268, 512])).
% 0.68/0.90 tff(515,plain,
% 0.68/0.90 (c2_1(a444)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[276, 512])).
% 0.68/0.90 tff(516,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a486)) | (~c3_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a486)) | (~c3_1(a486)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(517,plain,
% 0.68/0.90 ((hskp14 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444))) <=> (hskp14 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a486)) | (~c3_1(a486)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(518,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a486)) | (~c3_1(a486))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[517])).
% 0.68/0.90 tff(519,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a486)) | (~c3_1(a486)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[518, 516])).
% 0.68/0.90 tff(520,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a486) | (~c2_1(a486)) | (~c3_1(a486)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(521,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a486)) | (~c3_1(a486))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.68/0.90 tff(522,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[521, 204, 53, 128, 515, 120, 514, 513, 64, 497])).
% 0.68/0.90 tff(523,plain,(c3_1(a445) | hskp14 | c0_1(a445) | c1_1(a445) | hskp10 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(524,plain,
% 0.68/0.90 (c3_1(a445)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[523, 52, 40, 53, 54, 102])).
% 0.68/0.90 tff(525,plain,
% 0.68/0.90 (((~hskp9) | (~c3_1(a445))) <=> ((~hskp9) | (~c3_1(a445)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(526,plain,
% 0.68/0.90 (((~c3_1(a445)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a445)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(527,axiom,((~c3_1(a445)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.68/0.90 tff(528,plain,
% 0.68/0.90 ((~hskp9) | (~c3_1(a445))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[527, 526])).
% 0.68/0.90 tff(529,plain,
% 0.68/0.90 ((~hskp9) | (~c3_1(a445))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[528, 525])).
% 0.68/0.90 tff(530,plain,
% 0.68/0.90 (~hskp9),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[529, 524])).
% 0.68/0.90 tff(531,plain,
% 0.68/0.90 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | c0_1(a445) | c1_1(a445) | (~c3_1(a445)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp8 | c0_1(a445) | c1_1(a445) | (~c3_1(a445)) | (~ndr1_0))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(532,plain,
% 0.68/0.90 ((hskp9 | hskp8 | (~ndr1_0) | c0_1(a445) | c1_1(a445) | (~c3_1(a445))) <=> (hskp9 | hskp8 | c0_1(a445) | c1_1(a445) | (~c3_1(a445)) | (~ndr1_0))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(533,plain,
% 0.68/0.90 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a445) | c1_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | c0_1(a445) | c1_1(a445) | (~c3_1(a445)) | (~ndr1_0)))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[532])).
% 0.68/0.90 tff(534,plain,
% 0.68/0.90 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a445) | c1_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp8 | c0_1(a445) | c1_1(a445) | (~c3_1(a445)) | (~ndr1_0))),
% 0.68/0.90 inference(transitivity,[status(thm)],[533, 531])).
% 0.68/0.90 tff(535,plain,
% 0.68/0.90 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a445) | c1_1(a445) | (~c3_1(a445)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(536,plain,
% 0.68/0.90 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp8 | c0_1(a445) | c1_1(a445) | (~c3_1(a445)) | (~ndr1_0)),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.68/0.90 tff(537,plain,
% 0.68/0.90 (hskp9 | hskp8 | c1_1(a445) | (~c3_1(a445))),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[536, 204, 40, 50])).
% 0.68/0.90 tff(538,plain,
% 0.68/0.90 (hskp8),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[537, 530, 52, 524])).
% 0.68/0.90 tff(539,plain,
% 0.68/0.90 (~c3_1(a444)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[262, 538])).
% 0.68/0.90 tff(540,plain,
% 0.68/0.90 (~c0_1(a444)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[268, 538])).
% 0.68/0.90 tff(541,plain,
% 0.68/0.90 (c2_1(a444)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[276, 538])).
% 0.68/0.90 tff(542,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(543,plain,
% 0.68/0.90 ((hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486))) <=> (hskp9 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(544,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486))))),
% 0.68/0.90 inference(monotonicity,[status(thm)],[543])).
% 0.68/0.90 tff(545,plain,
% 0.68/0.90 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)))),
% 0.68/0.90 inference(transitivity,[status(thm)],[544, 542])).
% 0.68/0.90 tff(546,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))),
% 0.68/0.90 inference(quant_inst,[status(thm)],[])).
% 0.68/0.90 tff(547,plain,
% 0.68/0.90 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a486) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486))),
% 0.68/0.90 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.68/0.90 tff(548,plain,
% 0.68/0.90 (c3_1(a486)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[547, 204, 530, 136, 541, 120, 540, 539, 30])).
% 0.68/0.90 tff(549,plain,
% 0.68/0.90 ($false),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[521, 204, 53, 128, 541, 120, 540, 539, 64, 548])).
% 0.68/0.90 tff(550,plain,(c1_1(a445) | hskp14 | c0_1(a445) | hskp10 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.68/0.90 tff(551,plain,
% 0.68/0.90 (c1_1(a445)),
% 0.68/0.90 inference(unit_resolution,[status(thm)],[550, 40, 53, 54, 102])).
% 0.68/0.90 tff(552,plain,
% 0.68/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.68/0.90 inference(bind,[status(th)],[])).
% 0.68/0.90 tff(553,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.68/0.90 inference(quant_intro,[status(thm)],[552])).
% 0.68/0.90 tff(554,plain,
% 0.68/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.68/0.90 inference(rewrite,[status(thm)],[])).
% 0.68/0.90 tff(555,plain,
% 0.68/0.90 (^[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))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_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) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(556,plain,
% 0.68/0.91 (![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))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.68/0.91 inference(quant_intro,[status(thm)],[555])).
% 0.68/0.91 tff(557,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))) | (~c0_1(W))) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 0.68/0.91 tff(558,plain,
% 0.68/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[557, 556])).
% 0.68/0.91 tff(559,plain,
% 0.68/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[558, 554])).
% 0.68/0.91 tff(560,plain,(
% 0.68/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.68/0.91 inference(skolemize,[status(sab)],[559])).
% 0.68/0.91 tff(561,plain,
% 0.68/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[560, 553])).
% 0.68/0.91 tff(562,assumption,(c1_1(a445)), introduced(assumption)).
% 0.68/0.91 tff(563,plain,
% 0.68/0.91 (((~hskp9) | (~c1_1(a445))) <=> ((~hskp9) | (~c1_1(a445)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(564,plain,
% 0.68/0.91 (((~c1_1(a445)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a445)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(565,axiom,((~c1_1(a445)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.68/0.91 tff(566,plain,
% 0.68/0.91 ((~hskp9) | (~c1_1(a445))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.68/0.91 tff(567,plain,
% 0.68/0.91 ((~hskp9) | (~c1_1(a445))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[566, 563])).
% 0.68/0.91 tff(568,plain,
% 0.68/0.91 (~hskp9),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[567, 562])).
% 0.68/0.91 tff(569,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a445) | (~c1_1(a445)) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a445) | (~c1_1(a445)) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(570,plain,
% 0.68/0.91 ((hskp9 | (~ndr1_0) | c3_1(a445) | c0_1(a445) | (~c2_1(a445)) | c0_1(a445) | c3_1(a445) | (~c1_1(a445))) <=> (hskp9 | c0_1(a445) | (~c1_1(a445)) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(571,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a445) | c0_1(a445) | (~c2_1(a445)) | c0_1(a445) | c3_1(a445) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a445) | (~c1_1(a445)) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445))))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[570])).
% 0.68/0.91 tff(572,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a445) | c0_1(a445) | (~c2_1(a445)) | c0_1(a445) | c3_1(a445) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a445) | (~c1_1(a445)) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)))),
% 0.68/0.91 inference(transitivity,[status(thm)],[571, 569])).
% 0.68/0.91 tff(573,plain,
% 0.68/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a445) | c0_1(a445) | (~c2_1(a445)) | c0_1(a445) | c3_1(a445) | (~c1_1(a445)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(574,plain,
% 0.68/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a445) | (~c1_1(a445)) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.68/0.91 tff(575,plain,
% 0.68/0.91 (~c2_1(a445)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[574, 204, 568, 40, 562, 51, 30])).
% 0.68/0.91 tff(576,plain,
% 0.68/0.91 (^[U: $i] : refl((hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(577,plain,
% 0.68/0.91 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(quant_intro,[status(thm)],[576])).
% 0.68/0.91 tff(578,plain,
% 0.68/0.91 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(579,plain,
% 0.68/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp2) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp2))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp2) <=> (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp2) <=> (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(580,plain,
% 0.68/0.91 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp2) <=> ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(quant_intro,[status(thm)],[579])).
% 0.68/0.91 tff(581,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.68/0.91 tff(582,plain,
% 0.68/0.91 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.68/0.91 tff(583,plain,
% 0.68/0.91 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[582, 578])).
% 0.68/0.91 tff(584,plain,(
% 0.68/0.91 ![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(skolemize,[status(sab)],[583])).
% 0.68/0.91 tff(585,plain,
% 0.68/0.91 (![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[584, 577])).
% 0.68/0.91 tff(586,plain,
% 0.68/0.91 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp14 | hskp2 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(587,plain,
% 0.68/0.91 ((hskp14 | hskp2 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c1_1(a445))) <=> (hskp14 | hskp2 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(588,plain,
% 0.68/0.91 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c1_1(a445)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445)))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[587])).
% 0.68/0.91 tff(589,plain,
% 0.68/0.91 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c1_1(a445)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp14 | hskp2 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445))),
% 0.68/0.91 inference(transitivity,[status(thm)],[588, 586])).
% 0.68/0.91 tff(590,plain,
% 0.68/0.91 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c1_1(a445)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(591,plain,
% 0.68/0.91 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp14 | hskp2 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.68/0.91 tff(592,plain,
% 0.68/0.91 (hskp2 | (~c1_1(a445)) | c2_1(a445)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[591, 204, 53, 40, 585])).
% 0.68/0.91 tff(593,plain,
% 0.68/0.91 (hskp2),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[592, 575, 562])).
% 0.68/0.91 tff(594,plain,
% 0.68/0.91 (((~hskp2) | (~c3_1(a434))) <=> ((~hskp2) | (~c3_1(a434)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(595,plain,
% 0.68/0.91 (((~c3_1(a434)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a434)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(596,axiom,((~c3_1(a434)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.68/0.91 tff(597,plain,
% 0.68/0.91 ((~hskp2) | (~c3_1(a434))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.68/0.91 tff(598,plain,
% 0.68/0.91 ((~hskp2) | (~c3_1(a434))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[597, 594])).
% 0.68/0.91 tff(599,plain,
% 0.68/0.91 (~c3_1(a434)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[598, 593])).
% 0.68/0.91 tff(600,plain,
% 0.68/0.91 (((~hskp2) | (~c1_1(a434))) <=> ((~hskp2) | (~c1_1(a434)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(601,plain,
% 0.68/0.91 (((~c1_1(a434)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a434)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(602,axiom,((~c1_1(a434)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.68/0.91 tff(603,plain,
% 0.68/0.91 ((~hskp2) | (~c1_1(a434))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.68/0.91 tff(604,plain,
% 0.68/0.91 ((~hskp2) | (~c1_1(a434))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[603, 600])).
% 0.68/0.91 tff(605,plain,
% 0.68/0.91 (~c1_1(a434)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[604, 593])).
% 0.68/0.91 tff(606,plain,
% 0.68/0.91 (((~hskp2) | c0_1(a434)) <=> ((~hskp2) | c0_1(a434))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(607,axiom,((~hskp2) | c0_1(a434)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.68/0.91 tff(608,plain,
% 0.68/0.91 ((~hskp2) | c0_1(a434)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.68/0.91 tff(609,plain,
% 0.68/0.91 ((~hskp2) | c0_1(a434)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[608, 606])).
% 0.68/0.91 tff(610,plain,
% 0.68/0.91 ((~hskp2) | c0_1(a434)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[609, 606])).
% 0.68/0.91 tff(611,plain,
% 0.68/0.91 ((~hskp2) | c0_1(a434)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[610, 606])).
% 0.68/0.91 tff(612,plain,
% 0.68/0.91 ((~hskp2) | c0_1(a434)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[611, 606])).
% 0.68/0.91 tff(613,plain,
% 0.68/0.91 (c0_1(a434)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[612, 593])).
% 0.68/0.91 tff(614,plain,
% 0.68/0.91 (hskp29),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[456, 575, 51])).
% 0.68/0.91 tff(615,plain,
% 0.68/0.91 (c3_1(a447)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[464, 614])).
% 0.68/0.91 tff(616,plain,
% 0.68/0.91 (c2_1(a447)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[472, 614])).
% 0.68/0.91 tff(617,plain,
% 0.68/0.91 (c1_1(a447)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[504, 614])).
% 0.68/0.91 tff(618,plain,
% 0.68/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(619,plain,
% 0.68/0.91 (((~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)) | c1_1(a434) | c3_1(a434) | (~c0_1(a434))) <=> (c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(620,plain,
% 0.68/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)) | c1_1(a434) | c3_1(a434) | (~c0_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447))))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[619])).
% 0.68/0.91 tff(621,plain,
% 0.68/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)) | c1_1(a434) | c3_1(a434) | (~c0_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))),
% 0.68/0.91 inference(transitivity,[status(thm)],[620, 618])).
% 0.68/0.91 tff(622,plain,
% 0.68/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)) | c1_1(a434) | c3_1(a434) | (~c0_1(a434)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(623,plain,
% 0.68/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)) | (~c2_1(a447))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.68/0.91 tff(624,plain,
% 0.68/0.91 (~c0_1(a447)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[623, 204, 617, 616, 615, 613, 605, 599, 561])).
% 0.68/0.91 tff(625,plain,
% 0.68/0.91 (^[U: $i] : refl((hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(626,plain,
% 0.68/0.91 (![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(quant_intro,[status(thm)],[625])).
% 0.68/0.91 tff(627,plain,
% 0.68/0.91 (![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(628,plain,
% 0.68/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp9) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9) <=> (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp9) <=> (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(629,plain,
% 0.68/0.91 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp9) <=> ![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(quant_intro,[status(thm)],[628])).
% 0.68/0.91 tff(630,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.68/0.91 tff(631,plain,
% 0.68/0.91 (![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.68/0.91 tff(632,plain,
% 0.68/0.91 (![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[631, 627])).
% 0.68/0.91 tff(633,plain,(
% 0.68/0.91 ![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(skolemize,[status(sab)],[632])).
% 0.68/0.91 tff(634,plain,
% 0.68/0.91 (![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[633, 626])).
% 0.68/0.91 tff(635,plain,
% 0.68/0.91 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(636,plain,
% 0.68/0.91 ((hskp15 | hskp9 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c1_1(a445))) <=> (hskp15 | hskp9 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(637,plain,
% 0.68/0.91 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c1_1(a445)))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445)))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[636])).
% 0.68/0.91 tff(638,plain,
% 0.68/0.91 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c1_1(a445)))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445))),
% 0.68/0.91 inference(transitivity,[status(thm)],[637, 635])).
% 0.68/0.91 tff(639,plain,
% 0.68/0.91 ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c1_1(a445)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(640,plain,
% 0.68/0.91 ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a445) | (~c1_1(a445)) | (~ndr1_0) | c2_1(a445)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.68/0.91 tff(641,plain,
% 0.68/0.91 (hskp15 | hskp9 | (~c1_1(a445)) | c2_1(a445)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[640, 204, 40, 634])).
% 0.68/0.91 tff(642,plain,
% 0.68/0.91 (hskp15),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[641, 575, 568, 562])).
% 0.68/0.91 tff(643,plain,
% 0.68/0.91 (((~hskp15) | (~c1_1(a454))) <=> ((~hskp15) | (~c1_1(a454)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(644,plain,
% 0.68/0.91 (((~c1_1(a454)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a454)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(645,axiom,((~c1_1(a454)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.68/0.91 tff(646,plain,
% 0.68/0.91 ((~hskp15) | (~c1_1(a454))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.68/0.91 tff(647,plain,
% 0.68/0.91 ((~hskp15) | (~c1_1(a454))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[646, 643])).
% 0.68/0.91 tff(648,plain,
% 0.68/0.91 (~c1_1(a454)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[647, 642])).
% 0.68/0.91 tff(649,plain,
% 0.68/0.91 (((~hskp15) | (~c0_1(a454))) <=> ((~hskp15) | (~c0_1(a454)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(650,plain,
% 0.68/0.91 (((~c0_1(a454)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a454)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(651,axiom,((~c0_1(a454)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.68/0.91 tff(652,plain,
% 0.68/0.91 ((~hskp15) | (~c0_1(a454))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.68/0.91 tff(653,plain,
% 0.68/0.91 ((~hskp15) | (~c0_1(a454))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[652, 649])).
% 0.68/0.91 tff(654,plain,
% 0.68/0.91 (~c0_1(a454)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[653, 642])).
% 0.68/0.91 tff(655,plain,
% 0.68/0.91 (((~hskp15) | c3_1(a454)) <=> ((~hskp15) | c3_1(a454))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(656,axiom,((~hskp15) | c3_1(a454)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.68/0.91 tff(657,plain,
% 0.68/0.91 ((~hskp15) | c3_1(a454)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.68/0.91 tff(658,plain,
% 0.68/0.91 ((~hskp15) | c3_1(a454)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[657, 655])).
% 0.68/0.91 tff(659,plain,
% 0.68/0.91 ((~hskp15) | c3_1(a454)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[658, 655])).
% 0.68/0.91 tff(660,plain,
% 0.68/0.91 ((~hskp15) | c3_1(a454)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[659, 655])).
% 0.68/0.91 tff(661,plain,
% 0.68/0.91 ((~hskp15) | c3_1(a454)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[660, 655])).
% 0.68/0.91 tff(662,plain,
% 0.68/0.91 (c3_1(a454)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[661, 642])).
% 0.68/0.91 tff(663,plain,
% 0.68/0.91 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | c0_1(a454) | c1_1(a454) | (~ndr1_0) | (~c3_1(a454)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp8 | c0_1(a454) | c1_1(a454) | (~ndr1_0) | (~c3_1(a454)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(664,plain,
% 0.68/0.91 ((hskp9 | hskp8 | (~ndr1_0) | c0_1(a454) | c1_1(a454) | (~c3_1(a454))) <=> (hskp9 | hskp8 | c0_1(a454) | c1_1(a454) | (~ndr1_0) | (~c3_1(a454)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(665,plain,
% 0.68/0.91 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a454) | c1_1(a454) | (~c3_1(a454)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | c0_1(a454) | c1_1(a454) | (~ndr1_0) | (~c3_1(a454))))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[664])).
% 0.68/0.91 tff(666,plain,
% 0.68/0.91 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a454) | c1_1(a454) | (~c3_1(a454)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp8 | c0_1(a454) | c1_1(a454) | (~ndr1_0) | (~c3_1(a454)))),
% 0.68/0.91 inference(transitivity,[status(thm)],[665, 663])).
% 0.68/0.91 tff(667,plain,
% 0.68/0.91 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a454) | c1_1(a454) | (~c3_1(a454)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(668,plain,
% 0.68/0.91 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp8 | c0_1(a454) | c1_1(a454) | (~ndr1_0) | (~c3_1(a454))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[667, 666])).
% 0.68/0.91 tff(669,plain,
% 0.68/0.91 (hskp8),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[668, 204, 568, 662, 654, 648, 50])).
% 0.68/0.91 tff(670,plain,
% 0.68/0.91 (~c3_1(a444)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[262, 669])).
% 0.68/0.91 tff(671,plain,
% 0.68/0.91 (~c0_1(a444)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[268, 669])).
% 0.68/0.91 tff(672,plain,
% 0.68/0.91 (c2_1(a444)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[276, 669])).
% 0.68/0.91 tff(673,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(674,plain,
% 0.68/0.91 ((hskp14 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444))) <=> (hskp14 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(675,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[674])).
% 0.68/0.91 tff(676,plain,
% 0.68/0.91 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.91 inference(transitivity,[status(thm)],[675, 673])).
% 0.68/0.91 tff(677,plain,
% 0.68/0.91 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(678,plain,
% 0.68/0.91 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.68/0.92 tff(679,plain,
% 0.68/0.92 ($false),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[678, 204, 53, 616, 615, 672, 671, 670, 64, 624])).
% 0.68/0.92 tff(680,plain,(c3_1(a445) | hskp14 | (~c1_1(a445)) | c0_1(a445) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.68/0.92 tff(681,plain,
% 0.68/0.92 (c3_1(a445)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[680, 551, 53, 40, 54])).
% 0.68/0.92 tff(682,assumption,(c3_1(a445)), introduced(assumption)).
% 0.68/0.92 tff(683,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)) | (~ndr1_0) | (~c2_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)) | (~ndr1_0) | (~c2_1(a445)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(684,plain,
% 0.68/0.92 ((hskp8 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445)) | (~c2_1(a445))) <=> (hskp8 | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)) | (~ndr1_0) | (~c2_1(a445)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(685,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445)) | (~c2_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)) | (~ndr1_0) | (~c2_1(a445))))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[684])).
% 0.68/0.92 tff(686,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445)) | (~c2_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)) | (~ndr1_0) | (~c2_1(a445)))),
% 0.68/0.92 inference(transitivity,[status(thm)],[685, 683])).
% 0.68/0.92 tff(687,plain,
% 0.68/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445)) | (~c2_1(a445)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(688,plain,
% 0.68/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)) | (~ndr1_0) | (~c2_1(a445))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[687, 686])).
% 0.68/0.92 tff(689,plain,
% 0.68/0.92 (hskp8 | (~c1_1(a445)) | (~c3_1(a445)) | (~c2_1(a445))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[688, 204, 40, 249])).
% 0.68/0.92 tff(690,plain,
% 0.68/0.92 (~c2_1(a445)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[689, 32, 562, 682])).
% 0.68/0.92 tff(691,plain,
% 0.68/0.92 (hskp15),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[641, 690, 568, 562])).
% 0.68/0.92 tff(692,plain,
% 0.68/0.92 (~c1_1(a454)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[647, 691])).
% 0.68/0.92 tff(693,plain,
% 0.68/0.92 (~c0_1(a454)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[653, 691])).
% 0.68/0.92 tff(694,plain,
% 0.68/0.92 (c3_1(a454)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[661, 691])).
% 0.68/0.92 tff(695,plain,
% 0.68/0.92 ($false),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[668, 204, 568, 32, 694, 693, 692, 50])).
% 0.68/0.92 tff(696,plain,(hskp8 | (~c1_1(a445)) | c0_1(a445) | (~c3_1(a445))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.92 tff(697,plain,
% 0.68/0.92 (hskp8),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[696, 551, 40, 681])).
% 0.68/0.92 tff(698,plain,
% 0.68/0.92 (~c3_1(a444)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[262, 697])).
% 0.68/0.92 tff(699,plain,
% 0.68/0.92 (~c0_1(a444)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[268, 697])).
% 0.68/0.92 tff(700,plain,
% 0.68/0.92 (c2_1(a444)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[276, 697])).
% 0.68/0.92 tff(701,plain,
% 0.68/0.92 (~hskp9),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[567, 551])).
% 0.68/0.92 tff(702,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | (~c2_1(a444)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(703,plain,
% 0.68/0.92 ((hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444))) <=> (hskp9 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | (~c2_1(a444)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(704,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | (~c2_1(a444))))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[703])).
% 0.68/0.92 tff(705,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | (~c2_1(a444)))),
% 0.68/0.92 inference(transitivity,[status(thm)],[704, 702])).
% 0.68/0.92 tff(706,plain,
% 0.68/0.92 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(707,plain,
% 0.68/0.92 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | (~c2_1(a444))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[706, 705])).
% 0.68/0.92 tff(708,plain,
% 0.68/0.92 (~c1_1(a444)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[707, 204, 701, 700, 699, 698, 30])).
% 0.68/0.92 tff(709,plain,
% 0.68/0.92 (~c3_1(a486)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[521, 204, 53, 128, 700, 120, 699, 698, 64])).
% 0.68/0.92 tff(710,plain,
% 0.68/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(711,plain,
% 0.68/0.92 (((~ndr1_0) | c3_1(a444) | c1_1(a444) | (~c2_1(a444)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486))) <=> (c0_1(a486) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(712,plain,
% 0.68/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a444) | c1_1(a444) | (~c2_1(a444)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[711])).
% 0.68/0.92 tff(713,plain,
% 0.68/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a444) | c1_1(a444) | (~c2_1(a444)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.92 inference(transitivity,[status(thm)],[712, 710])).
% 0.68/0.92 tff(714,plain,
% 0.68/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a444) | c1_1(a444) | (~c2_1(a444)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(715,plain,
% 0.68/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c2_1(a444)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.68/0.92 tff(716,plain,
% 0.68/0.92 ($false),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[715, 204, 136, 128, 700, 120, 698, 10, 709, 708])).
% 0.68/0.92 tff(717,plain,(c0_1(a445) | hskp14 | hskp10 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.68/0.92 tff(718,plain,
% 0.68/0.92 (c0_1(a445)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[717, 102, 54, 53])).
% 0.68/0.92 tff(719,plain,
% 0.68/0.92 (((~hskp9) | (~c0_1(a445))) <=> ((~hskp9) | (~c0_1(a445)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(720,plain,
% 0.68/0.92 (((~c0_1(a445)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a445)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(721,axiom,((~c0_1(a445)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.68/0.92 tff(722,plain,
% 0.68/0.92 ((~hskp9) | (~c0_1(a445))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.68/0.92 tff(723,plain,
% 0.68/0.92 ((~hskp9) | (~c0_1(a445))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[722, 719])).
% 0.68/0.92 tff(724,plain,
% 0.68/0.92 (~hskp9),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[723, 718])).
% 0.68/0.92 tff(725,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a486) | (~ndr1_0) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a486) | (~ndr1_0) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(726,plain,
% 0.68/0.92 ((hskp9 | (~ndr1_0) | c3_1(a486) | c0_1(a486) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486))) <=> (hskp9 | c0_1(a486) | (~ndr1_0) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(727,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a486) | c0_1(a486) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a486) | (~ndr1_0) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[726])).
% 0.68/0.92 tff(728,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a486) | c0_1(a486) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a486) | (~ndr1_0) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.68/0.92 inference(transitivity,[status(thm)],[727, 725])).
% 0.68/0.92 tff(729,plain,
% 0.68/0.92 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a486) | c0_1(a486) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(730,plain,
% 0.68/0.92 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a486) | (~ndr1_0) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[729, 728])).
% 0.68/0.92 tff(731,plain,
% 0.68/0.92 ($false),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[730, 204, 31, 177, 179, 178, 30, 181])).
% 0.68/0.92 tff(732,plain,(c3_1(a486) | hskp9 | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.92 tff(733,plain,
% 0.68/0.92 (c3_1(a486)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[732, 724, 136, 128, 120])).
% 0.68/0.92 tff(734,plain,
% 0.68/0.92 (hskp8 | (~c3_1(a486))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[255, 204, 136, 128, 120, 249])).
% 0.68/0.92 tff(735,plain,
% 0.68/0.92 (hskp8),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[734, 733])).
% 0.68/0.92 tff(736,plain,
% 0.68/0.92 (~c3_1(a444)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[262, 735])).
% 0.68/0.92 tff(737,plain,
% 0.68/0.92 (~c0_1(a444)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[268, 735])).
% 0.68/0.92 tff(738,plain,
% 0.68/0.92 (c2_1(a444)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[276, 735])).
% 0.68/0.92 tff(739,plain,
% 0.68/0.92 ($false),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[521, 204, 53, 128, 738, 120, 737, 736, 64, 733])).
% 0.68/0.92 tff(740,plain,(hskp30 | hskp14 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.68/0.92 tff(741,plain,
% 0.68/0.92 (hskp30),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[740, 54, 53])).
% 0.68/0.92 tff(742,plain,
% 0.68/0.92 (((~hskp30) | c2_1(a456)) <=> ((~hskp30) | c2_1(a456))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(743,axiom,((~hskp30) | c2_1(a456)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.68/0.92 tff(744,plain,
% 0.68/0.92 ((~hskp30) | c2_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.68/0.92 tff(745,plain,
% 0.68/0.92 ((~hskp30) | c2_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[744, 742])).
% 0.68/0.92 tff(746,plain,
% 0.68/0.92 ((~hskp30) | c2_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[745, 742])).
% 0.68/0.92 tff(747,plain,
% 0.68/0.92 ((~hskp30) | c2_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[746, 742])).
% 0.68/0.92 tff(748,plain,
% 0.68/0.92 ((~hskp30) | c2_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[747, 742])).
% 0.68/0.92 tff(749,plain,
% 0.68/0.92 (c2_1(a456)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[748, 741])).
% 0.68/0.92 tff(750,plain,
% 0.68/0.92 (((~hskp30) | c0_1(a456)) <=> ((~hskp30) | c0_1(a456))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(751,axiom,((~hskp30) | c0_1(a456)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.68/0.92 tff(752,plain,
% 0.68/0.92 ((~hskp30) | c0_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[751, 750])).
% 0.68/0.92 tff(753,plain,
% 0.68/0.92 ((~hskp30) | c0_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[752, 750])).
% 0.68/0.92 tff(754,plain,
% 0.68/0.92 ((~hskp30) | c0_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[753, 750])).
% 0.68/0.92 tff(755,plain,
% 0.68/0.92 ((~hskp30) | c0_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[754, 750])).
% 0.68/0.92 tff(756,plain,
% 0.68/0.92 ((~hskp30) | c0_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[755, 750])).
% 0.68/0.92 tff(757,plain,
% 0.68/0.92 (c0_1(a456)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[756, 741])).
% 0.68/0.92 tff(758,plain,
% 0.68/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c3_1(a445) | c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(759,plain,
% 0.68/0.92 (((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a433) | c1_1(a433) | c0_1(a433)) <=> (c0_1(a445) | c1_1(a445) | c3_1(a445) | c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(760,plain,
% 0.68/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a433) | c1_1(a433) | c0_1(a433))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c3_1(a445) | c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456))))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[759])).
% 0.68/0.92 tff(761,plain,
% 0.68/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a433) | c1_1(a433) | c0_1(a433))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)))),
% 0.68/0.92 inference(transitivity,[status(thm)],[760, 758])).
% 0.68/0.92 tff(762,plain,
% 0.68/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a433) | c1_1(a433) | c0_1(a433))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(763,plain,
% 0.68/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.68/0.92 tff(764,plain,
% 0.68/0.92 (~c3_1(a456)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[763, 204, 757, 749, 40, 52, 51, 101, 95, 89, 74])).
% 0.68/0.92 tff(765,plain,
% 0.68/0.92 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | (~c2_1(a456)) | (~c0_1(a456)) | c3_1(a456))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp12 | (~ndr1_0) | (~c2_1(a456)) | (~c0_1(a456)) | c3_1(a456))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(766,plain,
% 0.68/0.92 ((hskp14 | hskp12 | (~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c0_1(a456))) <=> (hskp14 | hskp12 | (~ndr1_0) | (~c2_1(a456)) | (~c0_1(a456)) | c3_1(a456))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(767,plain,
% 0.68/0.92 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c0_1(a456)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | (~c2_1(a456)) | (~c0_1(a456)) | c3_1(a456)))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[766])).
% 0.68/0.92 tff(768,plain,
% 0.68/0.92 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c0_1(a456)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp12 | (~ndr1_0) | (~c2_1(a456)) | (~c0_1(a456)) | c3_1(a456))),
% 0.68/0.92 inference(transitivity,[status(thm)],[767, 765])).
% 0.68/0.92 tff(769,plain,
% 0.68/0.92 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c0_1(a456)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(770,plain,
% 0.68/0.92 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp12 | (~ndr1_0) | (~c2_1(a456)) | (~c0_1(a456)) | c3_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.68/0.92 tff(771,plain,
% 0.68/0.92 (hskp12 | c3_1(a456)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[770, 204, 53, 757, 749, 156])).
% 0.68/0.92 tff(772,plain,
% 0.68/0.92 (hskp12),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[771, 764])).
% 0.68/0.92 tff(773,plain,
% 0.68/0.92 (~c0_1(a450)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[376, 772])).
% 0.68/0.92 tff(774,plain,
% 0.68/0.92 (c3_1(a450)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[407, 772])).
% 0.68/0.92 tff(775,plain,
% 0.68/0.92 (c1_1(a450)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[415, 772])).
% 0.68/0.92 tff(776,plain,
% 0.68/0.92 (((~hskp30) | c1_1(a456)) <=> ((~hskp30) | c1_1(a456))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(777,axiom,((~hskp30) | c1_1(a456)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.68/0.92 tff(778,plain,
% 0.68/0.92 ((~hskp30) | c1_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[777, 776])).
% 0.68/0.92 tff(779,plain,
% 0.68/0.92 ((~hskp30) | c1_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[778, 776])).
% 0.68/0.92 tff(780,plain,
% 0.68/0.92 ((~hskp30) | c1_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[779, 776])).
% 0.68/0.92 tff(781,plain,
% 0.68/0.92 ((~hskp30) | c1_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[780, 776])).
% 0.68/0.92 tff(782,plain,
% 0.68/0.92 ((~hskp30) | c1_1(a456)),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[781, 776])).
% 0.68/0.92 tff(783,plain,
% 0.68/0.92 (c1_1(a456)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[782, 741])).
% 0.68/0.92 tff(784,plain,
% 0.68/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(785,plain,
% 0.68/0.92 (((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445))) <=> (c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(786,plain,
% 0.68/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450))))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[785])).
% 0.68/0.92 tff(787,plain,
% 0.68/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450)))),
% 0.68/0.92 inference(transitivity,[status(thm)],[786, 784])).
% 0.68/0.92 tff(788,plain,
% 0.68/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(789,plain,
% 0.68/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a450)) | (~c3_1(a450))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.68/0.92 tff(790,plain,
% 0.68/0.92 (~c2_1(a445)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[789, 204, 783, 749, 775, 774, 773, 40, 52, 146, 764])).
% 0.68/0.92 tff(791,plain,
% 0.68/0.92 (hskp29),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[456, 790, 51])).
% 0.68/0.92 tff(792,plain,
% 0.68/0.92 (c3_1(a447)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[464, 791])).
% 0.68/0.92 tff(793,plain,
% 0.68/0.92 (c2_1(a447)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[472, 791])).
% 0.68/0.92 tff(794,plain,
% 0.68/0.92 (~c0_1(a447)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[479, 204, 793, 792, 40, 52, 51, 74, 790])).
% 0.68/0.92 tff(795,plain,
% 0.68/0.92 (c1_1(a447)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[504, 791])).
% 0.68/0.92 tff(796,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(797,plain,
% 0.68/0.92 ((hskp8 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a447) | (~c1_1(a447)) | (~c2_1(a447))) <=> (hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.92 inference(rewrite,[status(thm)],[])).
% 0.68/0.92 tff(798,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a447) | (~c1_1(a447)) | (~c2_1(a447)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447))))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[797])).
% 0.68/0.92 tff(799,plain,
% 0.68/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a447) | (~c1_1(a447)) | (~c2_1(a447)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.68/0.92 inference(transitivity,[status(thm)],[798, 796])).
% 0.68/0.92 tff(800,plain,
% 0.68/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a447) | (~c1_1(a447)) | (~c2_1(a447)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(801,plain,
% 0.68/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | c0_1(a447) | (~c2_1(a447))),
% 0.68/0.92 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.68/0.92 tff(802,plain,
% 0.68/0.92 ($false),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[801, 204, 32, 795, 793, 792, 249, 794])).
% 0.68/0.92 tff(803,plain,(hskp8 | c0_1(a445) | c1_1(a445) | c3_1(a445) | hskp10 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.68/0.92 tff(804,plain,
% 0.68/0.92 (hskp8),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[803, 51, 52, 40, 54, 53])).
% 0.68/0.92 tff(805,plain,
% 0.68/0.92 (~c3_1(a444)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[262, 804])).
% 0.68/0.92 tff(806,plain,
% 0.68/0.92 (~c0_1(a444)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[268, 804])).
% 0.68/0.92 tff(807,assumption,(~c3_1(a456)), introduced(assumption)).
% 0.68/0.92 tff(808,plain,
% 0.68/0.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.68/0.92 inference(bind,[status(th)],[])).
% 0.68/0.92 tff(809,plain,
% 0.68/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.68/0.93 inference(quant_intro,[status(thm)],[808])).
% 0.68/0.93 tff(810,plain,
% 0.68/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.68/0.93 inference(rewrite,[status(thm)],[])).
% 0.68/0.93 tff(811,plain,
% 0.68/0.93 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.68/0.93 inference(bind,[status(th)],[])).
% 0.68/0.93 tff(812,plain,
% 0.68/0.93 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.68/0.93 inference(quant_intro,[status(thm)],[811])).
% 0.68/0.93 tff(813,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 0.68/0.93 tff(814,plain,
% 0.68/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.68/0.93 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.68/0.93 tff(815,plain,
% 0.68/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.68/0.93 inference(modus_ponens,[status(thm)],[814, 810])).
% 0.68/0.93 tff(816,plain,(
% 0.68/0.93 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.68/0.93 inference(skolemize,[status(sab)],[815])).
% 0.68/0.93 tff(817,plain,
% 0.68/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.68/0.93 inference(modus_ponens,[status(thm)],[816, 809])).
% 0.68/0.93 tff(818,plain,
% 0.68/0.93 (c2_1(a444)),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[276, 804])).
% 0.68/0.93 tff(819,plain,
% 0.68/0.93 (hskp12),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[771, 807])).
% 0.68/0.93 tff(820,plain,
% 0.68/0.93 (~c0_1(a450)),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[376, 819])).
% 0.68/0.93 tff(821,plain,
% 0.68/0.93 (c3_1(a450)),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[407, 819])).
% 0.68/0.93 tff(822,plain,
% 0.68/0.93 (c1_1(a450)),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[415, 819])).
% 0.68/0.93 tff(823,plain,
% 0.68/0.93 (~c2_1(a445)),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[789, 204, 783, 749, 822, 821, 820, 40, 52, 146, 807])).
% 0.68/0.93 tff(824,plain,
% 0.68/0.93 (hskp29),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[456, 823, 51])).
% 0.68/0.93 tff(825,plain,
% 0.68/0.93 (c3_1(a447)),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[464, 824])).
% 0.68/0.93 tff(826,plain,
% 0.68/0.93 (c2_1(a447)),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[472, 824])).
% 0.68/0.93 tff(827,plain,
% 0.68/0.93 (c1_1(a447)),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[504, 824])).
% 0.68/0.93 tff(828,plain,
% 0.68/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a444)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c2_1(a447)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a444)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c2_1(a447)))),
% 0.68/0.93 inference(rewrite,[status(thm)],[])).
% 0.68/0.93 tff(829,plain,
% 0.68/0.93 (((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c1_1(a447)) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444))) <=> (c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a444)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c2_1(a447)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(830,plain,
% 0.78/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c1_1(a447)) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a444)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c2_1(a447))))),
% 0.78/0.93 inference(monotonicity,[status(thm)],[829])).
% 0.78/0.93 tff(831,plain,
% 0.78/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c1_1(a447)) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a444)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c2_1(a447)))),
% 0.78/0.93 inference(transitivity,[status(thm)],[830, 828])).
% 0.78/0.93 tff(832,plain,
% 0.78/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c1_1(a447)) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))),
% 0.78/0.93 inference(quant_inst,[status(thm)],[])).
% 0.78/0.93 tff(833,plain,
% 0.78/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a444)) | (~c3_1(a447)) | (~c1_1(a447)) | (~c2_1(a447))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.78/0.93 tff(834,plain,
% 0.78/0.93 ($false),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[833, 204, 757, 783, 827, 826, 825, 818, 806, 805, 817, 807])).
% 0.78/0.93 tff(835,plain,(c3_1(a456) | c3_1(a445) | hskp10 | c0_1(a445) | c1_1(a445) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.93 tff(836,plain,
% 0.78/0.93 (c3_1(a456)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[835, 51, 54, 40, 52, 53])).
% 0.78/0.93 tff(837,plain,
% 0.78/0.93 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.78/0.93 inference(bind,[status(th)],[])).
% 0.78/0.93 tff(838,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.78/0.93 inference(quant_intro,[status(thm)],[837])).
% 0.78/0.93 tff(839,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(840,plain,
% 0.78/0.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp25))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.78/0.93 inference(bind,[status(th)],[])).
% 0.78/0.93 tff(841,plain,
% 0.78/0.93 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.78/0.93 inference(quant_intro,[status(thm)],[840])).
% 0.78/0.93 tff(842,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.78/0.93 tff(843,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.78/0.93 tff(844,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[843, 839])).
% 0.78/0.93 tff(845,plain,(
% 0.78/0.93 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.78/0.93 inference(skolemize,[status(sab)],[844])).
% 0.78/0.93 tff(846,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[845, 838])).
% 0.78/0.93 tff(847,plain,
% 0.78/0.93 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.78/0.93 inference(bind,[status(th)],[])).
% 0.78/0.93 tff(848,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.93 inference(quant_intro,[status(thm)],[847])).
% 0.78/0.93 tff(849,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(850,plain,
% 0.78/0.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.78/0.93 inference(bind,[status(th)],[])).
% 0.78/0.93 tff(851,plain,
% 0.78/0.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.93 inference(quant_intro,[status(thm)],[850])).
% 0.78/0.93 tff(852,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.78/0.93 tff(853,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.78/0.93 tff(854,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[853, 849])).
% 0.78/0.93 tff(855,plain,(
% 0.78/0.93 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.93 inference(skolemize,[status(sab)],[854])).
% 0.78/0.93 tff(856,plain,
% 0.78/0.93 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[855, 848])).
% 0.78/0.93 tff(857,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp16 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp16 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | (~c2_1(a444)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(858,plain,
% 0.78/0.93 ((hskp16 | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444))) <=> (hskp16 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | (~c2_1(a444)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(859,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp16 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | (~c2_1(a444))))),
% 0.78/0.93 inference(monotonicity,[status(thm)],[858])).
% 0.78/0.93 tff(860,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp16 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | (~c2_1(a444)))),
% 0.78/0.93 inference(transitivity,[status(thm)],[859, 857])).
% 0.78/0.93 tff(861,plain,
% 0.78/0.93 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))),
% 0.78/0.93 inference(quant_inst,[status(thm)],[])).
% 0.78/0.93 tff(862,plain,
% 0.78/0.93 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp16 | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c1_1(a456)) | (~c2_1(a444))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.78/0.93 tff(863,plain,
% 0.78/0.93 (hskp16 | (~c3_1(a456))),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[862, 204, 783, 749, 818, 806, 805, 856])).
% 0.78/0.93 tff(864,plain,
% 0.78/0.93 (hskp16),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[863, 836])).
% 0.78/0.93 tff(865,plain,
% 0.78/0.93 (~c2_1(a457)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[318, 864])).
% 0.78/0.93 tff(866,plain,
% 0.78/0.93 (c3_1(a457)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[326, 864])).
% 0.78/0.93 tff(867,plain,
% 0.78/0.93 (c1_1(a457)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[334, 864])).
% 0.78/0.93 tff(868,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a457) | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c3_1(a457)) | (~c1_1(a457)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a457) | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(869,plain,
% 0.78/0.93 ((hskp25 | (~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457))) <=> (hskp25 | c2_1(a457) | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(870,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | c2_1(a457) | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c3_1(a457)) | (~c1_1(a457))))),
% 0.78/0.93 inference(monotonicity,[status(thm)],[869])).
% 0.78/0.93 tff(871,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a457) | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.78/0.93 inference(transitivity,[status(thm)],[870, 868])).
% 0.78/0.93 tff(872,plain,
% 0.78/0.93 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.78/0.93 inference(quant_inst,[status(thm)],[])).
% 0.78/0.93 tff(873,plain,
% 0.78/0.93 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp25 | c2_1(a457) | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c3_1(a457)) | (~c1_1(a457))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.78/0.93 tff(874,plain,
% 0.78/0.93 (hskp25),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[873, 204, 757, 783, 867, 866, 865, 846, 836])).
% 0.78/0.93 tff(875,plain,
% 0.78/0.93 (((~hskp25) | (~c0_1(a489))) <=> ((~hskp25) | (~c0_1(a489)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(876,plain,
% 0.78/0.93 (((~c0_1(a489)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a489)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(877,axiom,((~c0_1(a489)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.78/0.93 tff(878,plain,
% 0.78/0.93 ((~hskp25) | (~c0_1(a489))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[877, 876])).
% 0.78/0.93 tff(879,plain,
% 0.78/0.93 ((~hskp25) | (~c0_1(a489))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[878, 875])).
% 0.78/0.93 tff(880,plain,
% 0.78/0.93 (~c0_1(a489)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[879, 874])).
% 0.78/0.93 tff(881,plain,
% 0.78/0.93 (((~hskp25) | c3_1(a489)) <=> ((~hskp25) | c3_1(a489))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(882,axiom,((~hskp25) | c3_1(a489)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.78/0.93 tff(883,plain,
% 0.78/0.93 ((~hskp25) | c3_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[882, 881])).
% 0.78/0.93 tff(884,plain,
% 0.78/0.93 ((~hskp25) | c3_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[883, 881])).
% 0.78/0.93 tff(885,plain,
% 0.78/0.93 ((~hskp25) | c3_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[884, 881])).
% 0.78/0.93 tff(886,plain,
% 0.78/0.93 ((~hskp25) | c3_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[885, 881])).
% 0.78/0.93 tff(887,plain,
% 0.78/0.93 ((~hskp25) | c3_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[886, 881])).
% 0.78/0.93 tff(888,plain,
% 0.78/0.93 (c3_1(a489)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[887, 874])).
% 0.78/0.93 tff(889,plain,
% 0.78/0.93 (((~hskp25) | c2_1(a489)) <=> ((~hskp25) | c2_1(a489))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(890,axiom,((~hskp25) | c2_1(a489)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.78/0.93 tff(891,plain,
% 0.78/0.93 ((~hskp25) | c2_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.78/0.93 tff(892,plain,
% 0.78/0.93 ((~hskp25) | c2_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[891, 889])).
% 0.78/0.93 tff(893,plain,
% 0.78/0.93 ((~hskp25) | c2_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[892, 889])).
% 0.78/0.93 tff(894,plain,
% 0.78/0.93 ((~hskp25) | c2_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[893, 889])).
% 0.78/0.93 tff(895,plain,
% 0.78/0.93 ((~hskp25) | c2_1(a489)),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[894, 889])).
% 0.78/0.93 tff(896,plain,
% 0.78/0.93 (c2_1(a489)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[895, 874])).
% 0.78/0.93 tff(897,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a489) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a489)) | (~c3_1(a489)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a489) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a489)) | (~c3_1(a489)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(898,plain,
% 0.78/0.93 ((hskp14 | (~ndr1_0) | c0_1(a489) | (~c2_1(a489)) | (~c3_1(a489)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444))) <=> (hskp14 | c0_1(a489) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a489)) | (~c3_1(a489)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(899,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a489) | (~c2_1(a489)) | (~c3_1(a489)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a489) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a489)) | (~c3_1(a489))))),
% 0.78/0.93 inference(monotonicity,[status(thm)],[898])).
% 0.78/0.93 tff(900,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a489) | (~c2_1(a489)) | (~c3_1(a489)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a489) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a489)) | (~c3_1(a489)))),
% 0.78/0.93 inference(transitivity,[status(thm)],[899, 897])).
% 0.78/0.93 tff(901,plain,
% 0.78/0.93 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a489) | (~c2_1(a489)) | (~c3_1(a489)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))),
% 0.78/0.93 inference(quant_inst,[status(thm)],[])).
% 0.78/0.93 tff(902,plain,
% 0.78/0.93 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a489) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a489)) | (~c3_1(a489))),
% 0.78/0.93 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.78/0.93 tff(903,plain,
% 0.78/0.93 ($false),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[902, 204, 53, 896, 888, 818, 880, 806, 805, 64])).
% 0.78/0.93 tff(904,plain,(c3_1(a445) | hskp14 | hskp10 | c0_1(a445) | c1_1(a445)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.93 tff(905,plain,
% 0.78/0.93 (c3_1(a445)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[904, 52, 54, 40, 53])).
% 0.78/0.93 tff(906,plain,
% 0.78/0.93 (~hskp9),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[529, 905])).
% 0.78/0.93 tff(907,plain,
% 0.78/0.93 (hskp8),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[537, 906, 52, 905])).
% 0.78/0.93 tff(908,plain,
% 0.78/0.93 (~c3_1(a444)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[262, 907])).
% 0.78/0.93 tff(909,plain,
% 0.78/0.93 (~c0_1(a444)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[268, 907])).
% 0.78/0.93 tff(910,plain,
% 0.78/0.93 (c2_1(a444)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[276, 907])).
% 0.78/0.93 tff(911,plain,
% 0.78/0.93 (~c1_1(a444)),
% 0.78/0.93 inference(unit_resolution,[status(thm)],[707, 204, 906, 910, 909, 908, 30])).
% 0.78/0.93 tff(912,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a445) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a445) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a445)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(913,plain,
% 0.78/0.93 ((hskp14 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444))) <=> (hskp14 | c0_1(a445) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a445)))),
% 0.78/0.93 inference(rewrite,[status(thm)],[])).
% 0.78/0.93 tff(914,plain,
% 0.78/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a445) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a445))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[913])).
% 0.78/0.94 tff(915,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a445) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a445)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[914, 912])).
% 0.78/0.94 tff(916,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(917,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a445) | (~c3_1(a445)) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a445))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[916, 915])).
% 0.78/0.94 tff(918,plain,
% 0.78/0.94 (~c2_1(a445)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[917, 204, 53, 910, 40, 905, 909, 908, 64])).
% 0.78/0.94 tff(919,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a445))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a445))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(920,plain,
% 0.78/0.94 (((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c0_1(a444) | c3_1(a444) | c2_1(a445) | c1_1(a445) | c0_1(a445)) <=> (c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a445))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(921,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c0_1(a444) | c3_1(a444) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a445)))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[920])).
% 0.78/0.94 tff(922,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c0_1(a444) | c3_1(a444) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a445))),
% 0.78/0.94 inference(transitivity,[status(thm)],[921, 919])).
% 0.78/0.94 tff(923,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c0_1(a444) | c3_1(a444) | c2_1(a445) | c1_1(a445) | c0_1(a445))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(924,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a445)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[923, 922])).
% 0.78/0.94 tff(925,plain,
% 0.78/0.94 (~c3_1(a456)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[924, 204, 757, 749, 40, 52, 909, 908, 74, 918, 911])).
% 0.78/0.94 tff(926,plain,
% 0.78/0.94 (hskp12),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[771, 925])).
% 0.78/0.94 tff(927,plain,
% 0.78/0.94 (~c0_1(a450)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[376, 926])).
% 0.78/0.94 tff(928,plain,
% 0.78/0.94 (c3_1(a450)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[407, 926])).
% 0.78/0.94 tff(929,plain,
% 0.78/0.94 (c1_1(a450)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[415, 926])).
% 0.78/0.94 tff(930,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c0_1(a444) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a450)) | (~c3_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c0_1(a444) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a450)) | (~c3_1(a450)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(931,plain,
% 0.78/0.94 (((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a444) | c0_1(a444) | (~c2_1(a444))) <=> (c0_1(a450) | c0_1(a444) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a450)) | (~c3_1(a450)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(932,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a444) | c0_1(a444) | (~c2_1(a444)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c0_1(a444) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a450)) | (~c3_1(a450))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[931])).
% 0.78/0.94 tff(933,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a444) | c0_1(a444) | (~c2_1(a444)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c0_1(a444) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a450)) | (~c3_1(a450)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[932, 930])).
% 0.78/0.94 tff(934,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a444) | c0_1(a444) | (~c2_1(a444)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(935,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c0_1(a444) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a450)) | (~c3_1(a450))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[934, 933])).
% 0.78/0.94 tff(936,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[935, 204, 783, 749, 929, 928, 910, 927, 909, 146, 925, 911])).
% 0.78/0.94 tff(937,plain,(c1_1(a445) | hskp14 | c0_1(a445) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(938,plain,
% 0.78/0.94 (c1_1(a445)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[937, 40, 53, 54])).
% 0.78/0.94 tff(939,plain,
% 0.78/0.94 (c3_1(a445)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[680, 938, 53, 40, 54])).
% 0.78/0.94 tff(940,plain,
% 0.78/0.94 (hskp8),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[696, 938, 40, 939])).
% 0.78/0.94 tff(941,plain,
% 0.78/0.94 (~c3_1(a444)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[262, 940])).
% 0.78/0.94 tff(942,plain,
% 0.78/0.94 (~c0_1(a444)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[268, 940])).
% 0.78/0.94 tff(943,plain,
% 0.78/0.94 (c2_1(a444)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[276, 940])).
% 0.78/0.94 tff(944,plain,
% 0.78/0.94 (~hskp9),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[567, 938])).
% 0.78/0.94 tff(945,plain,
% 0.78/0.94 (~c1_1(a444)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[707, 204, 944, 943, 942, 941, 30])).
% 0.78/0.94 tff(946,plain,
% 0.78/0.94 (~c2_1(a445)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[917, 204, 53, 943, 40, 939, 942, 941, 64])).
% 0.78/0.94 tff(947,plain,
% 0.78/0.94 (hskp15),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[641, 946, 944, 938])).
% 0.78/0.94 tff(948,plain,
% 0.78/0.94 (~c0_1(a454)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[653, 947])).
% 0.78/0.94 tff(949,plain,
% 0.78/0.94 (c3_1(a454)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[661, 947])).
% 0.78/0.94 tff(950,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a454)) | (~c2_1(a454)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a454)) | (~c2_1(a454)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(951,plain,
% 0.78/0.94 ((hskp14 | (~ndr1_0) | c0_1(a454) | (~c2_1(a454)) | (~c3_1(a454)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444))) <=> (hskp14 | c0_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a454)) | (~c2_1(a454)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(952,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a454) | (~c2_1(a454)) | (~c3_1(a454)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a454)) | (~c2_1(a454))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[951])).
% 0.78/0.94 tff(953,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a454) | (~c2_1(a454)) | (~c3_1(a454)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a454)) | (~c2_1(a454)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[952, 950])).
% 0.78/0.94 tff(954,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a454) | (~c2_1(a454)) | (~c3_1(a454)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(955,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c3_1(a454)) | (~c2_1(a454))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.78/0.94 tff(956,plain,
% 0.78/0.94 (~c2_1(a454)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[955, 204, 53, 949, 943, 948, 942, 941, 64])).
% 0.78/0.94 tff(957,plain,
% 0.78/0.94 (~c1_1(a454)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[647, 947])).
% 0.78/0.94 tff(958,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a454) | c1_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a454))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a454) | c1_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a454))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(959,plain,
% 0.78/0.94 (((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c0_1(a444) | c3_1(a444) | c2_1(a454) | c1_1(a454) | c0_1(a454)) <=> (c0_1(a454) | c1_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a454))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(960,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c0_1(a444) | c3_1(a444) | c2_1(a454) | c1_1(a454) | c0_1(a454))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a454) | c1_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a454)))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[959])).
% 0.78/0.94 tff(961,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c0_1(a444) | c3_1(a444) | c2_1(a454) | c1_1(a454) | c0_1(a454))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a454) | c1_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a454))),
% 0.78/0.94 inference(transitivity,[status(thm)],[960, 958])).
% 0.78/0.94 tff(962,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c0_1(a444) | c3_1(a444) | c2_1(a454) | c1_1(a454) | c0_1(a454))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(963,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a454) | c1_1(a454) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | c1_1(a444) | c2_1(a454)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[962, 961])).
% 0.78/0.94 tff(964,plain,
% 0.78/0.94 (~c3_1(a456)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[963, 204, 757, 749, 948, 957, 942, 941, 74, 945, 956])).
% 0.78/0.94 tff(965,plain,
% 0.78/0.94 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(966,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[965])).
% 0.78/0.94 tff(967,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(968,plain,
% 0.78/0.94 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(969,plain,
% 0.78/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[968])).
% 0.78/0.94 tff(970,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.78/0.94 tff(971,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[970, 969])).
% 0.78/0.94 tff(972,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[971, 967])).
% 0.78/0.94 tff(973,plain,(
% 0.78/0.94 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.94 inference(skolemize,[status(sab)],[972])).
% 0.78/0.94 tff(974,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[973, 966])).
% 0.78/0.94 tff(975,plain,
% 0.78/0.94 (hskp2),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[592, 946, 938])).
% 0.78/0.94 tff(976,plain,
% 0.78/0.94 (~c3_1(a434)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[598, 975])).
% 0.78/0.94 tff(977,plain,
% 0.78/0.94 (~c1_1(a434)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[604, 975])).
% 0.78/0.94 tff(978,plain,
% 0.78/0.94 (c0_1(a434)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[612, 975])).
% 0.78/0.94 tff(979,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a445) | (~c1_1(a445)) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | c2_1(a445))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a445) | (~c1_1(a445)) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | c2_1(a445))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(980,plain,
% 0.78/0.94 ((hskp12 | (~ndr1_0) | c3_1(a434) | c1_1(a434) | (~c0_1(a434)) | c2_1(a445) | c0_1(a445) | (~c1_1(a445))) <=> (hskp12 | c0_1(a445) | (~c1_1(a445)) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | c2_1(a445))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(981,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a434) | c1_1(a434) | (~c0_1(a434)) | c2_1(a445) | c0_1(a445) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a445) | (~c1_1(a445)) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | c2_1(a445)))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[980])).
% 0.78/0.94 tff(982,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a434) | c1_1(a434) | (~c0_1(a434)) | c2_1(a445) | c0_1(a445) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a445) | (~c1_1(a445)) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | c2_1(a445))),
% 0.78/0.94 inference(transitivity,[status(thm)],[981, 979])).
% 0.78/0.94 tff(983,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a434) | c1_1(a434) | (~c0_1(a434)) | c2_1(a445) | c0_1(a445) | (~c1_1(a445)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(984,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a445) | (~c1_1(a445)) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | c2_1(a445)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[983, 982])).
% 0.78/0.94 tff(985,plain,
% 0.78/0.94 (hskp12),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[984, 204, 978, 40, 938, 977, 976, 974, 946])).
% 0.78/0.94 tff(986,plain,
% 0.78/0.94 (~c0_1(a450)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[376, 985])).
% 0.78/0.94 tff(987,plain,
% 0.78/0.94 (c3_1(a450)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[407, 985])).
% 0.78/0.94 tff(988,plain,
% 0.78/0.94 (c1_1(a450)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[415, 985])).
% 0.78/0.94 tff(989,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[935, 204, 783, 749, 988, 987, 943, 986, 942, 146, 964, 945])).
% 0.78/0.94 tff(990,plain,(c0_1(a445) | hskp14 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(991,plain,
% 0.78/0.94 (c0_1(a445)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[990, 54, 53])).
% 0.78/0.94 tff(992,plain,
% 0.78/0.94 (~hskp9),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[723, 991])).
% 0.78/0.94 tff(993,assumption,(hskp8), introduced(assumption)).
% 0.78/0.94 tff(994,plain,
% 0.78/0.94 (~c3_1(a444)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[262, 993])).
% 0.78/0.94 tff(995,plain,
% 0.78/0.94 (~c0_1(a444)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[268, 993])).
% 0.78/0.94 tff(996,assumption,(c0_1(a456)), introduced(assumption)).
% 0.78/0.94 tff(997,assumption,(c1_1(a456)), introduced(assumption)).
% 0.78/0.94 tff(998,plain,
% 0.78/0.94 (c2_1(a444)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[276, 993])).
% 0.78/0.94 tff(999,assumption,(c2_1(a456)), introduced(assumption)).
% 0.78/0.94 tff(1000,plain,
% 0.78/0.94 (~c1_1(a444)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[707, 204, 31, 998, 995, 994, 30])).
% 0.78/0.94 tff(1001,assumption,(~c1_1(a444)), introduced(assumption)).
% 0.78/0.94 tff(1002,assumption,(~c0_1(a444)), introduced(assumption)).
% 0.78/0.94 tff(1003,plain,
% 0.78/0.94 (hskp12 | c3_1(a456)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[770, 204, 53, 996, 999, 156])).
% 0.78/0.94 tff(1004,plain,
% 0.78/0.94 (hskp12),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1003, 807])).
% 0.78/0.94 tff(1005,plain,
% 0.78/0.94 (~c0_1(a450)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[376, 1004])).
% 0.78/0.94 tff(1006,assumption,(c2_1(a444)), introduced(assumption)).
% 0.78/0.94 tff(1007,plain,
% 0.78/0.94 (c3_1(a450)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[407, 1004])).
% 0.78/0.94 tff(1008,plain,
% 0.78/0.94 (c1_1(a450)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[415, 1004])).
% 0.78/0.94 tff(1009,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[935, 204, 997, 999, 1008, 1007, 1006, 1005, 1002, 146, 807, 1001])).
% 0.78/0.94 tff(1010,plain,(c3_1(a456) | (~c1_1(a456)) | (~c2_1(a456)) | (~c2_1(a444)) | c0_1(a444) | c1_1(a444) | hskp14 | (~c0_1(a456))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1011,plain,
% 0.78/0.94 (c3_1(a456)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1010, 1000, 999, 998, 995, 997, 53, 996])).
% 0.78/0.94 tff(1012,plain,
% 0.78/0.94 (hskp16 | (~c3_1(a456))),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[862, 204, 997, 999, 998, 995, 994, 856])).
% 0.78/0.94 tff(1013,plain,
% 0.78/0.94 (hskp16),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1012, 1011])).
% 0.78/0.94 tff(1014,plain,
% 0.78/0.94 (~c2_1(a457)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[318, 1013])).
% 0.78/0.94 tff(1015,plain,
% 0.78/0.94 (c3_1(a457)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[326, 1013])).
% 0.78/0.94 tff(1016,plain,
% 0.78/0.94 (c1_1(a457)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[334, 1013])).
% 0.78/0.94 tff(1017,plain,
% 0.78/0.94 (hskp25),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[873, 204, 996, 997, 1016, 1015, 1014, 846, 1011])).
% 0.78/0.94 tff(1018,plain,
% 0.78/0.94 (~c0_1(a489)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[879, 1017])).
% 0.78/0.94 tff(1019,plain,
% 0.78/0.94 (c3_1(a489)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[887, 1017])).
% 0.78/0.94 tff(1020,plain,
% 0.78/0.94 (c2_1(a489)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[895, 1017])).
% 0.78/0.94 tff(1021,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[902, 204, 53, 1020, 1019, 998, 1018, 995, 994, 64])).
% 0.78/0.94 tff(1022,plain,((~hskp8) | hskp14 | (~c0_1(a456)) | (~c1_1(a456)) | (~c2_1(a456)) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1023,plain,
% 0.78/0.94 (~hskp8),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1022, 757, 53, 783, 749, 992])).
% 0.78/0.94 tff(1024,plain,
% 0.78/0.94 (hskp1),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[82, 1023, 54])).
% 0.78/0.94 tff(1025,plain,
% 0.78/0.94 (~c1_1(a433)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[94, 1024])).
% 0.78/0.94 tff(1026,plain,
% 0.78/0.94 (~c0_1(a433)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[100, 1024])).
% 0.78/0.94 tff(1027,plain,
% 0.78/0.94 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | c0_1(a433) | c1_1(a433) | (~ndr1_0) | (~c3_1(a433)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp8 | c0_1(a433) | c1_1(a433) | (~ndr1_0) | (~c3_1(a433)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1028,plain,
% 0.78/0.94 ((hskp9 | hskp8 | (~ndr1_0) | c0_1(a433) | c1_1(a433) | (~c3_1(a433))) <=> (hskp9 | hskp8 | c0_1(a433) | c1_1(a433) | (~ndr1_0) | (~c3_1(a433)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1029,plain,
% 0.78/0.94 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a433) | c1_1(a433) | (~c3_1(a433)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | c0_1(a433) | c1_1(a433) | (~ndr1_0) | (~c3_1(a433))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1028])).
% 0.78/0.94 tff(1030,plain,
% 0.78/0.94 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a433) | c1_1(a433) | (~c3_1(a433)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp8 | c0_1(a433) | c1_1(a433) | (~ndr1_0) | (~c3_1(a433)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1029, 1027])).
% 0.78/0.94 tff(1031,plain,
% 0.78/0.94 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a433) | c1_1(a433) | (~c3_1(a433)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1032,plain,
% 0.78/0.94 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp8 | c0_1(a433) | c1_1(a433) | (~ndr1_0) | (~c3_1(a433))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 0.78/0.95 tff(1033,plain,
% 0.78/0.95 (~c3_1(a433)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1032, 204, 992, 1023, 1026, 1025, 50])).
% 0.78/0.95 tff(1034,plain,
% 0.78/0.95 (~c2_1(a433)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[88, 1024])).
% 0.78/0.95 tff(1035,plain,
% 0.78/0.95 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | c0_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp29 | hskp10 | c0_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1036,plain,
% 0.78/0.95 ((hskp29 | hskp10 | (~ndr1_0) | c3_1(a433) | c2_1(a433) | c0_1(a433)) <=> (hskp29 | hskp10 | c0_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1037,plain,
% 0.78/0.95 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a433) | c2_1(a433) | c0_1(a433))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | c0_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433)))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1036])).
% 0.78/0.95 tff(1038,plain,
% 0.78/0.95 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a433) | c2_1(a433) | c0_1(a433))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp29 | hskp10 | c0_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1037, 1035])).
% 0.78/0.95 tff(1039,plain,
% 0.78/0.95 ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a433) | c2_1(a433) | c0_1(a433))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1040,plain,
% 0.78/0.95 ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp29 | hskp10 | c0_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 0.78/0.95 tff(1041,plain,
% 0.78/0.95 (hskp29),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1040, 204, 54, 1026, 1034, 449, 1033])).
% 0.78/0.95 tff(1042,plain,
% 0.78/0.95 (c3_1(a447)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[464, 1041])).
% 0.78/0.95 tff(1043,plain,
% 0.78/0.95 (c2_1(a447)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[472, 1041])).
% 0.78/0.95 tff(1044,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1045,plain,
% 0.78/0.95 (((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c0_1(a447)) | c1_1(a433) | c0_1(a433) | c3_1(a433) | c2_1(a433) | c1_1(a433) | c0_1(a433)) <=> (c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1046,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c0_1(a447)) | c1_1(a433) | c0_1(a433) | c3_1(a433) | c2_1(a433) | c1_1(a433) | c0_1(a433))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1045])).
% 0.78/0.95 tff(1047,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c0_1(a447)) | c1_1(a433) | c0_1(a433) | c3_1(a433) | c2_1(a433) | c1_1(a433) | c0_1(a433))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1046, 1044])).
% 0.78/0.95 tff(1048,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a447)) | (~c3_1(a447)) | (~c0_1(a447)) | c1_1(a433) | c0_1(a433) | c3_1(a433) | c2_1(a433) | c1_1(a433) | c0_1(a433))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1049,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a433) | c1_1(a433) | c2_1(a433) | (~ndr1_0) | c3_1(a433) | (~c3_1(a447)) | (~c0_1(a447)) | (~c2_1(a447))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.78/0.95 tff(1050,plain,
% 0.78/0.95 (~c0_1(a447)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1049, 204, 1043, 1042, 1026, 1025, 1034, 74, 1033])).
% 0.78/0.95 tff(1051,plain,
% 0.78/0.95 (c1_1(a447)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[504, 1041])).
% 0.78/0.95 tff(1052,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[801, 204, 1023, 1051, 1043, 1042, 249, 1050])).
% 0.78/0.95 tff(1053,plain,(hskp10 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1054,plain,
% 0.78/0.95 (hskp10),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1053, 53])).
% 0.78/0.95 tff(1055,plain,
% 0.78/0.95 (((~hskp10) | (~c2_1(a448))) <=> ((~hskp10) | (~c2_1(a448)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1056,plain,
% 0.78/0.95 (((~c2_1(a448)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a448)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1057,axiom,((~c2_1(a448)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.78/0.95 tff(1058,plain,
% 0.78/0.95 ((~hskp10) | (~c2_1(a448))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.78/0.95 tff(1059,plain,
% 0.78/0.95 ((~hskp10) | (~c2_1(a448))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1058, 1055])).
% 0.78/0.95 tff(1060,plain,
% 0.78/0.95 (~c2_1(a448)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1059, 1054])).
% 0.78/0.95 tff(1061,plain,
% 0.78/0.95 (((~hskp10) | (~c0_1(a448))) <=> ((~hskp10) | (~c0_1(a448)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1062,plain,
% 0.78/0.95 (((~c0_1(a448)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a448)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1063,axiom,((~c0_1(a448)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.78/0.95 tff(1064,plain,
% 0.78/0.95 ((~hskp10) | (~c0_1(a448))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 0.78/0.95 tff(1065,plain,
% 0.78/0.95 ((~hskp10) | (~c0_1(a448))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1064, 1061])).
% 0.78/0.95 tff(1066,plain,
% 0.78/0.95 (~c0_1(a448)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1065, 1054])).
% 0.78/0.95 tff(1067,plain,
% 0.78/0.95 (((~hskp10) | c1_1(a448)) <=> ((~hskp10) | c1_1(a448))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1068,axiom,((~hskp10) | c1_1(a448)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.78/0.95 tff(1069,plain,
% 0.78/0.95 ((~hskp10) | c1_1(a448)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 0.78/0.95 tff(1070,plain,
% 0.78/0.95 ((~hskp10) | c1_1(a448)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1069, 1067])).
% 0.78/0.95 tff(1071,plain,
% 0.78/0.95 ((~hskp10) | c1_1(a448)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1070, 1067])).
% 0.78/0.95 tff(1072,plain,
% 0.78/0.95 ((~hskp10) | c1_1(a448)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1071, 1067])).
% 0.78/0.95 tff(1073,plain,
% 0.78/0.95 ((~hskp10) | c1_1(a448)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1072, 1067])).
% 0.78/0.95 tff(1074,plain,
% 0.78/0.95 (c1_1(a448)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1073, 1054])).
% 0.78/0.95 tff(1075,assumption,(~c3_1(a444)), introduced(assumption)).
% 0.78/0.95 tff(1076,plain,
% 0.78/0.95 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp14 | hskp2 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1077,plain,
% 0.78/0.95 ((hskp14 | hskp2 | (~ndr1_0) | c2_1(a448) | c0_1(a448) | (~c1_1(a448))) <=> (hskp14 | hskp2 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1078,plain,
% 0.78/0.95 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1077])).
% 0.78/0.95 tff(1079,plain,
% 0.78/0.95 (((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))) <=> ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp14 | hskp2 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1078, 1076])).
% 0.78/0.95 tff(1080,plain,
% 0.78/0.95 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp14 | hskp2 | (~ndr1_0) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1081,plain,
% 0.78/0.95 ((~![U: $i] : (hskp14 | hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp14 | hskp2 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 0.78/0.95 tff(1082,plain,
% 0.78/0.95 (hskp2),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1081, 204, 53, 1074, 1066, 1060, 585])).
% 0.78/0.95 tff(1083,plain,
% 0.78/0.95 (~c3_1(a434)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[598, 1082])).
% 0.78/0.95 tff(1084,plain,
% 0.78/0.95 (~c1_1(a434)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[604, 1082])).
% 0.78/0.95 tff(1085,plain,
% 0.78/0.95 (c0_1(a434)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[612, 1082])).
% 0.78/0.95 tff(1086,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a448) | c2_1(a448) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c1_1(a448)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a448) | c2_1(a448) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c1_1(a448)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1087,plain,
% 0.78/0.95 ((hskp12 | (~ndr1_0) | c3_1(a434) | c1_1(a434) | (~c0_1(a434)) | c2_1(a448) | c0_1(a448) | (~c1_1(a448))) <=> (hskp12 | c0_1(a448) | c2_1(a448) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c1_1(a448)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1088,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a434) | c1_1(a434) | (~c0_1(a434)) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a448) | c2_1(a448) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c1_1(a448))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1087])).
% 0.78/0.95 tff(1089,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a434) | c1_1(a434) | (~c0_1(a434)) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a448) | c2_1(a448) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c1_1(a448)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1088, 1086])).
% 0.78/0.95 tff(1090,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a434) | c1_1(a434) | (~c0_1(a434)) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1091,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a448) | c2_1(a448) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c1_1(a448))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.78/0.95 tff(1092,plain,
% 0.78/0.95 (hskp12),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1091, 204, 1074, 1085, 1066, 1060, 1084, 1083, 974])).
% 0.78/0.95 tff(1093,plain,
% 0.78/0.95 (~c0_1(a450)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[376, 1092])).
% 0.78/0.95 tff(1094,plain,
% 0.78/0.95 (c3_1(a450)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[407, 1092])).
% 0.78/0.95 tff(1095,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a450) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a450)) | (~c3_1(a450)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a450) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a450)) | (~c3_1(a450)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1096,plain,
% 0.78/0.95 ((hskp14 | (~ndr1_0) | c0_1(a450) | (~c2_1(a450)) | (~c3_1(a450)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444))) <=> (hskp14 | c0_1(a450) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a450)) | (~c3_1(a450)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1097,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a450) | (~c2_1(a450)) | (~c3_1(a450)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a450) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a450)) | (~c3_1(a450))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1096])).
% 0.78/0.95 tff(1098,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a450) | (~c2_1(a450)) | (~c3_1(a450)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a450) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a450)) | (~c3_1(a450)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1097, 1095])).
% 0.78/0.95 tff(1099,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a450) | (~c2_1(a450)) | (~c3_1(a450)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1100,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a450) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c2_1(a450)) | (~c3_1(a450))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.78/0.95 tff(1101,plain,
% 0.78/0.95 (~c2_1(a450)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1100, 204, 53, 1094, 1006, 1093, 1002, 1075, 64])).
% 0.78/0.95 tff(1102,plain,
% 0.78/0.95 (~c3_1(a486)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[521, 204, 53, 128, 1006, 120, 1002, 1075, 64])).
% 0.78/0.95 tff(1103,plain,
% 0.78/0.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1104,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1103])).
% 0.78/0.95 tff(1105,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1106,plain,
% 0.78/0.95 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1107,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1106])).
% 0.78/0.95 tff(1108,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 0.78/0.95 tff(1109,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 0.78/0.95 tff(1110,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1109, 1105])).
% 0.78/0.95 tff(1111,plain,(
% 0.78/0.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(skolemize,[status(sab)],[1110])).
% 0.78/0.95 tff(1112,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1111, 1104])).
% 0.78/0.95 tff(1113,plain,
% 0.78/0.95 (((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | c0_1(a450) | (~ndr1_0) | c2_1(a450) | (~c3_1(a450)))) <=> ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp16 | c0_1(a450) | (~ndr1_0) | c2_1(a450) | (~c3_1(a450)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1114,plain,
% 0.78/0.95 ((hskp30 | hskp16 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | (~c3_1(a450))) <=> (hskp30 | hskp16 | c0_1(a450) | (~ndr1_0) | c2_1(a450) | (~c3_1(a450)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1115,plain,
% 0.78/0.95 (((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | (~c3_1(a450)))) <=> ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | c0_1(a450) | (~ndr1_0) | c2_1(a450) | (~c3_1(a450))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1114])).
% 0.78/0.95 tff(1116,plain,
% 0.78/0.95 (((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | (~c3_1(a450)))) <=> ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp16 | c0_1(a450) | (~ndr1_0) | c2_1(a450) | (~c3_1(a450)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1115, 1113])).
% 0.78/0.95 tff(1117,plain,
% 0.78/0.95 ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp16 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | (~c3_1(a450)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1118,plain,
% 0.78/0.95 ((~![U: $i] : (hskp30 | hskp16 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp16 | c0_1(a450) | (~ndr1_0) | c2_1(a450) | (~c3_1(a450))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 0.78/0.95 tff(1119,plain,
% 0.78/0.95 (hskp30 | hskp16 | c2_1(a450)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1118, 204, 1094, 1093, 176])).
% 0.78/0.95 tff(1120,plain,
% 0.78/0.95 (hskp16),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1119, 102, 1101])).
% 0.78/0.95 tff(1121,plain,
% 0.78/0.95 (~c2_1(a457)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[318, 1120])).
% 0.78/0.95 tff(1122,plain,
% 0.78/0.95 (c3_1(a457)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[326, 1120])).
% 0.78/0.95 tff(1123,plain,
% 0.78/0.95 (c1_1(a457)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[334, 1120])).
% 0.78/0.95 tff(1124,plain,
% 0.78/0.95 (hskp6),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[341, 204, 136, 128, 1123, 1122, 120, 1121, 166])).
% 0.78/0.95 tff(1125,plain,
% 0.78/0.95 (~c3_1(a442)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[347, 1124])).
% 0.78/0.95 tff(1126,plain,
% 0.78/0.95 (c0_1(a442)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[363, 1124])).
% 0.78/0.95 tff(1127,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c2_1(a457) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c3_1(a457)) | (~c1_1(a457)) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c2_1(a457) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c3_1(a457)) | (~c1_1(a457)) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1128,plain,
% 0.78/0.95 (((~ndr1_0) | c3_1(a442) | (~c1_1(a442)) | (~c0_1(a442)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486))) <=> (c0_1(a486) | c2_1(a457) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c3_1(a457)) | (~c1_1(a457)) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1129,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a442) | (~c1_1(a442)) | (~c0_1(a442)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c2_1(a457) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c3_1(a457)) | (~c1_1(a457)) | c3_1(a486) | (~c1_1(a486))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1128])).
% 0.78/0.95 tff(1130,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a442) | (~c1_1(a442)) | (~c0_1(a442)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c2_1(a457) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c3_1(a457)) | (~c1_1(a457)) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1129, 1127])).
% 0.78/0.95 tff(1131,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a442) | (~c1_1(a442)) | (~c0_1(a442)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1132,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c2_1(a457) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c3_1(a457)) | (~c1_1(a457)) | c3_1(a486) | (~c1_1(a486))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.78/0.95 tff(1133,plain,
% 0.78/0.95 (~c1_1(a442)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1132, 204, 136, 1123, 1122, 1126, 120, 1121, 1125, 1112, 1102])).
% 0.78/0.95 tff(1134,plain,
% 0.78/0.95 (c2_1(a442)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[355, 1124])).
% 0.78/0.95 tff(1135,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c3_1(a442) | (~ndr1_0) | c1_1(a442) | (~c2_1(a442)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a442) | (~ndr1_0) | c1_1(a442) | (~c2_1(a442)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1136,plain,
% 0.78/0.95 (((~ndr1_0) | c3_1(a442) | c1_1(a442) | (~c2_1(a442)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486))) <=> (c0_1(a486) | c3_1(a442) | (~ndr1_0) | c1_1(a442) | (~c2_1(a442)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1137,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a442) | c1_1(a442) | (~c2_1(a442)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c3_1(a442) | (~ndr1_0) | c1_1(a442) | (~c2_1(a442)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1136])).
% 0.78/0.95 tff(1138,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a442) | c1_1(a442) | (~c2_1(a442)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a442) | (~ndr1_0) | c1_1(a442) | (~c2_1(a442)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1137, 1135])).
% 0.78/0.95 tff(1139,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a442) | c1_1(a442) | (~c2_1(a442)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1140,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a442) | (~ndr1_0) | c1_1(a442) | (~c2_1(a442)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 0.78/0.95 tff(1141,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1140, 204, 136, 128, 1134, 120, 1125, 10, 1102, 1133])).
% 0.78/0.95 tff(1142,plain,(hskp30 | hskp14 | (~c2_1(a444)) | c0_1(a444) | c3_1(a444)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1143,plain,
% 0.78/0.95 (hskp30),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1142, 1006, 53, 1002, 1075])).
% 0.78/0.95 tff(1144,plain,
% 0.78/0.95 (c1_1(a456)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[782, 1143])).
% 0.78/0.95 tff(1145,plain,
% 0.78/0.95 (c2_1(a456)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[748, 1143])).
% 0.78/0.95 tff(1146,plain,
% 0.78/0.95 (c0_1(a456)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[756, 1143])).
% 0.78/0.95 tff(1147,plain,
% 0.78/0.95 (c1_1(a444)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1010, 807, 1006, 1002, 1146, 1145, 53, 1144])).
% 0.78/0.95 tff(1148,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a448) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a444)) | (~c3_1(a448)) | (~c1_1(a448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a448) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a444)) | (~c3_1(a448)) | (~c1_1(a448)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1149,plain,
% 0.78/0.95 (((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a448) | (~c3_1(a448)) | (~c1_1(a448)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444))) <=> (c2_1(a448) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a444)) | (~c3_1(a448)) | (~c1_1(a448)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1150,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a448) | (~c3_1(a448)) | (~c1_1(a448)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a448) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a444)) | (~c3_1(a448)) | (~c1_1(a448))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1149])).
% 0.78/0.96 tff(1151,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a448) | (~c3_1(a448)) | (~c1_1(a448)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a448) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a444)) | (~c3_1(a448)) | (~c1_1(a448)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1150, 1148])).
% 0.78/0.96 tff(1152,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a448) | (~c3_1(a448)) | (~c1_1(a448)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1153,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a448) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a444)) | (~c3_1(a448)) | (~c1_1(a448))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 0.78/0.96 tff(1154,plain,
% 0.78/0.96 (~c3_1(a448)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1153, 204, 1146, 1144, 1074, 1060, 1002, 1075, 1112, 807, 1147])).
% 0.78/0.96 tff(1155,plain,
% 0.78/0.96 (c1_1(a450)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[415, 1092])).
% 0.78/0.96 tff(1156,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a448) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c3_1(a448) | (~c1_1(a448)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a448) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c3_1(a448) | (~c1_1(a448)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1157,plain,
% 0.78/0.96 (((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448))) <=> (c0_1(a448) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c3_1(a448) | (~c1_1(a448)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1158,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a448) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c3_1(a448) | (~c1_1(a448)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1157])).
% 0.78/0.96 tff(1159,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a448) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c3_1(a448) | (~c1_1(a448)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1158, 1156])).
% 0.78/0.96 tff(1160,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1161,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a448) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c3_1(a448) | (~c1_1(a448)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 0.78/0.96 tff(1162,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1161, 204, 1146, 1144, 1155, 1094, 1074, 1066, 1112, 807, 1154, 1101])).
% 0.78/0.96 tff(1163,plain,(c3_1(a456) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(1164,plain,
% 0.78/0.96 (c3_1(a456)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1163, 995, 994, 998, 53])).
% 0.78/0.96 tff(1165,plain,
% 0.78/0.96 (hskp30),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1142, 998, 53, 995, 994])).
% 0.78/0.96 tff(1166,plain,
% 0.78/0.96 (c2_1(a456)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[748, 1165])).
% 0.78/0.96 tff(1167,plain,
% 0.78/0.96 (c1_1(a456)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[782, 1165])).
% 0.78/0.96 tff(1168,plain,
% 0.78/0.96 (c0_1(a456)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[756, 1165])).
% 0.78/0.96 tff(1169,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1170,plain,
% 0.78/0.96 (((~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | (~c2_1(a456)) | c1_1(a434) | c3_1(a434) | (~c0_1(a434))) <=> (c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1171,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | (~c2_1(a456)) | c1_1(a434) | c3_1(a434) | (~c0_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1170])).
% 0.78/0.96 tff(1172,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | (~c2_1(a456)) | c1_1(a434) | c3_1(a434) | (~c0_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1171, 1169])).
% 0.78/0.96 tff(1173,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)) | (~c2_1(a456)) | c1_1(a434) | c3_1(a434) | (~c0_1(a434)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1174,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a434) | c3_1(a434) | (~ndr1_0) | (~c0_1(a434)) | (~c2_1(a456)) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.78/0.96 tff(1175,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1174, 204, 1168, 1167, 1166, 1085, 1084, 1083, 561, 1164])).
% 0.78/0.96 tff(1176,plain,((~hskp8) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(1177,plain,
% 0.78/0.96 (~hskp8),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1176, 53])).
% 0.78/0.96 tff(1178,assumption,(~c2_1(a448)), introduced(assumption)).
% 0.78/0.96 tff(1179,assumption,(~c0_1(a448)), introduced(assumption)).
% 0.78/0.96 tff(1180,assumption,(c1_1(a448)), introduced(assumption)).
% 0.78/0.96 tff(1181,plain,
% 0.78/0.96 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1182,plain,
% 0.78/0.96 ((hskp15 | hskp9 | (~ndr1_0) | c2_1(a448) | c0_1(a448) | (~c1_1(a448))) <=> (hskp15 | hskp9 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1183,plain,
% 0.78/0.96 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1182])).
% 0.78/0.96 tff(1184,plain,
% 0.78/0.96 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1183, 1181])).
% 0.78/0.96 tff(1185,plain,
% 0.78/0.96 ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1186,plain,
% 0.78/0.96 ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 0.78/0.96 tff(1187,plain,
% 0.78/0.96 (hskp15 | hskp9),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1186, 204, 1180, 1179, 1178, 634])).
% 0.78/0.96 tff(1188,plain,
% 0.78/0.96 (hskp15),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1187, 31])).
% 0.78/0.96 tff(1189,plain,
% 0.78/0.96 (~c1_1(a454)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[647, 1188])).
% 0.78/0.96 tff(1190,plain,
% 0.78/0.96 (~c0_1(a454)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[653, 1188])).
% 0.78/0.96 tff(1191,plain,
% 0.78/0.96 (c3_1(a454)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[661, 1188])).
% 0.78/0.96 tff(1192,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[668, 204, 31, 32, 1191, 1190, 1189, 50])).
% 0.78/0.96 tff(1193,plain,(hskp9 | hskp8 | (~c1_1(a448)) | c0_1(a448) | c2_1(a448)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(1194,plain,
% 0.78/0.96 (hskp9),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1193, 1177, 1074, 1066, 1060])).
% 0.78/0.96 tff(1195,plain,
% 0.78/0.96 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(1196,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[1195])).
% 0.78/0.96 tff(1197,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1198,plain,
% 0.78/0.96 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_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)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(1199,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_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)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[1198])).
% 0.78/0.96 tff(1200,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 0.78/0.96 tff(1201,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 0.78/0.96 tff(1202,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1201, 1197])).
% 0.78/0.96 tff(1203,plain,(
% 0.78/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[1202])).
% 0.78/0.96 tff(1204,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1203, 1196])).
% 0.78/0.96 tff(1205,plain,
% 0.78/0.96 (~c3_1(a486)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[255, 204, 32, 136, 128, 120, 249])).
% 0.78/0.96 tff(1206,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | (~c2_1(a450)) | (~c3_1(a450)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | (~c2_1(a450)) | (~c3_1(a450)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1207,plain,
% 0.78/0.96 ((hskp8 | (~ndr1_0) | c0_1(a450) | (~c2_1(a450)) | (~c3_1(a450)) | c0_1(a450) | (~c1_1(a450)) | (~c2_1(a450))) <=> (hskp8 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | (~c2_1(a450)) | (~c3_1(a450)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1208,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a450) | (~c2_1(a450)) | (~c3_1(a450)) | c0_1(a450) | (~c1_1(a450)) | (~c2_1(a450)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | (~c2_1(a450)) | (~c3_1(a450))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1207])).
% 0.78/0.96 tff(1209,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a450) | (~c2_1(a450)) | (~c3_1(a450)) | c0_1(a450) | (~c1_1(a450)) | (~c2_1(a450)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | (~c2_1(a450)) | (~c3_1(a450)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1208, 1206])).
% 0.78/0.96 tff(1210,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a450) | (~c2_1(a450)) | (~c3_1(a450)) | c0_1(a450) | (~c1_1(a450)) | (~c2_1(a450)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1211,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp8 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | (~c2_1(a450)) | (~c3_1(a450))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1210, 1209])).
% 0.78/0.96 tff(1212,plain,
% 0.78/0.96 (hskp8 | (~c2_1(a450))),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1211, 204, 1155, 1094, 1093, 249])).
% 0.78/0.96 tff(1213,plain,
% 0.78/0.96 (~c2_1(a450)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1212, 32])).
% 0.78/0.96 tff(1214,plain,
% 0.78/0.96 (hskp16),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1119, 102, 1213])).
% 0.78/0.96 tff(1215,plain,
% 0.78/0.96 (~c2_1(a457)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[318, 1214])).
% 0.78/0.96 tff(1216,plain,
% 0.78/0.96 (c3_1(a457)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[326, 1214])).
% 0.78/0.96 tff(1217,plain,
% 0.78/0.96 (c1_1(a457)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[334, 1214])).
% 0.78/0.96 tff(1218,plain,
% 0.78/0.96 (hskp6),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[341, 204, 136, 128, 1217, 1216, 120, 1215, 166])).
% 0.78/0.96 tff(1219,plain,
% 0.78/0.96 (~c3_1(a442)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[347, 1218])).
% 0.78/0.96 tff(1220,plain,
% 0.78/0.96 (c0_1(a442)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[363, 1218])).
% 0.78/0.96 tff(1221,plain,
% 0.78/0.96 (~c1_1(a442)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1132, 204, 136, 1217, 1216, 1220, 120, 1215, 1219, 1112, 1205])).
% 0.78/0.96 tff(1222,plain,
% 0.78/0.96 (c2_1(a442)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[355, 1218])).
% 0.78/0.96 tff(1223,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1140, 204, 136, 128, 1222, 120, 1219, 10, 1205, 1221])).
% 0.78/0.96 tff(1224,plain,(hskp30 | hskp8 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(1225,plain,
% 0.78/0.96 (hskp30),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1224, 32, 53])).
% 0.78/0.96 tff(1226,plain,
% 0.78/0.96 (c0_1(a456)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[756, 1225])).
% 0.78/0.96 tff(1227,plain,
% 0.78/0.96 (c2_1(a456)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[748, 1225])).
% 0.78/0.96 tff(1228,plain,
% 0.78/0.96 (c1_1(a456)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[782, 1225])).
% 0.78/0.96 tff(1229,assumption,(~c0_1(a450)), introduced(assumption)).
% 0.78/0.96 tff(1230,assumption,(c3_1(a450)), introduced(assumption)).
% 0.78/0.96 tff(1231,assumption,(c1_1(a450)), introduced(assumption)).
% 0.78/0.96 tff(1232,plain,
% 0.78/0.96 (hskp8 | (~c2_1(a450))),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1211, 204, 1231, 1230, 1229, 249])).
% 0.78/0.96 tff(1233,plain,
% 0.78/0.96 (~c2_1(a450)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1232, 32])).
% 0.78/0.96 tff(1234,plain,
% 0.78/0.96 (hskp9),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1193, 32, 1180, 1179, 1178])).
% 0.78/0.96 tff(1235,plain,
% 0.78/0.96 (~c3_1(a445)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[529, 1234])).
% 0.78/0.96 tff(1236,plain,
% 0.78/0.96 (~c1_1(a445)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[567, 1234])).
% 0.78/0.96 tff(1237,assumption,(~c1_1(a486)), introduced(assumption)).
% 0.78/0.96 tff(1238,plain,
% 0.78/0.96 (~hskp24),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[135, 1237])).
% 0.78/0.96 tff(1239,plain,
% 0.78/0.96 (^[U: $i] : refl((hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(1240,plain,
% 0.78/0.96 (![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[1239])).
% 0.78/0.96 tff(1241,plain,
% 0.78/0.96 (![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1242,plain,
% 0.78/0.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp8) <=> ((hskp24 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp8))), rewrite(((hskp24 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp8) <=> (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(1243,plain,
% 0.78/0.96 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp8) <=> ![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[1242])).
% 0.78/0.96 tff(1244,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp24) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.78/0.96 tff(1245,plain,
% 0.78/0.96 (![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 0.78/0.96 tff(1246,plain,
% 0.78/0.96 (![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1245, 1241])).
% 0.78/0.96 tff(1247,plain,(
% 0.78/0.96 ![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[1246])).
% 0.78/0.96 tff(1248,plain,
% 0.78/0.96 (![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1247, 1240])).
% 0.78/0.96 tff(1249,plain,
% 0.78/0.96 (((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)))) <=> ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1250,plain,
% 0.78/0.96 ((hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456))) <=> (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1251,plain,
% 0.78/0.96 (((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)))) <=> ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1250])).
% 0.78/0.96 tff(1252,plain,
% 0.78/0.96 (((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)))) <=> ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1251, 1249])).
% 0.78/0.97 tff(1253,plain,
% 0.78/0.97 ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c1_1(a456)) | (~c0_1(a456)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1254,plain,
% 0.78/0.97 ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a456)) | (~c0_1(a456)) | (~c1_1(a456))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 0.78/0.97 tff(1255,plain,
% 0.78/0.97 (hskp24 | (~c3_1(a456))),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1254, 204, 32, 996, 997, 1248])).
% 0.78/0.97 tff(1256,plain,
% 0.78/0.97 (~c3_1(a456)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1255, 1238])).
% 0.78/0.97 tff(1257,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a486) | c0_1(a486) | c0_1(a450) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a486) | c0_1(a486) | c0_1(a450) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c2_1(a486)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1258,plain,
% 0.78/0.97 (((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a486) | c0_1(a486) | (~c2_1(a486))) <=> (c1_1(a486) | c0_1(a486) | c0_1(a450) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c2_1(a486)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1259,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a486) | c0_1(a486) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a486) | c0_1(a486) | c0_1(a450) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c2_1(a486))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1258])).
% 0.78/0.97 tff(1260,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a486) | c0_1(a486) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a486) | c0_1(a486) | c0_1(a450) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c2_1(a486)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1259, 1257])).
% 0.78/0.97 tff(1261,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a486) | c0_1(a486) | (~c2_1(a486)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1262,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a486) | c0_1(a486) | c0_1(a450) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | (~c3_1(a450)) | (~c2_1(a486))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 0.78/0.97 tff(1263,plain,
% 0.78/0.97 (~c2_1(a486)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1262, 204, 997, 999, 1237, 1231, 1230, 178, 1229, 146, 1256])).
% 0.78/0.97 tff(1264,plain,
% 0.78/0.97 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1265,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1264])).
% 0.78/0.97 tff(1266,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1267,plain,
% 0.78/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1268,plain,
% 0.78/0.97 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1267])).
% 0.78/0.97 tff(1269,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.78/0.97 tff(1270,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 0.78/0.97 tff(1271,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1270, 1266])).
% 0.78/0.97 tff(1272,plain,(
% 0.78/0.97 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(skolemize,[status(sab)],[1271])).
% 0.78/0.97 tff(1273,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1272, 1265])).
% 0.78/0.97 tff(1274,plain,
% 0.78/0.97 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1275,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1274])).
% 0.78/0.97 tff(1276,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1277,plain,
% 0.78/0.97 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_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))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_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))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_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) | (~c1_1(V))) | c2_1(V)))), rewrite((((~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)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1278,plain,
% 0.78/0.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1277])).
% 0.78/0.97 tff(1279,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.78/0.97 tff(1280,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 0.78/0.97 tff(1281,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1280, 1276])).
% 0.78/0.97 tff(1282,plain,(
% 0.78/0.97 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.97 inference(skolemize,[status(sab)],[1281])).
% 0.78/0.97 tff(1283,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1282, 1275])).
% 0.78/0.97 tff(1284,plain,
% 0.78/0.97 (~c2_1(a445)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[789, 204, 997, 999, 1231, 1230, 1229, 40, 1236, 146, 1256])).
% 0.78/0.97 tff(1285,plain,
% 0.78/0.97 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1286,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1285])).
% 0.78/0.97 tff(1287,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1288,plain,
% 0.78/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1289,plain,
% 0.78/0.97 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1288])).
% 0.78/0.97 tff(1290,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.78/0.97 tff(1291,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 0.78/0.97 tff(1292,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1291, 1287])).
% 0.78/0.97 tff(1293,plain,(
% 0.78/0.97 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.78/0.97 inference(skolemize,[status(sab)],[1292])).
% 0.78/0.97 tff(1294,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1293, 1286])).
% 0.78/0.97 tff(1295,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp19 | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c2_1(a445))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp19 | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c2_1(a445))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1296,plain,
% 0.78/0.97 ((hskp19 | (~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c2_1(a445) | c1_1(a445) | c3_1(a445)) <=> (hskp19 | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c2_1(a445))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1297,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp19 | (~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c2_1(a445) | c1_1(a445) | c3_1(a445))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp19 | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c2_1(a445)))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1296])).
% 0.78/0.97 tff(1298,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp19 | (~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c2_1(a445) | c1_1(a445) | c3_1(a445))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp19 | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c2_1(a445))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1297, 1295])).
% 0.78/0.97 tff(1299,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp19 | (~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c2_1(a445) | c1_1(a445) | c3_1(a445))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1300,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp19 | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c2_1(a445)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 0.78/0.97 tff(1301,plain,
% 0.78/0.97 (hskp19),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1300, 204, 997, 999, 1236, 1235, 1294, 1256, 1284])).
% 0.78/0.97 tff(1302,plain,
% 0.78/0.97 (((~hskp19) | (~c2_1(a467))) <=> ((~hskp19) | (~c2_1(a467)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1303,plain,
% 0.78/0.97 (((~c2_1(a467)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a467)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1304,axiom,((~c2_1(a467)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.78/0.97 tff(1305,plain,
% 0.78/0.97 ((~hskp19) | (~c2_1(a467))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 0.78/0.97 tff(1306,plain,
% 0.78/0.97 ((~hskp19) | (~c2_1(a467))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1305, 1302])).
% 0.78/0.97 tff(1307,plain,
% 0.78/0.97 (~c2_1(a467)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1306, 1301])).
% 0.78/0.97 tff(1308,plain,
% 0.78/0.97 (((~hskp19) | (~c1_1(a467))) <=> ((~hskp19) | (~c1_1(a467)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1309,plain,
% 0.78/0.97 (((~c1_1(a467)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a467)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1310,axiom,((~c1_1(a467)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.78/0.97 tff(1311,plain,
% 0.78/0.97 ((~hskp19) | (~c1_1(a467))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.78/0.97 tff(1312,plain,
% 0.78/0.97 ((~hskp19) | (~c1_1(a467))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1311, 1308])).
% 0.78/0.97 tff(1313,plain,
% 0.78/0.97 (~c1_1(a467)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1312, 1301])).
% 0.78/0.97 tff(1314,plain,
% 0.78/0.97 (((~hskp19) | c0_1(a467)) <=> ((~hskp19) | c0_1(a467))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1315,axiom,((~hskp19) | c0_1(a467)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.78/0.97 tff(1316,plain,
% 0.78/0.97 ((~hskp19) | c0_1(a467)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 0.78/0.97 tff(1317,plain,
% 0.78/0.97 ((~hskp19) | c0_1(a467)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1316, 1314])).
% 0.78/0.97 tff(1318,plain,
% 0.78/0.97 ((~hskp19) | c0_1(a467)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1317, 1314])).
% 0.78/0.97 tff(1319,plain,
% 0.78/0.97 ((~hskp19) | c0_1(a467)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1318, 1314])).
% 0.78/0.97 tff(1320,plain,
% 0.78/0.97 ((~hskp19) | c0_1(a467)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1319, 1314])).
% 0.78/0.97 tff(1321,plain,
% 0.78/0.97 (c0_1(a467)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1320, 1301])).
% 0.78/0.97 tff(1322,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a467) | c2_1(a467) | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a467) | c2_1(a467) | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)) | (~c0_1(a467)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1323,plain,
% 0.78/0.97 ((hskp11 | (~ndr1_0) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)) | c2_1(a448) | c0_1(a448) | (~c1_1(a448))) <=> (hskp11 | c1_1(a467) | c2_1(a467) | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)) | (~c0_1(a467)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1324,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a467) | c2_1(a467) | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)) | (~c0_1(a467))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1323])).
% 0.78/0.97 tff(1325,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a467) | c2_1(a467) | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)) | (~c0_1(a467)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1324, 1322])).
% 0.78/0.97 tff(1326,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)) | c2_1(a448) | c0_1(a448) | (~c1_1(a448)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1327,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a467) | c2_1(a467) | c0_1(a448) | c2_1(a448) | (~ndr1_0) | (~c1_1(a448)) | (~c0_1(a467))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 0.78/0.97 tff(1328,plain,
% 0.78/0.97 (hskp11),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1327, 204, 1321, 1180, 1313, 1307, 1179, 1178, 1283])).
% 0.78/0.97 tff(1329,plain,
% 0.78/0.97 (((~hskp11) | (~c1_1(a449))) <=> ((~hskp11) | (~c1_1(a449)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1330,plain,
% 0.78/0.97 (((~c1_1(a449)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a449)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1331,axiom,((~c1_1(a449)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.78/0.97 tff(1332,plain,
% 0.78/0.97 ((~hskp11) | (~c1_1(a449))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 0.78/0.97 tff(1333,plain,
% 0.78/0.97 ((~hskp11) | (~c1_1(a449))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1332, 1329])).
% 0.78/0.97 tff(1334,plain,
% 0.78/0.97 (~c1_1(a449)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1333, 1328])).
% 0.78/0.97 tff(1335,plain,
% 0.78/0.97 (((~hskp11) | c2_1(a449)) <=> ((~hskp11) | c2_1(a449))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1336,axiom,((~hskp11) | c2_1(a449)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.78/0.97 tff(1337,plain,
% 0.78/0.97 ((~hskp11) | c2_1(a449)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.78/0.97 tff(1338,plain,
% 0.78/0.97 ((~hskp11) | c2_1(a449)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1337, 1335])).
% 0.78/0.97 tff(1339,plain,
% 0.78/0.97 ((~hskp11) | c2_1(a449)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1338, 1335])).
% 0.78/0.97 tff(1340,plain,
% 0.78/0.97 ((~hskp11) | c2_1(a449)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1339, 1335])).
% 0.78/0.97 tff(1341,plain,
% 0.78/0.97 ((~hskp11) | c2_1(a449)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1340, 1335])).
% 0.78/0.97 tff(1342,plain,
% 0.78/0.97 (c2_1(a449)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1341, 1328])).
% 0.78/0.97 tff(1343,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a450)) | (~c3_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a450)) | (~c3_1(a450)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1344,plain,
% 0.78/0.97 (((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a449) | c0_1(a449) | (~c2_1(a449))) <=> (c0_1(a450) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a450)) | (~c3_1(a450)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1345,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a449) | c0_1(a449) | (~c2_1(a449)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a450)) | (~c3_1(a450))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[1344])).
% 0.78/0.97 tff(1346,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a449) | c0_1(a449) | (~c2_1(a449)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a450)) | (~c3_1(a450)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[1345, 1343])).
% 0.78/0.97 tff(1347,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c1_1(a449) | c0_1(a449) | (~c2_1(a449)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(1348,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a450)) | (~c3_1(a450))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 0.78/0.97 tff(1349,plain,
% 0.78/0.97 (c0_1(a449)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1348, 204, 997, 999, 1231, 1230, 1342, 1229, 1334, 146, 1256])).
% 0.78/0.97 tff(1350,assumption,(c0_1(a449)), introduced(assumption)).
% 0.78/0.97 tff(1351,plain,
% 0.78/0.97 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1352,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1351])).
% 0.78/0.97 tff(1353,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1354,plain,
% 0.78/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(1355,plain,
% 0.78/0.97 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1354])).
% 0.78/0.97 tff(1356,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.78/0.97 tff(1357,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 0.78/0.97 tff(1358,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1357, 1353])).
% 0.78/0.97 tff(1359,plain,(
% 0.78/0.97 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.78/0.97 inference(skolemize,[status(sab)],[1358])).
% 0.78/0.97 tff(1360,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1359, 1352])).
% 0.78/0.97 tff(1361,assumption,(~c1_1(a449)), introduced(assumption)).
% 0.78/0.97 tff(1362,assumption,(hskp23), introduced(assumption)).
% 0.78/0.97 tff(1363,plain,
% 0.78/0.97 (((~hskp23) | (~c3_1(a484))) <=> ((~hskp23) | (~c3_1(a484)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1364,plain,
% 0.78/0.97 (((~c3_1(a484)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a484)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1365,axiom,((~c3_1(a484)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.78/0.97 tff(1366,plain,
% 0.78/0.97 ((~hskp23) | (~c3_1(a484))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 0.78/0.97 tff(1367,plain,
% 0.78/0.97 ((~hskp23) | (~c3_1(a484))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1366, 1363])).
% 0.78/0.97 tff(1368,plain,
% 0.78/0.97 (~c3_1(a484)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1367, 1362])).
% 0.78/0.97 tff(1369,plain,
% 0.78/0.97 (((~hskp23) | (~c2_1(a484))) <=> ((~hskp23) | (~c2_1(a484)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1370,plain,
% 0.78/0.97 (((~c2_1(a484)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a484)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(1371,axiom,((~c2_1(a484)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.78/0.97 tff(1372,plain,
% 0.78/0.97 ((~hskp23) | (~c2_1(a484))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 0.78/0.97 tff(1373,plain,
% 0.78/0.97 ((~hskp23) | (~c2_1(a484))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[1372, 1369])).
% 0.78/0.97 tff(1374,plain,
% 0.78/0.97 (~c2_1(a484)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1373, 1362])).
% 0.78/0.98 tff(1375,assumption,(c2_1(a449)), introduced(assumption)).
% 0.78/0.98 tff(1376,plain,
% 0.78/0.98 (((~hskp23) | c1_1(a484)) <=> ((~hskp23) | c1_1(a484))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1377,axiom,((~hskp23) | c1_1(a484)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.78/0.98 tff(1378,plain,
% 0.78/0.98 ((~hskp23) | c1_1(a484)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 0.78/0.98 tff(1379,plain,
% 0.78/0.98 ((~hskp23) | c1_1(a484)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1378, 1376])).
% 0.78/0.98 tff(1380,plain,
% 0.78/0.98 ((~hskp23) | c1_1(a484)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1379, 1376])).
% 0.78/0.98 tff(1381,plain,
% 0.78/0.98 ((~hskp23) | c1_1(a484)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1380, 1376])).
% 0.78/0.98 tff(1382,plain,
% 0.78/0.98 ((~hskp23) | c1_1(a484)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1381, 1376])).
% 0.78/0.98 tff(1383,plain,
% 0.78/0.98 (c1_1(a484)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1382, 1362])).
% 0.78/0.98 tff(1384,assumption,(~hskp24), introduced(assumption)).
% 0.78/0.98 tff(1385,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a449) | (~ndr1_0) | (~c0_1(a449)) | (~c2_1(a449)) | (~c1_1(a484)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a449) | (~ndr1_0) | (~c0_1(a449)) | (~c2_1(a449)) | (~c1_1(a484)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1386,plain,
% 0.78/0.98 ((hskp24 | (~ndr1_0) | c3_1(a484) | c2_1(a484) | (~c1_1(a484)) | c1_1(a449) | (~c0_1(a449)) | (~c2_1(a449))) <=> (hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a449) | (~ndr1_0) | (~c0_1(a449)) | (~c2_1(a449)) | (~c1_1(a484)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1387,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a484) | c2_1(a484) | (~c1_1(a484)) | c1_1(a449) | (~c0_1(a449)) | (~c2_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a449) | (~ndr1_0) | (~c0_1(a449)) | (~c2_1(a449)) | (~c1_1(a484))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1386])).
% 0.78/0.98 tff(1388,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a484) | c2_1(a484) | (~c1_1(a484)) | c1_1(a449) | (~c0_1(a449)) | (~c2_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a449) | (~ndr1_0) | (~c0_1(a449)) | (~c2_1(a449)) | (~c1_1(a484)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1387, 1385])).
% 0.78/0.98 tff(1389,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a484) | c2_1(a484) | (~c1_1(a484)) | c1_1(a449) | (~c0_1(a449)) | (~c2_1(a449)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1390,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a449) | (~ndr1_0) | (~c0_1(a449)) | (~c2_1(a449)) | (~c1_1(a484))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 0.78/0.98 tff(1391,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1390, 204, 1384, 1383, 1375, 1374, 1368, 1361, 1360, 1350])).
% 0.78/0.98 tff(1392,plain,((~hskp23) | hskp24 | (~c2_1(a449)) | c1_1(a449) | (~c0_1(a449))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(1393,plain,
% 0.78/0.98 (~hskp23),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1392, 1238, 1342, 1334, 1349])).
% 0.78/0.98 tff(1394,plain,
% 0.78/0.98 (^[U: $i] : refl((hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(1395,plain,
% 0.78/0.98 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[1394])).
% 0.78/0.98 tff(1396,plain,
% 0.78/0.98 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1397,plain,
% 0.78/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp23))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) | hskp7) <=> ((hskp23 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7))), rewrite(((hskp23 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp7) <=> (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) | hskp7) <=> (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(1398,plain,
% 0.78/0.98 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) | hskp7) <=> ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[1397])).
% 0.78/0.98 tff(1399,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.78/0.98 tff(1400,plain,
% 0.78/0.98 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 0.78/0.98 tff(1401,plain,
% 0.78/0.98 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1400, 1396])).
% 0.78/0.98 tff(1402,plain,(
% 0.78/0.98 ![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.78/0.98 inference(skolemize,[status(sab)],[1401])).
% 0.78/0.98 tff(1403,plain,
% 0.78/0.98 (![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1402, 1395])).
% 0.78/0.98 tff(1404,plain,
% 0.78/0.98 (((~hskp11) | (~c3_1(a449))) <=> ((~hskp11) | (~c3_1(a449)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1405,plain,
% 0.78/0.98 (((~c3_1(a449)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a449)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1406,axiom,((~c3_1(a449)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.78/0.98 tff(1407,plain,
% 0.78/0.98 ((~hskp11) | (~c3_1(a449))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 0.78/0.98 tff(1408,plain,
% 0.78/0.98 ((~hskp11) | (~c3_1(a449))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1407, 1404])).
% 0.78/0.98 tff(1409,plain,
% 0.78/0.98 (~c3_1(a449)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1408, 1328])).
% 0.78/0.98 tff(1410,plain,
% 0.78/0.98 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp7 | c1_1(a449) | c3_1(a449) | (~ndr1_0) | (~c2_1(a449)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp7 | c1_1(a449) | c3_1(a449) | (~ndr1_0) | (~c2_1(a449)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1411,plain,
% 0.78/0.98 ((hskp23 | hskp7 | (~ndr1_0) | c3_1(a449) | c1_1(a449) | (~c2_1(a449))) <=> (hskp23 | hskp7 | c1_1(a449) | c3_1(a449) | (~ndr1_0) | (~c2_1(a449)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1412,plain,
% 0.78/0.98 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c3_1(a449) | c1_1(a449) | (~c2_1(a449)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp7 | c1_1(a449) | c3_1(a449) | (~ndr1_0) | (~c2_1(a449))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1411])).
% 0.78/0.98 tff(1413,plain,
% 0.78/0.98 (((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c3_1(a449) | c1_1(a449) | (~c2_1(a449)))) <=> ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp7 | c1_1(a449) | c3_1(a449) | (~ndr1_0) | (~c2_1(a449)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1412, 1410])).
% 0.78/0.98 tff(1414,plain,
% 0.78/0.98 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp7 | (~ndr1_0) | c3_1(a449) | c1_1(a449) | (~c2_1(a449)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1415,plain,
% 0.78/0.98 ((~![U: $i] : (hskp23 | hskp7 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp7 | c1_1(a449) | c3_1(a449) | (~ndr1_0) | (~c2_1(a449))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 0.78/0.98 tff(1416,plain,
% 0.78/0.98 (hskp23 | hskp7),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1415, 204, 1342, 1334, 1409, 1403])).
% 0.78/0.98 tff(1417,plain,
% 0.78/0.98 (hskp7),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1416, 1393])).
% 0.78/0.98 tff(1418,plain,
% 0.78/0.98 (((~hskp7) | (~c2_1(a443))) <=> ((~hskp7) | (~c2_1(a443)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1419,plain,
% 0.78/0.98 (((~c2_1(a443)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a443)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1420,axiom,((~c2_1(a443)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.78/0.98 tff(1421,plain,
% 0.78/0.98 ((~hskp7) | (~c2_1(a443))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.78/0.98 tff(1422,plain,
% 0.78/0.98 ((~hskp7) | (~c2_1(a443))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1421, 1418])).
% 0.78/0.98 tff(1423,plain,
% 0.78/0.98 (~c2_1(a443)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1422, 1417])).
% 0.78/0.98 tff(1424,plain,
% 0.78/0.98 (((~hskp7) | (~c1_1(a443))) <=> ((~hskp7) | (~c1_1(a443)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1425,plain,
% 0.78/0.98 (((~c1_1(a443)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a443)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1426,axiom,((~c1_1(a443)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.78/0.98 tff(1427,plain,
% 0.78/0.98 ((~hskp7) | (~c1_1(a443))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 0.78/0.98 tff(1428,plain,
% 0.78/0.98 ((~hskp7) | (~c1_1(a443))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1427, 1424])).
% 0.78/0.98 tff(1429,plain,
% 0.78/0.98 (~c1_1(a443)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1428, 1417])).
% 0.78/0.98 tff(1430,plain,
% 0.78/0.98 (((~hskp7) | c3_1(a443)) <=> ((~hskp7) | c3_1(a443))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1431,axiom,((~hskp7) | c3_1(a443)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.78/0.98 tff(1432,plain,
% 0.78/0.98 ((~hskp7) | c3_1(a443)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 0.78/0.98 tff(1433,plain,
% 0.78/0.98 ((~hskp7) | c3_1(a443)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1432, 1430])).
% 0.78/0.98 tff(1434,plain,
% 0.78/0.98 ((~hskp7) | c3_1(a443)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1433, 1430])).
% 0.78/0.98 tff(1435,plain,
% 0.78/0.98 ((~hskp7) | c3_1(a443)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1434, 1430])).
% 0.78/0.98 tff(1436,plain,
% 0.78/0.98 ((~hskp7) | c3_1(a443)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1435, 1430])).
% 0.78/0.98 tff(1437,plain,
% 0.78/0.98 (c3_1(a443)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1436, 1417])).
% 0.78/0.98 tff(1438,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp28 | c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp28 | c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a467)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1439,plain,
% 0.78/0.98 ((hskp28 | (~ndr1_0) | c2_1(a443) | c1_1(a443) | (~c3_1(a443)) | c2_1(a467) | c1_1(a467) | (~c0_1(a467))) <=> (hskp28 | c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a467)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1440,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a443) | c1_1(a443) | (~c3_1(a443)) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp28 | c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a467))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1439])).
% 0.78/0.98 tff(1441,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a443) | c1_1(a443) | (~c3_1(a443)) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp28 | c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a467)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1440, 1438])).
% 0.78/0.98 tff(1442,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a443) | c1_1(a443) | (~c3_1(a443)) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1443,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp28 | c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a467))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 0.78/0.98 tff(1444,plain,
% 0.78/0.98 (hskp28),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1443, 204, 1321, 1437, 1313, 1307, 1429, 1423, 1273])).
% 0.78/0.98 tff(1445,plain,
% 0.78/0.98 (((~hskp28) | c3_1(a437)) <=> ((~hskp28) | c3_1(a437))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1446,axiom,((~hskp28) | c3_1(a437)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.78/0.98 tff(1447,plain,
% 0.78/0.98 ((~hskp28) | c3_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 0.78/0.98 tff(1448,plain,
% 0.78/0.98 ((~hskp28) | c3_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1447, 1445])).
% 0.78/0.98 tff(1449,plain,
% 0.78/0.98 ((~hskp28) | c3_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1448, 1445])).
% 0.78/0.98 tff(1450,plain,
% 0.78/0.98 ((~hskp28) | c3_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1449, 1445])).
% 0.78/0.98 tff(1451,plain,
% 0.78/0.98 ((~hskp28) | c3_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1450, 1445])).
% 0.78/0.98 tff(1452,plain,
% 0.78/0.98 (c3_1(a437)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1451, 1444])).
% 0.78/0.98 tff(1453,plain,
% 0.78/0.98 (((~hskp28) | c2_1(a437)) <=> ((~hskp28) | c2_1(a437))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1454,axiom,((~hskp28) | c2_1(a437)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.78/0.98 tff(1455,plain,
% 0.78/0.98 ((~hskp28) | c2_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 0.78/0.98 tff(1456,plain,
% 0.78/0.98 ((~hskp28) | c2_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1455, 1453])).
% 0.78/0.98 tff(1457,plain,
% 0.78/0.98 ((~hskp28) | c2_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1456, 1453])).
% 0.78/0.98 tff(1458,plain,
% 0.78/0.98 ((~hskp28) | c2_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1457, 1453])).
% 0.78/0.98 tff(1459,plain,
% 0.78/0.98 ((~hskp28) | c2_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1458, 1453])).
% 0.78/0.98 tff(1460,plain,
% 0.78/0.98 (c2_1(a437)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1459, 1444])).
% 0.78/0.98 tff(1461,plain,
% 0.78/0.98 (((~hskp28) | c0_1(a437)) <=> ((~hskp28) | c0_1(a437))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1462,axiom,((~hskp28) | c0_1(a437)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.78/0.98 tff(1463,plain,
% 0.78/0.98 ((~hskp28) | c0_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.78/0.98 tff(1464,plain,
% 0.78/0.98 ((~hskp28) | c0_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1463, 1461])).
% 0.78/0.98 tff(1465,plain,
% 0.78/0.98 ((~hskp28) | c0_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1464, 1461])).
% 0.78/0.98 tff(1466,plain,
% 0.78/0.98 ((~hskp28) | c0_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1465, 1461])).
% 0.78/0.98 tff(1467,plain,
% 0.78/0.98 ((~hskp28) | c0_1(a437)),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1466, 1461])).
% 0.78/0.98 tff(1468,plain,
% 0.78/0.98 (c0_1(a437)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1467, 1444])).
% 0.78/0.98 tff(1469,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a486) | c2_1(a486) | c0_1(a486) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a486) | c2_1(a486) | c0_1(a486) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1470,plain,
% 0.78/0.98 (((~ndr1_0) | (~c2_1(a437)) | (~c3_1(a437)) | (~c0_1(a437)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a486) | c1_1(a486) | c0_1(a486)) <=> (c1_1(a486) | c2_1(a486) | c0_1(a486) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1471,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a437)) | (~c3_1(a437)) | (~c0_1(a437)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a486) | c1_1(a486) | c0_1(a486))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a486) | c2_1(a486) | c0_1(a486) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1470])).
% 0.78/0.98 tff(1472,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a437)) | (~c3_1(a437)) | (~c0_1(a437)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a486) | c1_1(a486) | c0_1(a486))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a486) | c2_1(a486) | c0_1(a486) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1471, 1469])).
% 0.78/0.98 tff(1473,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a437)) | (~c3_1(a437)) | (~c0_1(a437)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a486) | c1_1(a486) | c0_1(a486))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1474,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a486) | c2_1(a486) | c0_1(a486) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 0.78/0.98 tff(1475,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1474, 204, 1468, 1460, 1452, 1237, 1263, 178, 40, 1236, 1235, 74])).
% 0.78/0.98 tff(1476,plain,(c1_1(a486) | c0_1(a486) | c0_1(a445) | (~c1_1(a456)) | (~c2_1(a456)) | (~c1_1(a450)) | (~c3_1(a450)) | c0_1(a450) | (~c1_1(a448)) | c0_1(a448) | c2_1(a448) | hskp8 | (~c0_1(a456))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(1477,plain,
% 0.78/0.98 (c1_1(a486)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1476, 178, 40, 997, 999, 1231, 1230, 1229, 1180, 1179, 1178, 32, 996])).
% 0.78/0.98 tff(1478,assumption,(~c2_1(a486)), introduced(assumption)).
% 0.78/0.98 tff(1479,plain,
% 0.78/0.98 (~hskp24),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[127, 1478])).
% 0.78/0.98 tff(1480,plain,
% 0.78/0.98 (~c3_1(a456)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1255, 1479])).
% 0.78/0.98 tff(1481,assumption,(~c2_1(a450)), introduced(assumption)).
% 0.78/0.98 tff(1482,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1483,plain,
% 0.78/0.98 (((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486))) <=> (c0_1(a486) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1484,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1483])).
% 0.78/0.98 tff(1485,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1484, 1482])).
% 0.78/0.98 tff(1486,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c1_1(a456)) | (~c0_1(a456)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1487,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | (~ndr1_0) | (~c0_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 0.78/0.98 tff(1488,plain,
% 0.78/0.98 (c3_1(a486)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1487, 204, 996, 997, 177, 1231, 1230, 178, 1112, 1480, 1481])).
% 0.78/0.98 tff(1489,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c3_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c3_1(a486)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1490,plain,
% 0.78/0.98 (((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a486) | (~c3_1(a486)) | (~c1_1(a486)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445))) <=> (c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c3_1(a486)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1491,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a486) | (~c3_1(a486)) | (~c1_1(a486)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c3_1(a486))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[1490])).
% 0.78/0.98 tff(1492,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a486) | (~c3_1(a486)) | (~c1_1(a486)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c3_1(a486)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[1491, 1489])).
% 0.78/0.98 tff(1493,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a486) | (~c3_1(a486)) | (~c1_1(a486)) | c1_1(a445) | c0_1(a445) | (~c2_1(a445)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(1494,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a486) | c0_1(a445) | c1_1(a445) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c3_1(a486))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 0.78/0.98 tff(1495,plain,
% 0.78/0.98 (~c2_1(a445)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1494, 204, 997, 999, 177, 178, 40, 52, 146, 1488, 1480])).
% 0.78/0.98 tff(1496,plain,
% 0.78/0.98 (hskp19),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1300, 204, 997, 999, 52, 51, 1294, 1480, 1495])).
% 0.78/0.98 tff(1497,plain,
% 0.78/0.98 (~c2_1(a467)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1306, 1496])).
% 0.78/0.98 tff(1498,plain,
% 0.78/0.98 (~c1_1(a467)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1312, 1496])).
% 0.78/0.98 tff(1499,plain,
% 0.78/0.98 (c0_1(a467)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1320, 1496])).
% 0.78/0.98 tff(1500,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a486) | c0_1(a486) | c1_1(a467) | c2_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a486) | c0_1(a486) | c1_1(a467) | c2_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a486)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1501,plain,
% 0.78/0.98 ((hskp11 | (~ndr1_0) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)) | c2_1(a486) | c0_1(a486) | (~c1_1(a486))) <=> (hskp11 | c2_1(a486) | c0_1(a486) | c1_1(a467) | c2_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a486)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(1502,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)) | c2_1(a486) | c0_1(a486) | (~c1_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a486) | c0_1(a486) | c1_1(a467) | c2_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a486))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1501])).
% 0.78/0.99 tff(1503,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)) | c2_1(a486) | c0_1(a486) | (~c1_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a486) | c0_1(a486) | c1_1(a467) | c2_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a486)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1502, 1500])).
% 0.78/0.99 tff(1504,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)) | c2_1(a486) | c0_1(a486) | (~c1_1(a486)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1505,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a486) | c0_1(a486) | c1_1(a467) | c2_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a486))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 0.78/0.99 tff(1506,plain,
% 0.78/0.99 (hskp11),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1505, 204, 177, 1478, 1499, 178, 1498, 1497, 1283])).
% 0.78/0.99 tff(1507,plain,
% 0.78/0.99 (~c1_1(a449)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1333, 1506])).
% 0.78/0.99 tff(1508,plain,
% 0.78/0.99 (c2_1(a449)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1341, 1506])).
% 0.78/0.99 tff(1509,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a486) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a486)) | (~c3_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a486) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a486)) | (~c3_1(a486)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1510,plain,
% 0.78/0.99 (((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a486) | (~c3_1(a486)) | (~c1_1(a486)) | c1_1(a449) | c0_1(a449) | (~c2_1(a449))) <=> (c0_1(a486) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a486)) | (~c3_1(a486)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1511,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a486) | (~c3_1(a486)) | (~c1_1(a486)) | c1_1(a449) | c0_1(a449) | (~c2_1(a449)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a486) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a486)) | (~c3_1(a486))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1510])).
% 0.78/0.99 tff(1512,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a486) | (~c3_1(a486)) | (~c1_1(a486)) | c1_1(a449) | c0_1(a449) | (~c2_1(a449)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a486) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a486)) | (~c3_1(a486)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1511, 1509])).
% 0.78/0.99 tff(1513,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a456) | (~c2_1(a456)) | (~c1_1(a456)) | c0_1(a486) | (~c3_1(a486)) | (~c1_1(a486)) | c1_1(a449) | c0_1(a449) | (~c2_1(a449)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1514,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a486) | c1_1(a449) | (~ndr1_0) | (~c2_1(a456)) | c3_1(a456) | (~c1_1(a456)) | c0_1(a449) | (~c2_1(a449)) | (~c1_1(a486)) | (~c3_1(a486))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 0.78/0.99 tff(1515,plain,
% 0.78/0.99 (c0_1(a449)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1514, 204, 997, 999, 177, 1508, 178, 1507, 146, 1488, 1480])).
% 0.78/0.99 tff(1516,plain,
% 0.78/0.99 (~hskp23),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1392, 1515, 1508, 1507, 1479])).
% 0.78/0.99 tff(1517,plain,
% 0.78/0.99 (~c3_1(a449)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1408, 1506])).
% 0.78/0.99 tff(1518,plain,
% 0.78/0.99 (hskp23 | hskp7),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1415, 204, 1508, 1507, 1517, 1403])).
% 0.78/0.99 tff(1519,plain,
% 0.78/0.99 (hskp7),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1518, 1516])).
% 0.78/0.99 tff(1520,plain,
% 0.78/0.99 (~c2_1(a443)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1422, 1519])).
% 0.78/0.99 tff(1521,plain,
% 0.78/0.99 (~c1_1(a443)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1428, 1519])).
% 0.78/0.99 tff(1522,plain,
% 0.78/0.99 (c3_1(a443)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1436, 1519])).
% 0.78/0.99 tff(1523,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a443)) | (~c0_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)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a443)) | (~c0_1(a467)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1524,plain,
% 0.78/0.99 (((~ndr1_0) | c2_1(a443) | (~c3_1(a443)) | (~c0_1(a443)) | c1_1(a443) | (~c3_1(a443)) | (~c0_1(a443)) | c2_1(a467) | c1_1(a467) | (~c0_1(a467))) <=> (c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a443)) | (~c0_1(a467)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1525,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a443) | (~c3_1(a443)) | (~c0_1(a443)) | c1_1(a443) | (~c3_1(a443)) | (~c0_1(a443)) | c2_1(a467) | c1_1(a467) | (~c0_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)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a443)) | (~c0_1(a467))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1524])).
% 0.78/0.99 tff(1526,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a443) | (~c3_1(a443)) | (~c0_1(a443)) | c1_1(a443) | (~c3_1(a443)) | (~c0_1(a443)) | c2_1(a467) | c1_1(a467) | (~c0_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)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a443)) | (~c0_1(a467)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1525, 1523])).
% 0.78/0.99 tff(1527,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a443) | (~c3_1(a443)) | (~c0_1(a443)) | c1_1(a443) | (~c3_1(a443)) | (~c0_1(a443)) | c2_1(a467) | c1_1(a467) | (~c0_1(a467)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1528,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a467) | c2_1(a467) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c3_1(a443)) | (~c0_1(a443)) | (~c0_1(a467))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 0.78/0.99 tff(1529,plain,
% 0.78/0.99 (~c0_1(a443)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1528, 204, 1499, 1522, 1498, 1497, 1521, 1520, 1204])).
% 0.78/0.99 tff(1530,plain,
% 0.78/0.99 (hskp28),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1443, 204, 1499, 1522, 1498, 1497, 1521, 1520, 1273])).
% 0.78/0.99 tff(1531,plain,
% 0.78/0.99 (c3_1(a437)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1451, 1530])).
% 0.78/0.99 tff(1532,plain,
% 0.78/0.99 (c2_1(a437)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1459, 1530])).
% 0.78/0.99 tff(1533,plain,
% 0.78/0.99 (c0_1(a437)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1467, 1530])).
% 0.78/0.99 tff(1534,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c3_1(a445) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)) | c0_1(a443))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)) | c0_1(a443))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1535,plain,
% 0.78/0.99 (((~ndr1_0) | (~c2_1(a437)) | (~c3_1(a437)) | (~c0_1(a437)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a443) | c1_1(a443) | c0_1(a443)) <=> (c0_1(a445) | c1_1(a445) | c3_1(a445) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)) | c0_1(a443))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1536,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a437)) | (~c3_1(a437)) | (~c0_1(a437)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a443) | c1_1(a443) | c0_1(a443))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c3_1(a445) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)) | c0_1(a443)))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1535])).
% 0.78/0.99 tff(1537,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a437)) | (~c3_1(a437)) | (~c0_1(a437)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a443) | c1_1(a443) | c0_1(a443))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)) | c0_1(a443))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1536, 1534])).
% 0.78/0.99 tff(1538,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a437)) | (~c3_1(a437)) | (~c0_1(a437)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a443) | c1_1(a443) | c0_1(a443))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1539,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | c1_1(a443) | c2_1(a443) | (~ndr1_0) | (~c0_1(a437)) | (~c3_1(a437)) | (~c2_1(a437)) | c0_1(a443)),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.78/0.99 tff(1540,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1539, 204, 1533, 1532, 1531, 40, 52, 51, 1521, 1520, 74, 1529])).
% 0.78/0.99 tff(1541,plain,(c2_1(a486) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~c1_1(a456)) | (~c2_1(a456)) | (~c1_1(a486)) | c0_1(a486) | (~c0_1(a456)) | (~c1_1(a450)) | (~c3_1(a450)) | c2_1(a450) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(1542,plain,
% 0.78/0.99 (c2_1(a486)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1541, 1477, 1236, 1235, 997, 999, 40, 178, 996, 1231, 1230, 1233, 32])).
% 0.78/0.99 tff(1543,plain,
% 0.78/0.99 ((~c1_1(a486)) | (~c2_1(a486)) | (~c3_1(a486))),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[255, 204, 32, 178, 249])).
% 0.78/0.99 tff(1544,plain,
% 0.78/0.99 (~c3_1(a486)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1543, 1542, 1477])).
% 0.78/0.99 tff(1545,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | c0_1(a486) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a486) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1546,plain,
% 0.78/0.99 ((hskp6 | (~ndr1_0) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486))) <=> (hskp6 | c0_1(a486) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1547,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | c0_1(a486) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1546])).
% 0.78/0.99 tff(1548,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a486) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1547, 1545])).
% 0.78/0.99 tff(1549,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1550,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a486) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 0.78/0.99 tff(1551,plain,
% 0.78/0.99 (hskp6 | (~c1_1(a486)) | (~c2_1(a486))),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1550, 204, 1231, 1230, 178, 166, 1233])).
% 0.78/0.99 tff(1552,plain,
% 0.78/0.99 (hskp6),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1551, 1542, 1477])).
% 0.78/0.99 tff(1553,plain,
% 0.78/0.99 (~c3_1(a442)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[347, 1552])).
% 0.78/0.99 tff(1554,plain,
% 0.78/0.99 (c0_1(a442)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[363, 1552])).
% 0.78/0.99 tff(1555,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1556,plain,
% 0.78/0.99 (((~ndr1_0) | c3_1(a442) | (~c1_1(a442)) | (~c0_1(a442)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486))) <=> (c0_1(a486) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(1557,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a442) | (~c1_1(a442)) | (~c0_1(a442)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[1556])).
% 0.78/0.99 tff(1558,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a442) | (~c1_1(a442)) | (~c0_1(a442)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[1557, 1555])).
% 0.78/0.99 tff(1559,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a442) | (~c1_1(a442)) | (~c0_1(a442)) | c2_1(a450) | (~c3_1(a450)) | (~c1_1(a450)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(1560,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a442) | (~ndr1_0) | (~c1_1(a442)) | (~c0_1(a442)) | (~c1_1(a450)) | c2_1(a450) | (~c3_1(a450)) | c3_1(a486) | (~c1_1(a486))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 0.78/0.99 tff(1561,plain,
% 0.78/0.99 (~c1_1(a442)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1560, 204, 1477, 1231, 1230, 1554, 178, 1553, 1112, 1544, 1233])).
% 0.78/0.99 tff(1562,plain,
% 0.78/0.99 (c2_1(a442)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[355, 1552])).
% 0.78/0.99 tff(1563,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1140, 204, 1477, 1542, 1562, 178, 1553, 10, 1544, 1561])).
% 0.78/0.99 tff(1564,plain,(c0_1(a486) | (~c1_1(a450)) | (~c3_1(a450)) | hskp8 | (~c1_1(a456)) | (~c2_1(a456)) | c0_1(a445) | (~c0_1(a456)) | c0_1(a450) | (~c1_1(a448)) | c0_1(a448) | c2_1(a448)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(1565,plain,
% 0.78/0.99 (c0_1(a486)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1564, 32, 1094, 1155, 1228, 1227, 40, 1226, 1093, 1074, 1066, 1060])).
% 0.78/0.99 tff(1566,plain,
% 0.78/0.99 (~hskp24),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[119, 1565])).
% 0.78/0.99 tff(1567,plain,
% 0.78/0.99 (hskp24 | (~c3_1(a456))),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1254, 204, 32, 1226, 1228, 1248])).
% 0.78/0.99 tff(1568,plain,
% 0.78/0.99 (~c3_1(a456)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1567, 1566])).
% 0.78/0.99 tff(1569,plain,
% 0.78/0.99 (hskp9),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1193, 32, 1074, 1066, 1060])).
% 0.78/0.99 tff(1570,plain,
% 0.78/0.99 (~c1_1(a445)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[567, 1569])).
% 0.78/0.99 tff(1571,plain,
% 0.78/0.99 (~c2_1(a445)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[789, 204, 1228, 1227, 1155, 1094, 1093, 40, 1570, 146, 1568])).
% 0.78/0.99 tff(1572,plain,
% 0.78/0.99 (~c3_1(a445)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[529, 1569])).
% 0.78/0.99 tff(1573,plain,
% 0.78/0.99 (hskp19),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1300, 204, 1228, 1227, 1570, 1572, 1294, 1568, 1571])).
% 0.78/0.99 tff(1574,plain,
% 0.78/0.99 (~c2_1(a467)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1306, 1573])).
% 0.78/0.99 tff(1575,plain,
% 0.78/0.99 (~c1_1(a467)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1312, 1573])).
% 0.78/0.99 tff(1576,plain,
% 0.78/0.99 (c0_1(a467)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1320, 1573])).
% 0.84/0.99 tff(1577,plain,
% 0.84/0.99 (hskp11),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1327, 204, 1576, 1074, 1575, 1574, 1066, 1060, 1283])).
% 0.84/0.99 tff(1578,plain,
% 0.84/0.99 (~c1_1(a449)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1333, 1577])).
% 0.84/0.99 tff(1579,plain,
% 0.84/0.99 (c2_1(a449)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1341, 1577])).
% 0.84/0.99 tff(1580,plain,
% 0.84/0.99 (c0_1(a449)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1348, 204, 1228, 1227, 1155, 1094, 1579, 1093, 1578, 146, 1568])).
% 0.84/0.99 tff(1581,plain,
% 0.84/0.99 (~hskp23),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1392, 1580, 1579, 1578, 1566])).
% 0.84/0.99 tff(1582,plain,
% 0.84/0.99 (~c3_1(a449)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1408, 1577])).
% 0.84/0.99 tff(1583,plain,
% 0.84/0.99 (hskp23 | hskp7),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1415, 204, 1579, 1578, 1582, 1403])).
% 0.84/0.99 tff(1584,plain,
% 0.84/0.99 (hskp7),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1583, 1581])).
% 0.84/0.99 tff(1585,plain,
% 0.84/0.99 (~c2_1(a443)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1422, 1584])).
% 0.84/0.99 tff(1586,plain,
% 0.84/0.99 (~c1_1(a443)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1428, 1584])).
% 0.84/0.99 tff(1587,plain,
% 0.84/0.99 (c3_1(a443)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1436, 1584])).
% 0.84/0.99 tff(1588,plain,
% 0.84/0.99 (~c0_1(a443)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1528, 204, 1576, 1587, 1575, 1574, 1586, 1585, 1204])).
% 0.84/0.99 tff(1589,plain,
% 0.84/0.99 (hskp28),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1443, 204, 1576, 1587, 1575, 1574, 1586, 1585, 1273])).
% 0.84/0.99 tff(1590,plain,
% 0.84/0.99 (c3_1(a437)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1451, 1589])).
% 0.84/0.99 tff(1591,plain,
% 0.84/0.99 (c2_1(a437)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1459, 1589])).
% 0.84/0.99 tff(1592,plain,
% 0.84/0.99 (c0_1(a437)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1467, 1589])).
% 0.84/0.99 tff(1593,plain,
% 0.84/0.99 ($false),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1539, 204, 1592, 1591, 1590, 40, 1570, 1572, 1586, 1585, 74, 1588])).
% 0.84/0.99 tff(1594,plain,(hskp8 | c0_1(a445) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.84/0.99 tff(1595,plain,
% 0.84/0.99 (c0_1(a445)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1594, 1177, 53])).
% 0.84/0.99 tff(1596,plain,
% 0.84/0.99 ($false),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[723, 1595, 1194])).
% 0.84/0.99 tff(1597,plain,(hskp14), inference(lemma,lemma(discharge,[]))).
% 0.84/0.99 tff(1598,plain,
% 0.84/0.99 (((~hskp14) | (~c2_1(a452))) <=> ((~hskp14) | (~c2_1(a452)))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1599,plain,
% 0.84/0.99 (((~c2_1(a452)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a452)))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1600,axiom,((~c2_1(a452)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.84/0.99 tff(1601,plain,
% 0.84/0.99 ((~hskp14) | (~c2_1(a452))),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 0.84/0.99 tff(1602,plain,
% 0.84/0.99 ((~hskp14) | (~c2_1(a452))),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1601, 1598])).
% 0.84/0.99 tff(1603,plain,
% 0.84/0.99 (~c2_1(a452)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1602, 1597])).
% 0.84/0.99 tff(1604,plain,
% 0.84/0.99 (((~hskp14) | c1_1(a452)) <=> ((~hskp14) | c1_1(a452))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1605,axiom,((~hskp14) | c1_1(a452)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.84/0.99 tff(1606,plain,
% 0.84/0.99 ((~hskp14) | c1_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 0.84/0.99 tff(1607,plain,
% 0.84/0.99 ((~hskp14) | c1_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1606, 1604])).
% 0.84/0.99 tff(1608,plain,
% 0.84/0.99 ((~hskp14) | c1_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1607, 1604])).
% 0.84/0.99 tff(1609,plain,
% 0.84/0.99 ((~hskp14) | c1_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1608, 1604])).
% 0.84/0.99 tff(1610,plain,
% 0.84/0.99 ((~hskp14) | c1_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1609, 1604])).
% 0.84/0.99 tff(1611,plain,
% 0.84/0.99 (c1_1(a452)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1610, 1597])).
% 0.84/0.99 tff(1612,plain,
% 0.84/0.99 (((~hskp14) | c0_1(a452)) <=> ((~hskp14) | c0_1(a452))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1613,axiom,((~hskp14) | c0_1(a452)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.84/0.99 tff(1614,plain,
% 0.84/0.99 ((~hskp14) | c0_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 0.84/0.99 tff(1615,plain,
% 0.84/0.99 ((~hskp14) | c0_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1614, 1612])).
% 0.84/0.99 tff(1616,plain,
% 0.84/0.99 ((~hskp14) | c0_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1615, 1612])).
% 0.84/0.99 tff(1617,plain,
% 0.84/0.99 ((~hskp14) | c0_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1616, 1612])).
% 0.84/0.99 tff(1618,plain,
% 0.84/0.99 ((~hskp14) | c0_1(a452)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1617, 1612])).
% 0.84/0.99 tff(1619,plain,
% 0.84/0.99 (c0_1(a452)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1618, 1597])).
% 0.84/0.99 tff(1620,plain,
% 0.84/0.99 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c2_1(a452) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a452) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1621,plain,
% 0.84/0.99 ((hskp3 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c1_1(a445) | c0_1(a445) | c3_1(a445)) <=> (hskp3 | c2_1(a452) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1622,plain,
% 0.84/0.99 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c1_1(a445) | c0_1(a445) | c3_1(a445))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c2_1(a452) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452))))),
% 0.84/0.99 inference(monotonicity,[status(thm)],[1621])).
% 0.84/0.99 tff(1623,plain,
% 0.84/0.99 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c1_1(a445) | c0_1(a445) | c3_1(a445))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a452) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/0.99 inference(transitivity,[status(thm)],[1622, 1620])).
% 0.84/0.99 tff(1624,plain,
% 0.84/0.99 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c1_1(a445) | c0_1(a445) | c3_1(a445))),
% 0.84/0.99 inference(quant_inst,[status(thm)],[])).
% 0.84/0.99 tff(1625,plain,
% 0.84/0.99 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a452) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452))),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 0.84/0.99 tff(1626,plain,
% 0.84/0.99 (hskp3),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1625, 204, 1619, 1611, 1603, 40, 52, 51, 20])).
% 0.84/0.99 tff(1627,plain,
% 0.84/0.99 (~c3_1(a435)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[38, 1626])).
% 0.84/0.99 tff(1628,plain,
% 0.84/0.99 (((~hskp3) | (~c0_1(a435))) <=> ((~hskp3) | (~c0_1(a435)))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1629,plain,
% 0.84/0.99 (((~c0_1(a435)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a435)))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1630,axiom,((~c0_1(a435)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.84/0.99 tff(1631,plain,
% 0.84/0.99 ((~hskp3) | (~c0_1(a435))),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 0.84/0.99 tff(1632,plain,
% 0.84/0.99 ((~hskp3) | (~c0_1(a435))),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1631, 1628])).
% 0.84/0.99 tff(1633,plain,
% 0.84/0.99 (~c0_1(a435)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1632, 1626])).
% 0.84/0.99 tff(1634,plain,
% 0.84/0.99 (((~hskp3) | c1_1(a435)) <=> ((~hskp3) | c1_1(a435))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1635,axiom,((~hskp3) | c1_1(a435)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.84/0.99 tff(1636,plain,
% 0.84/0.99 ((~hskp3) | c1_1(a435)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 0.84/0.99 tff(1637,plain,
% 0.84/0.99 ((~hskp3) | c1_1(a435)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1636, 1634])).
% 0.84/0.99 tff(1638,plain,
% 0.84/0.99 ((~hskp3) | c1_1(a435)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1637, 1634])).
% 0.84/0.99 tff(1639,plain,
% 0.84/0.99 ((~hskp3) | c1_1(a435)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1638, 1634])).
% 0.84/0.99 tff(1640,plain,
% 0.84/0.99 ((~hskp3) | c1_1(a435)),
% 0.84/0.99 inference(modus_ponens,[status(thm)],[1639, 1634])).
% 0.84/0.99 tff(1641,plain,
% 0.84/0.99 (c1_1(a435)),
% 0.84/0.99 inference(unit_resolution,[status(thm)],[1640, 1626])).
% 0.84/0.99 tff(1642,plain,
% 0.84/0.99 (((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c1_1(a452)))) <=> ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/0.99 inference(rewrite,[status(thm)],[])).
% 0.84/0.99 tff(1643,plain,
% 0.84/0.99 ((hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c1_1(a452)) | (~c0_1(a452))) <=> (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1644,plain,
% 0.84/1.00 (((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c1_1(a452)) | (~c0_1(a452)))) <=> ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c1_1(a452))))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1643])).
% 0.84/1.00 tff(1645,plain,
% 0.84/1.00 (((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c1_1(a452)) | (~c0_1(a452)))) <=> ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1644, 1642])).
% 0.84/1.00 tff(1646,plain,
% 0.84/1.00 ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c1_1(a452)) | (~c0_1(a452)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1647,plain,
% 0.84/1.00 ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c1_1(a452))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 0.84/1.00 tff(1648,plain,
% 0.84/1.00 (hskp24 | hskp8 | (~c3_1(a452))),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1647, 204, 1619, 1611, 1248])).
% 0.84/1.00 tff(1649,plain,
% 0.84/1.00 (~c3_1(a452)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1648, 1384, 32])).
% 0.84/1.00 tff(1650,assumption,(~c3_1(a435)), introduced(assumption)).
% 0.84/1.00 tff(1651,assumption,(~c0_1(a435)), introduced(assumption)).
% 0.84/1.00 tff(1652,assumption,(c1_1(a435)), introduced(assumption)).
% 0.84/1.00 tff(1653,assumption,(~c3_1(a452)), introduced(assumption)).
% 0.84/1.00 tff(1654,assumption,(hskp17), introduced(assumption)).
% 0.84/1.00 tff(1655,plain,
% 0.84/1.00 (((~hskp17) | (~c1_1(a463))) <=> ((~hskp17) | (~c1_1(a463)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1656,plain,
% 0.84/1.00 (((~c1_1(a463)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a463)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1657,axiom,((~c1_1(a463)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.84/1.00 tff(1658,plain,
% 0.84/1.00 ((~hskp17) | (~c1_1(a463))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 0.84/1.00 tff(1659,plain,
% 0.84/1.00 ((~hskp17) | (~c1_1(a463))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1658, 1655])).
% 0.84/1.00 tff(1660,plain,
% 0.84/1.00 (~c1_1(a463)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1659, 1654])).
% 0.84/1.00 tff(1661,plain,
% 0.84/1.00 (((~hskp17) | c2_1(a463)) <=> ((~hskp17) | c2_1(a463))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1662,axiom,((~hskp17) | c2_1(a463)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.84/1.00 tff(1663,plain,
% 0.84/1.00 ((~hskp17) | c2_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 0.84/1.00 tff(1664,plain,
% 0.84/1.00 ((~hskp17) | c2_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1663, 1661])).
% 0.84/1.00 tff(1665,plain,
% 0.84/1.00 ((~hskp17) | c2_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1664, 1661])).
% 0.84/1.00 tff(1666,plain,
% 0.84/1.00 ((~hskp17) | c2_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1665, 1661])).
% 0.84/1.00 tff(1667,plain,
% 0.84/1.00 ((~hskp17) | c2_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1666, 1661])).
% 0.84/1.00 tff(1668,plain,
% 0.84/1.00 (c2_1(a463)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1667, 1654])).
% 0.84/1.00 tff(1669,plain,
% 0.84/1.00 (((~hskp17) | c0_1(a463)) <=> ((~hskp17) | c0_1(a463))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1670,axiom,((~hskp17) | c0_1(a463)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.84/1.00 tff(1671,plain,
% 0.84/1.00 ((~hskp17) | c0_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 0.84/1.00 tff(1672,plain,
% 0.84/1.00 ((~hskp17) | c0_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1671, 1669])).
% 0.84/1.00 tff(1673,plain,
% 0.84/1.00 ((~hskp17) | c0_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1672, 1669])).
% 0.84/1.00 tff(1674,plain,
% 0.84/1.00 ((~hskp17) | c0_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1673, 1669])).
% 0.84/1.00 tff(1675,plain,
% 0.84/1.00 ((~hskp17) | c0_1(a463)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1674, 1669])).
% 0.84/1.00 tff(1676,plain,
% 0.84/1.00 (c0_1(a463)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1675, 1654])).
% 0.84/1.00 tff(1677,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a463)) | (~c2_1(a463)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp24 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1678,plain,
% 0.84/1.00 ((hskp24 | (~ndr1_0) | c3_1(a452) | c2_1(a452) | (~c1_1(a452)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463))) <=> (hskp24 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1679,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a452) | c2_1(a452) | (~c1_1(a452)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a463)) | (~c2_1(a463))))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1678])).
% 0.84/1.00 tff(1680,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a452) | c2_1(a452) | (~c1_1(a452)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp24 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1679, 1677])).
% 0.84/1.00 tff(1681,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a452) | c2_1(a452) | (~c1_1(a452)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1682,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp24 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a463)) | (~c2_1(a463))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 0.84/1.00 tff(1683,plain,
% 0.84/1.00 ($false),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1682, 204, 1384, 1676, 1668, 1611, 1660, 1603, 1360, 1653])).
% 0.84/1.00 tff(1684,plain,((~hskp17) | hskp24 | c3_1(a452)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.00 tff(1685,plain,
% 0.84/1.00 (~hskp17),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1684, 1384, 1649])).
% 0.84/1.00 tff(1686,plain,
% 0.84/1.00 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.84/1.00 inference(bind,[status(th)],[])).
% 0.84/1.00 tff(1687,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.84/1.00 inference(quant_intro,[status(thm)],[1686])).
% 0.84/1.00 tff(1688,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1689,plain,
% 0.84/1.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.84/1.00 inference(bind,[status(th)],[])).
% 0.84/1.00 tff(1690,plain,
% 0.84/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.84/1.00 inference(quant_intro,[status(thm)],[1689])).
% 0.84/1.00 tff(1691,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.84/1.00 tff(1692,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 0.84/1.00 tff(1693,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1692, 1688])).
% 0.84/1.00 tff(1694,plain,(
% 0.84/1.00 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.84/1.00 inference(skolemize,[status(sab)],[1693])).
% 0.84/1.00 tff(1695,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1694, 1687])).
% 0.84/1.00 tff(1696,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | c2_1(a452) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c0_1(a452)) | (~c1_1(a452)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp17 | c2_1(a452) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1697,plain,
% 0.84/1.00 ((hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a445) | c3_1(a445) | (~c2_1(a445))) <=> (hskp17 | c2_1(a452) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1698,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a445) | c3_1(a445) | (~c2_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | c2_1(a452) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c0_1(a452)) | (~c1_1(a452))))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1697])).
% 0.84/1.00 tff(1699,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a445) | c3_1(a445) | (~c2_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp17 | c2_1(a452) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1698, 1696])).
% 0.84/1.00 tff(1700,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a445) | c3_1(a445) | (~c2_1(a445)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1701,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp17 | c2_1(a452) | c0_1(a445) | c3_1(a445) | (~ndr1_0) | (~c2_1(a445)) | (~c0_1(a452)) | (~c1_1(a452))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1700, 1699])).
% 0.84/1.00 tff(1702,plain,
% 0.84/1.00 (hskp17 | c3_1(a445) | (~c2_1(a445))),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1701, 204, 1619, 1611, 1603, 40, 1695])).
% 0.84/1.00 tff(1703,plain,
% 0.84/1.00 (~c2_1(a445)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1702, 1685, 51])).
% 0.84/1.00 tff(1704,plain,
% 0.84/1.00 (hskp29 | hskp10 | c3_1(a445) | c2_1(a445)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[455, 204, 40, 449])).
% 0.84/1.00 tff(1705,plain,
% 0.84/1.00 (hskp29),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1704, 1703, 51, 54])).
% 0.84/1.00 tff(1706,plain,
% 0.84/1.00 (c3_1(a447)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[464, 1705])).
% 0.84/1.00 tff(1707,plain,
% 0.84/1.00 (c1_1(a447)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[504, 1705])).
% 0.84/1.00 tff(1708,plain,
% 0.84/1.00 (((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)))) <=> ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1709,plain,
% 0.84/1.00 ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1710,plain,
% 0.84/1.00 ((~![U: $i] : (hskp24 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp8 | (~ndr1_0) | (~c3_1(a447)) | (~c1_1(a447)) | (~c0_1(a447))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 0.84/1.00 tff(1711,plain,
% 0.84/1.00 (~c0_1(a447)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1710, 204, 1384, 32, 1707, 1706, 1248])).
% 0.84/1.00 tff(1712,plain,
% 0.84/1.00 (^[U: $i] : refl((hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.84/1.00 inference(bind,[status(th)],[])).
% 0.84/1.00 tff(1713,plain,
% 0.84/1.00 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.84/1.00 inference(quant_intro,[status(thm)],[1712])).
% 0.84/1.00 tff(1714,plain,
% 0.84/1.00 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1715,plain,
% 0.84/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp0) <=> ((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp0))), rewrite(((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp0) <=> (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp0) <=> (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.84/1.00 inference(bind,[status(th)],[])).
% 0.84/1.00 tff(1716,plain,
% 0.84/1.00 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp0) <=> ![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.84/1.00 inference(quant_intro,[status(thm)],[1715])).
% 0.84/1.00 tff(1717,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.84/1.00 tff(1718,plain,
% 0.84/1.00 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 0.84/1.00 tff(1719,plain,
% 0.84/1.00 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1718, 1714])).
% 0.84/1.00 tff(1720,plain,(
% 0.84/1.00 ![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.84/1.00 inference(skolemize,[status(sab)],[1719])).
% 0.84/1.00 tff(1721,plain,
% 0.84/1.00 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1720, 1713])).
% 0.84/1.00 tff(1722,plain,
% 0.84/1.00 (c2_1(a447)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[472, 1705])).
% 0.84/1.00 tff(1723,plain,
% 0.84/1.00 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp0 | (~ndr1_0) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp0 | (~ndr1_0) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1724,plain,
% 0.84/1.00 ((hskp8 | hskp0 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447))) <=> (hskp8 | hskp0 | (~ndr1_0) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1725,plain,
% 0.84/1.00 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp0 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp0 | (~ndr1_0) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1724])).
% 0.84/1.00 tff(1726,plain,
% 0.84/1.00 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp0 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp0 | (~ndr1_0) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1725, 1723])).
% 0.84/1.00 tff(1727,plain,
% 0.84/1.00 ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp0 | (~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1728,plain,
% 0.84/1.00 ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp0 | (~ndr1_0) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 0.84/1.00 tff(1729,plain,
% 0.84/1.00 (hskp0),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1728, 204, 32, 1722, 1706, 1721, 1711])).
% 0.84/1.00 tff(1730,plain,
% 0.84/1.00 (~c2_1(a432)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[291, 1729])).
% 0.84/1.00 tff(1731,plain,
% 0.84/1.00 (~c0_1(a432)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[297, 1729])).
% 0.84/1.00 tff(1732,plain,
% 0.84/1.00 (c3_1(a432)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[305, 1729])).
% 0.84/1.00 tff(1733,plain,
% 0.84/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a435) | c3_1(a435) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c1_1(a435)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a435) | c3_1(a435) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c1_1(a435)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1734,plain,
% 0.84/1.00 (((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432))) <=> (c0_1(a435) | c3_1(a435) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c1_1(a435)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1735,plain,
% 0.84/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a435) | c3_1(a435) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c1_1(a435)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1734])).
% 0.84/1.00 tff(1736,plain,
% 0.84/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a435) | c3_1(a435) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c1_1(a435)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1735, 1733])).
% 0.84/1.00 tff(1737,plain,
% 0.84/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1738,plain,
% 0.84/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a435) | c3_1(a435) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c1_1(a435)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 0.84/1.00 tff(1739,plain,
% 0.84/1.00 ($false),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1738, 204, 1722, 1706, 1652, 1732, 1651, 1650, 1731, 1730, 490, 1711])).
% 0.84/1.00 tff(1740,plain,(hskp24 | (~c1_1(a435)) | c0_1(a435) | c3_1(a435) | hskp8 | c3_1(a445) | hskp10 | c0_1(a445)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.00 tff(1741,plain,
% 0.84/1.00 (hskp10),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1740, 1384, 1651, 1650, 32, 51, 1652, 40])).
% 0.84/1.00 tff(1742,plain,
% 0.84/1.00 (~c2_1(a448)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1059, 1741])).
% 0.84/1.00 tff(1743,plain,
% 0.84/1.00 (c1_1(a448)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1073, 1741])).
% 0.84/1.00 tff(1744,plain,
% 0.84/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a448) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c3_1(a448)) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a448) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c3_1(a448)) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1745,plain,
% 0.84/1.00 (((~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c2_1(a448) | (~c3_1(a448)) | (~c1_1(a448)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435))) <=> (c2_1(a448) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c3_1(a448)) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1746,plain,
% 0.84/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c2_1(a448) | (~c3_1(a448)) | (~c1_1(a448)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a448) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c3_1(a448)) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452))))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1745])).
% 0.84/1.00 tff(1747,plain,
% 0.84/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c2_1(a448) | (~c3_1(a448)) | (~c1_1(a448)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a448) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c3_1(a448)) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1746, 1744])).
% 0.84/1.00 tff(1748,plain,
% 0.84/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c2_1(a448) | (~c3_1(a448)) | (~c1_1(a448)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1749,plain,
% 0.84/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a448) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c3_1(a448)) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 0.84/1.01 tff(1750,plain,
% 0.84/1.01 (~c3_1(a448)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1749, 204, 1619, 1611, 1743, 1652, 1742, 1651, 1650, 1112, 1649])).
% 0.84/1.01 tff(1751,plain,
% 0.84/1.01 (~c0_1(a448)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1065, 1741])).
% 0.84/1.01 tff(1752,assumption,(~c3_1(a448)), introduced(assumption)).
% 0.84/1.01 tff(1753,assumption,(hskp16), introduced(assumption)).
% 0.84/1.01 tff(1754,plain,
% 0.84/1.01 (~c2_1(a457)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[318, 1753])).
% 0.84/1.01 tff(1755,plain,
% 0.84/1.01 (c3_1(a457)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[326, 1753])).
% 0.84/1.01 tff(1756,plain,
% 0.84/1.01 (c1_1(a457)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[334, 1753])).
% 0.84/1.01 tff(1757,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a457) | c0_1(a448) | (~ndr1_0) | c3_1(a448) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)) | (~c3_1(a457)) | (~c1_1(a457)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a457) | c0_1(a448) | (~ndr1_0) | c3_1(a448) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1758,plain,
% 0.84/1.01 (((~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448))) <=> (c2_1(a457) | c0_1(a448) | (~ndr1_0) | c3_1(a448) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1759,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a457) | c0_1(a448) | (~ndr1_0) | c3_1(a448) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)) | (~c3_1(a457)) | (~c1_1(a457))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1758])).
% 0.84/1.01 tff(1760,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a457) | c0_1(a448) | (~ndr1_0) | c3_1(a448) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)) | (~c3_1(a457)) | (~c1_1(a457)))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1759, 1757])).
% 0.84/1.01 tff(1761,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c2_1(a457) | (~c3_1(a457)) | (~c1_1(a457)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1762,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a457) | c0_1(a448) | (~ndr1_0) | c3_1(a448) | (~c1_1(a448)) | c3_1(a452) | (~c0_1(a452)) | (~c1_1(a452)) | (~c3_1(a457)) | (~c1_1(a457))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 0.84/1.01 tff(1763,plain,
% 0.84/1.01 ($false),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1762, 204, 1756, 1755, 1619, 1611, 1180, 1754, 1179, 1112, 1653, 1752])).
% 0.84/1.01 tff(1764,plain,((~hskp16) | (~c1_1(a448)) | c0_1(a448) | c3_1(a452) | c3_1(a448)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.01 tff(1765,plain,
% 0.84/1.01 (~hskp16),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1764, 1743, 1751, 1649, 1750])).
% 0.84/1.01 tff(1766,plain,
% 0.84/1.01 (^[U: $i] : refl((hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1767,plain,
% 0.84/1.01 (![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1766])).
% 0.84/1.01 tff(1768,plain,
% 0.84/1.01 (![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1769,plain,
% 0.84/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp16) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp16) <=> (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1770,plain,
% 0.84/1.01 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp16) <=> ![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1769])).
% 0.84/1.01 tff(1771,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.84/1.01 tff(1772,plain,
% 0.84/1.01 (![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 0.84/1.01 tff(1773,plain,
% 0.84/1.01 (![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1772, 1768])).
% 0.84/1.01 tff(1774,plain,(
% 0.84/1.01 ![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.01 inference(skolemize,[status(sab)],[1773])).
% 0.84/1.01 tff(1775,plain,
% 0.84/1.01 (![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1774, 1767])).
% 0.84/1.01 tff(1776,plain,
% 0.84/1.01 (((~![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp16 | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)))) <=> ((~![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp16 | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1777,plain,
% 0.84/1.01 ((hskp29 | hskp16 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452))) <=> (hskp29 | hskp16 | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1778,plain,
% 0.84/1.01 (((~![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp16 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)))) <=> ((~![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp16 | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1777])).
% 0.84/1.01 tff(1779,plain,
% 0.84/1.01 (((~![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp16 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)))) <=> ((~![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp16 | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1778, 1776])).
% 0.84/1.01 tff(1780,plain,
% 0.84/1.01 ((~![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp16 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1781,plain,
% 0.84/1.01 ((~![U: $i] : (hskp29 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp16 | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 0.84/1.01 tff(1782,plain,
% 0.84/1.01 (hskp29 | hskp16),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1781, 204, 1619, 1611, 1603, 1775])).
% 0.84/1.01 tff(1783,plain,
% 0.84/1.01 (hskp29),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1782, 1765])).
% 0.84/1.01 tff(1784,plain,
% 0.84/1.01 (c3_1(a447)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[464, 1783])).
% 0.84/1.01 tff(1785,plain,
% 0.84/1.01 (c1_1(a447)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[504, 1783])).
% 0.84/1.01 tff(1786,plain,
% 0.84/1.01 (~c0_1(a447)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1710, 204, 1384, 32, 1785, 1784, 1248])).
% 0.84/1.01 tff(1787,plain,
% 0.84/1.01 (c2_1(a447)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[472, 1783])).
% 0.84/1.01 tff(1788,plain,
% 0.84/1.01 (hskp0),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1728, 204, 32, 1787, 1784, 1721, 1786])).
% 0.84/1.01 tff(1789,plain,
% 0.84/1.01 (~c2_1(a432)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[291, 1788])).
% 0.84/1.01 tff(1790,plain,
% 0.84/1.01 (~c0_1(a432)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[297, 1788])).
% 0.84/1.01 tff(1791,plain,
% 0.84/1.01 (c3_1(a432)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[305, 1788])).
% 0.84/1.01 tff(1792,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a448) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a448) | (~c1_1(a448)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a448) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a448) | (~c1_1(a448)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1793,plain,
% 0.84/1.01 (((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432))) <=> (c0_1(a448) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a448) | (~c1_1(a448)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1794,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a448) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a448) | (~c1_1(a448)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1793])).
% 0.84/1.01 tff(1795,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a448) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a448) | (~c1_1(a448)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447)))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1794, 1792])).
% 0.84/1.01 tff(1796,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a447) | (~c2_1(a447)) | (~c3_1(a447)) | c0_1(a448) | c3_1(a448) | (~c1_1(a448)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1797,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a448) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | c3_1(a448) | (~c1_1(a448)) | (~c3_1(a447)) | c0_1(a447) | (~c2_1(a447))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 0.84/1.01 tff(1798,plain,
% 0.84/1.01 ($false),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1797, 204, 1787, 1784, 1743, 1791, 1751, 1790, 1789, 490, 1750, 1786])).
% 0.84/1.01 tff(1799,plain,(hskp24 | hskp8 | (~c1_1(a435)) | c0_1(a435) | c3_1(a435) | c3_1(a445) | c0_1(a445)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.01 tff(1800,plain,
% 0.84/1.01 (hskp24),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1799, 1641, 32, 1633, 1627, 51, 40])).
% 0.84/1.01 tff(1801,plain,
% 0.84/1.01 (~c0_1(a486)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[119, 1800])).
% 0.84/1.01 tff(1802,plain,
% 0.84/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1803,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1802])).
% 0.84/1.01 tff(1804,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1805,plain,
% 0.84/1.01 (^[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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1806,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1805])).
% 0.84/1.01 tff(1807,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 0.84/1.01 tff(1808,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 0.84/1.01 tff(1809,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1808, 1804])).
% 0.84/1.01 tff(1810,plain,(
% 0.84/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/1.01 inference(skolemize,[status(sab)],[1809])).
% 0.84/1.01 tff(1811,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1810, 1803])).
% 0.84/1.01 tff(1812,assumption,(hskp24), introduced(assumption)).
% 0.84/1.01 tff(1813,plain,
% 0.84/1.01 (c2_1(a486)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[127, 1812])).
% 0.84/1.01 tff(1814,plain,
% 0.84/1.01 (c1_1(a486)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[135, 1812])).
% 0.84/1.01 tff(1815,plain,
% 0.84/1.01 (~c3_1(a486)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1543, 1813, 1814])).
% 0.84/1.01 tff(1816,plain,
% 0.84/1.01 (hskp0),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[230, 1815, 51, 178, 40, 52, 1814, 1813])).
% 0.84/1.01 tff(1817,plain,
% 0.84/1.01 (~c2_1(a432)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[291, 1816])).
% 0.84/1.01 tff(1818,plain,
% 0.84/1.01 (~c0_1(a432)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[297, 1816])).
% 0.84/1.01 tff(1819,plain,
% 0.84/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | c0_1(a486) | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)) | c3_1(a486) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp17 | c0_1(a486) | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)) | c3_1(a486) | (~c2_1(a486)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1820,plain,
% 0.84/1.01 ((hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a486) | c3_1(a486) | (~c2_1(a486))) <=> (hskp17 | c0_1(a486) | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)) | c3_1(a486) | (~c2_1(a486)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1821,plain,
% 0.84/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a486) | c3_1(a486) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | c0_1(a486) | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)) | c3_1(a486) | (~c2_1(a486))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1820])).
% 0.84/1.01 tff(1822,plain,
% 0.84/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a486) | c3_1(a486) | (~c2_1(a486)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp17 | c0_1(a486) | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)) | c3_1(a486) | (~c2_1(a486)))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1821, 1819])).
% 0.84/1.01 tff(1823,plain,
% 0.84/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a486) | c3_1(a486) | (~c2_1(a486)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1824,plain,
% 0.84/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp17 | c0_1(a486) | c2_1(a452) | (~ndr1_0) | (~c0_1(a452)) | (~c1_1(a452)) | c3_1(a486) | (~c2_1(a486))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 0.84/1.01 tff(1825,plain,
% 0.84/1.01 (hskp17 | c3_1(a486) | (~c2_1(a486))),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1824, 204, 1619, 1611, 178, 1603, 1695])).
% 0.84/1.01 tff(1826,plain,
% 0.84/1.01 (hskp17),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1825, 1815, 1813])).
% 0.84/1.01 tff(1827,plain,
% 0.84/1.01 (~c1_1(a463)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1659, 1826])).
% 0.84/1.01 tff(1828,plain,
% 0.84/1.01 (c3_1(a432)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[305, 1816])).
% 0.84/1.01 tff(1829,plain,
% 0.84/1.01 (c0_1(a463)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1675, 1826])).
% 0.84/1.01 tff(1830,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a486) | c1_1(a463) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c3_1(a463)) | (~c0_1(a463)) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a486) | c1_1(a463) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c3_1(a463)) | (~c0_1(a463)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1831,plain,
% 0.84/1.01 (((~ndr1_0) | c1_1(a463) | (~c3_1(a463)) | (~c0_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432))) <=> (c0_1(a486) | c1_1(a463) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c3_1(a463)) | (~c0_1(a463)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1832,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a463) | (~c3_1(a463)) | (~c0_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a486) | c1_1(a463) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c3_1(a463)) | (~c0_1(a463)) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1831])).
% 0.84/1.01 tff(1833,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a463) | (~c3_1(a463)) | (~c0_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a486) | c1_1(a463) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c3_1(a463)) | (~c0_1(a463)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1832, 1830])).
% 0.84/1.01 tff(1834,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a463) | (~c3_1(a463)) | (~c0_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c2_1(a432) | c0_1(a432) | (~c3_1(a432)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1835,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a486) | c1_1(a463) | c0_1(a432) | c2_1(a432) | (~ndr1_0) | (~c3_1(a432)) | (~c3_1(a463)) | (~c0_1(a463)) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 0.84/1.01 tff(1836,plain,
% 0.84/1.01 (~c3_1(a463)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1835, 204, 1814, 1813, 1829, 1828, 178, 1827, 1818, 1817, 1811])).
% 0.84/1.01 tff(1837,plain,
% 0.84/1.01 (c2_1(a463)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1667, 1826])).
% 0.84/1.01 tff(1838,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c1_1(a463) | (~ndr1_0) | c3_1(a463) | (~c2_1(a463)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a463) | (~ndr1_0) | c3_1(a463) | (~c2_1(a463)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1839,plain,
% 0.84/1.01 (((~ndr1_0) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486))) <=> (c0_1(a486) | c1_1(a463) | (~ndr1_0) | c3_1(a463) | (~c2_1(a463)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1840,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c1_1(a463) | (~ndr1_0) | c3_1(a463) | (~c2_1(a463)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1839])).
% 0.84/1.01 tff(1841,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a463) | (~ndr1_0) | c3_1(a463) | (~c2_1(a463)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1840, 1838])).
% 0.84/1.01 tff(1842,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a486) | c3_1(a486) | (~c1_1(a486)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1843,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a463) | (~ndr1_0) | c3_1(a463) | (~c2_1(a463)) | c3_1(a486) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 0.84/1.01 tff(1844,plain,
% 0.84/1.01 ($false),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1843, 204, 1814, 1813, 1837, 178, 1827, 10, 1815, 1836])).
% 0.84/1.01 tff(1845,plain,((~hskp24) | c0_1(a486) | c3_1(a445) | c0_1(a445) | c1_1(a445) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.84/1.01 tff(1846,plain,
% 0.84/1.01 ($false),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1845, 1801, 1800, 51, 40, 52, 32])).
% 0.84/1.01 tff(1847,plain,(c1_1(a445) | c3_1(a445) | c0_1(a445) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.84/1.01 tff(1848,plain,
% 0.84/1.01 (c1_1(a445)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1847, 51, 40, 32])).
% 0.84/1.01 tff(1849,plain,
% 0.84/1.01 (~hskp9),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[567, 1848])).
% 0.84/1.01 tff(1850,plain,
% 0.84/1.01 (hskp9 | (~c1_1(a445)) | (~c2_1(a445))),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[574, 204, 40, 51, 30])).
% 0.84/1.01 tff(1851,plain,
% 0.84/1.01 (~c2_1(a445)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1850, 1849, 1848])).
% 0.84/1.01 tff(1852,plain,
% 0.84/1.01 (hskp15),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[641, 1851, 1849, 1848])).
% 0.84/1.01 tff(1853,plain,
% 0.84/1.01 (~c1_1(a454)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[647, 1852])).
% 0.84/1.01 tff(1854,plain,
% 0.84/1.01 (~c0_1(a454)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[653, 1852])).
% 0.84/1.01 tff(1855,plain,
% 0.84/1.01 (c3_1(a454)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[661, 1852])).
% 0.84/1.01 tff(1856,plain,
% 0.84/1.01 ($false),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[668, 204, 1849, 32, 1855, 1854, 1853, 50])).
% 0.84/1.01 tff(1857,plain,(c3_1(a445) | hskp8 | c0_1(a445)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.01 tff(1858,plain,
% 0.84/1.01 (c3_1(a445)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1857, 40, 32])).
% 0.84/1.01 tff(1859,plain,
% 0.84/1.01 (~c1_1(a445)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[696, 1858, 40, 32])).
% 0.84/1.01 tff(1860,plain,
% 0.84/1.01 (~hskp9),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[529, 1858])).
% 0.84/1.01 tff(1861,plain,
% 0.84/1.01 (hskp9 | c1_1(a445) | (~c3_1(a445))),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[536, 204, 32, 40, 50])).
% 0.84/1.01 tff(1862,plain,
% 0.84/1.01 ($false),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1861, 1860, 1858, 1859])).
% 0.84/1.01 tff(1863,plain,(c0_1(a445) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.84/1.01 tff(1864,plain,
% 0.84/1.01 (c0_1(a445)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1863, 32])).
% 0.84/1.01 tff(1865,plain,
% 0.84/1.01 (~hskp9),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[723, 1864])).
% 0.84/1.01 tff(1866,plain,
% 0.84/1.01 (c1_1(a435)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1640, 33])).
% 0.84/1.01 tff(1867,plain,
% 0.84/1.01 (~c0_1(a435)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1632, 33])).
% 0.84/1.02 tff(1868,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a435)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a435)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1869,plain,
% 0.84/1.02 ((hskp9 | (~ndr1_0) | c3_1(a435) | c0_1(a435) | (~c2_1(a435)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435))) <=> (hskp9 | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a435)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1870,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a435) | c0_1(a435) | (~c2_1(a435)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a435))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1869])).
% 0.84/1.02 tff(1871,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a435) | c0_1(a435) | (~c2_1(a435)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a435)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1870, 1868])).
% 0.84/1.02 tff(1872,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a435) | c0_1(a435) | (~c2_1(a435)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1873,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a435))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 0.84/1.02 tff(1874,plain,
% 0.84/1.02 (hskp9 | (~c2_1(a435))),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1873, 204, 1652, 1651, 1650, 30])).
% 0.84/1.02 tff(1875,plain,
% 0.84/1.02 (~c2_1(a435)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1874, 31])).
% 0.84/1.02 tff(1876,plain,
% 0.84/1.02 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | c0_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c2_1(a435))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c2_1(a435))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1877,plain,
% 0.84/1.02 ((hskp15 | hskp9 | (~ndr1_0) | c2_1(a435) | c0_1(a435) | (~c1_1(a435))) <=> (hskp15 | hskp9 | c0_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c2_1(a435))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1878,plain,
% 0.84/1.02 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a435) | c0_1(a435) | (~c1_1(a435)))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | c0_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c2_1(a435)))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1877])).
% 0.84/1.02 tff(1879,plain,
% 0.84/1.02 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a435) | c0_1(a435) | (~c1_1(a435)))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c2_1(a435))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1878, 1876])).
% 0.84/1.02 tff(1880,plain,
% 0.84/1.02 ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a435) | c0_1(a435) | (~c1_1(a435)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1881,plain,
% 0.84/1.02 ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c2_1(a435)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 0.84/1.02 tff(1882,plain,
% 0.84/1.02 (hskp15 | hskp9 | c2_1(a435)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1881, 204, 1652, 1651, 634])).
% 0.84/1.02 tff(1883,plain,
% 0.84/1.02 (hskp15),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1882, 1875, 31])).
% 0.84/1.02 tff(1884,plain,
% 0.84/1.02 (~c1_1(a454)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[647, 1883])).
% 0.84/1.02 tff(1885,plain,
% 0.84/1.02 (~c0_1(a454)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[653, 1883])).
% 0.84/1.02 tff(1886,plain,
% 0.84/1.02 (c3_1(a454)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[661, 1883])).
% 0.84/1.02 tff(1887,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[668, 204, 31, 32, 1886, 1885, 1884, 50])).
% 0.84/1.02 tff(1888,plain,(hskp9 | hskp8 | (~c1_1(a435)) | c0_1(a435) | c3_1(a435)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.02 tff(1889,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1888, 1867, 1866, 32, 1865, 39])).
% 0.84/1.02 tff(1890,plain,((~hskp3) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.84/1.02 tff(1891,plain,
% 0.84/1.02 (~hskp3),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1890, 32])).
% 0.84/1.02 tff(1892,assumption,(hskp12), introduced(assumption)).
% 0.84/1.02 tff(1893,plain,
% 0.84/1.02 (~c0_1(a450)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[376, 1892])).
% 0.84/1.02 tff(1894,plain,
% 0.84/1.02 (c1_1(a450)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[415, 1892])).
% 0.84/1.02 tff(1895,assumption,(hskp15), introduced(assumption)).
% 0.84/1.02 tff(1896,plain,
% 0.84/1.02 (~c1_1(a454)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[647, 1895])).
% 0.84/1.02 tff(1897,plain,
% 0.84/1.02 (~c0_1(a454)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[653, 1895])).
% 0.84/1.02 tff(1898,plain,
% 0.84/1.02 (c3_1(a454)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[661, 1895])).
% 0.84/1.02 tff(1899,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[668, 204, 1865, 32, 1898, 1897, 1896, 50])).
% 0.84/1.02 tff(1900,plain,((~hskp15) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.84/1.02 tff(1901,plain,
% 0.84/1.02 (~hskp15),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1900, 32])).
% 0.84/1.02 tff(1902,plain,
% 0.84/1.02 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1903,plain,
% 0.84/1.02 ((hskp15 | hskp9 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | (~c1_1(a450))) <=> (hskp15 | hskp9 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1904,plain,
% 0.84/1.02 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | (~c1_1(a450)))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450)))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1903])).
% 0.84/1.02 tff(1905,plain,
% 0.84/1.02 (((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | (~c1_1(a450)))) <=> ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1904, 1902])).
% 0.84/1.02 tff(1906,plain,
% 0.84/1.02 ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp9 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | (~c1_1(a450)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1907,plain,
% 0.84/1.02 ((~![U: $i] : (hskp15 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp9 | c0_1(a450) | (~ndr1_0) | (~c1_1(a450)) | c2_1(a450)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 0.84/1.02 tff(1908,plain,
% 0.84/1.02 (c2_1(a450)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1907, 204, 1901, 1865, 1894, 1893, 634])).
% 0.84/1.02 tff(1909,plain,
% 0.84/1.02 (c3_1(a450)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[407, 1892])).
% 0.84/1.02 tff(1910,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1211, 204, 32, 1894, 1909, 1893, 249, 1908])).
% 0.84/1.02 tff(1911,plain,((~hskp12) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.84/1.02 tff(1912,plain,
% 0.84/1.02 (~hskp12),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1911, 32])).
% 0.84/1.02 tff(1913,plain,
% 0.84/1.02 ((hskp24 | hskp12 | hskp3) <=> (hskp24 | hskp12 | hskp3)),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1914,plain,
% 0.84/1.02 (((hskp24 | hskp12) | hskp3) <=> (hskp24 | hskp12 | hskp3)),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1915,plain,
% 0.84/1.02 ((hskp24 | hskp12) <=> (hskp24 | hskp12)),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1916,plain,
% 0.84/1.02 (((hskp24 | hskp12) | hskp3) <=> ((hskp24 | hskp12) | hskp3)),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1915])).
% 0.84/1.02 tff(1917,plain,
% 0.84/1.02 (((hskp24 | hskp12) | hskp3) <=> (hskp24 | hskp12 | hskp3)),
% 0.84/1.02 inference(transitivity,[status(thm)],[1916, 1914])).
% 0.84/1.02 tff(1918,axiom,((hskp24 | hskp12) | hskp3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.84/1.02 tff(1919,plain,
% 0.84/1.02 (hskp24 | hskp12 | hskp3),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 0.84/1.02 tff(1920,plain,
% 0.84/1.02 (hskp24 | hskp12 | hskp3),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1919, 1913])).
% 0.84/1.02 tff(1921,plain,
% 0.84/1.02 (hskp24 | hskp12 | hskp3),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1920, 1913])).
% 0.84/1.02 tff(1922,plain,
% 0.84/1.02 (hskp24 | hskp12 | hskp3),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1921, 1913])).
% 0.84/1.02 tff(1923,plain,
% 0.84/1.02 (hskp24 | hskp12 | hskp3),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1922, 1913])).
% 0.84/1.02 tff(1924,plain,
% 0.84/1.02 (hskp24),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1923, 1912, 1891])).
% 0.84/1.02 tff(1925,plain,
% 0.84/1.02 (c1_1(a486)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[135, 1924])).
% 0.84/1.02 tff(1926,plain,
% 0.84/1.02 (c2_1(a486)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[127, 1924])).
% 0.84/1.02 tff(1927,plain,
% 0.84/1.02 (~c0_1(a486)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[119, 1924])).
% 0.84/1.02 tff(1928,plain,
% 0.84/1.02 (c3_1(a486)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[732, 1927, 1865, 1926, 1925])).
% 0.84/1.02 tff(1929,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[255, 204, 32, 1925, 1926, 1927, 249, 1928])).
% 0.84/1.02 tff(1930,plain,(hskp8), inference(lemma,lemma(discharge,[]))).
% 0.84/1.02 tff(1931,plain,
% 0.84/1.02 (~c3_1(a444)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[262, 1930])).
% 0.84/1.02 tff(1932,plain,
% 0.84/1.02 (~c0_1(a444)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[268, 1930])).
% 0.84/1.02 tff(1933,plain,
% 0.84/1.02 (c2_1(a444)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[276, 1930])).
% 0.84/1.02 tff(1934,plain,
% 0.84/1.02 (hskp9 | (~c1_1(a444))),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[707, 204, 1933, 1932, 1931, 30])).
% 0.84/1.02 tff(1935,plain,
% 0.84/1.02 (~c1_1(a444)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1934, 31])).
% 0.84/1.02 tff(1936,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c0_1(a452)) | (~c1_1(a452)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1937,plain,
% 0.84/1.02 ((hskp3 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c1_1(a444) | c0_1(a444) | c3_1(a444)) <=> (hskp3 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1938,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c1_1(a444) | c0_1(a444) | c3_1(a444))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c0_1(a452)) | (~c1_1(a452))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1937])).
% 0.84/1.02 tff(1939,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c1_1(a444) | c0_1(a444) | c3_1(a444))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1938, 1936])).
% 0.84/1.02 tff(1940,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c1_1(a444) | c0_1(a444) | c3_1(a444))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1941,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | c1_1(a444) | (~c0_1(a452)) | (~c1_1(a452))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 0.84/1.02 tff(1942,plain,
% 0.84/1.02 (hskp3),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1941, 204, 1619, 1611, 1603, 1932, 1931, 20, 1935])).
% 0.84/1.02 tff(1943,plain,
% 0.84/1.02 (~c3_1(a435)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[38, 1942])).
% 0.84/1.02 tff(1944,plain,
% 0.84/1.02 (~c0_1(a435)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1632, 1942])).
% 0.84/1.02 tff(1945,plain,
% 0.84/1.02 (c1_1(a435)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1640, 1942])).
% 0.84/1.02 tff(1946,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a444) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a444) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a444)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1947,plain,
% 0.84/1.02 ((hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435))) <=> (hskp9 | c0_1(a444) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a444)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1948,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a444) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a444))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1947])).
% 0.84/1.02 tff(1949,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a444) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a444)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1948, 1946])).
% 0.84/1.02 tff(1950,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a444) | c0_1(a444) | (~c2_1(a444)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1951,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a444) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a444))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1950, 1949])).
% 0.84/1.02 tff(1952,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1951, 204, 31, 1933, 1945, 1932, 1931, 1944, 1943, 30])).
% 0.84/1.02 tff(1953,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 0.84/1.02 tff(1954,plain,
% 0.84/1.02 (~c3_1(a445)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[529, 1953])).
% 0.84/1.02 tff(1955,plain,
% 0.84/1.02 (~c1_1(a445)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[567, 1953])).
% 0.84/1.02 tff(1956,plain,
% 0.84/1.02 (~c0_1(a445)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[723, 1953])).
% 0.84/1.02 tff(1957,plain,
% 0.84/1.02 (hskp3),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1625, 204, 1619, 1611, 1603, 1956, 1955, 1954, 20])).
% 0.84/1.02 tff(1958,plain,
% 0.84/1.02 (~c3_1(a435)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[38, 1957])).
% 0.84/1.02 tff(1959,plain,
% 0.84/1.02 (~c0_1(a435)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1632, 1957])).
% 0.84/1.02 tff(1960,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c0_1(a452)) | (~c1_1(a452)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp17 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1961,plain,
% 0.84/1.02 ((hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444))) <=> (hskp17 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1962,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c0_1(a452)) | (~c1_1(a452))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1961])).
% 0.84/1.02 tff(1963,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp17 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c0_1(a452)) | (~c1_1(a452)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1962, 1960])).
% 0.84/1.02 tff(1964,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a452) | (~c1_1(a452)) | (~c0_1(a452)) | c0_1(a444) | c3_1(a444) | (~c2_1(a444)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1965,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp17 | c2_1(a452) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c2_1(a444)) | (~c0_1(a452)) | (~c1_1(a452))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1964, 1963])).
% 0.84/1.02 tff(1966,plain,
% 0.84/1.02 (hskp17),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1965, 204, 1619, 1611, 1933, 1603, 1932, 1931, 1695])).
% 0.84/1.02 tff(1967,plain,
% 0.84/1.02 (~c1_1(a463)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1659, 1966])).
% 0.84/1.02 tff(1968,plain,
% 0.84/1.02 (c3_1(a452)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1684, 1384, 1966])).
% 0.84/1.02 tff(1969,plain,
% 0.84/1.02 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(1970,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[1969])).
% 0.84/1.02 tff(1971,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1972,plain,
% 0.84/1.02 (^[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)) | (~c0_1(V)) | (~c2_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))))), (((((((~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)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_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)) | (~c0_1(V)) | (~c2_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)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_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) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(1973,plain,
% 0.84/1.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[1972])).
% 0.84/1.02 tff(1974,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)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.84/1.02 tff(1975,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1974, 1973])).
% 0.84/1.02 tff(1976,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1975, 1971])).
% 0.84/1.02 tff(1977,plain,(
% 0.84/1.02 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(skolemize,[status(sab)],[1976])).
% 0.84/1.02 tff(1978,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1977, 1970])).
% 0.84/1.02 tff(1979,plain,
% 0.84/1.02 (c2_1(a463)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1667, 1966])).
% 0.84/1.02 tff(1980,plain,
% 0.84/1.02 (c0_1(a463)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1675, 1966])).
% 0.84/1.02 tff(1981,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp23 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c0_1(a463)) | (~c2_1(a463)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp23 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1982,plain,
% 0.84/1.02 ((hskp23 | (~ndr1_0) | c2_1(a452) | (~c3_1(a452)) | (~c0_1(a452)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463))) <=> (hskp23 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1983,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a452) | (~c3_1(a452)) | (~c0_1(a452)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp23 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c0_1(a463)) | (~c2_1(a463))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1982])).
% 0.84/1.02 tff(1984,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a452) | (~c3_1(a452)) | (~c0_1(a452)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp23 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1983, 1981])).
% 0.84/1.02 tff(1985,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a452) | (~c3_1(a452)) | (~c0_1(a452)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1986,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp23 | c1_1(a463) | c2_1(a452) | (~ndr1_0) | (~c3_1(a452)) | (~c0_1(a452)) | (~c0_1(a463)) | (~c2_1(a463))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1985, 1984])).
% 0.84/1.02 tff(1987,plain,
% 0.84/1.02 (hskp23 | (~c3_1(a452))),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1986, 204, 1980, 1979, 1619, 1967, 1603, 1978])).
% 0.84/1.02 tff(1988,plain,
% 0.84/1.02 (hskp23),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1987, 1968])).
% 0.84/1.02 tff(1989,plain,
% 0.84/1.02 (~c3_1(a484)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1367, 1988])).
% 0.84/1.02 tff(1990,plain,
% 0.84/1.02 (~c2_1(a484)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1373, 1988])).
% 0.84/1.02 tff(1991,plain,
% 0.84/1.02 (c1_1(a484)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1382, 1988])).
% 0.84/1.02 tff(1992,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a463) | (~ndr1_0) | (~c0_1(a463)) | (~c2_1(a463)) | (~c1_1(a484)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a463) | (~ndr1_0) | (~c0_1(a463)) | (~c2_1(a463)) | (~c1_1(a484)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1993,plain,
% 0.84/1.02 ((hskp24 | (~ndr1_0) | c3_1(a484) | c2_1(a484) | (~c1_1(a484)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463))) <=> (hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a463) | (~ndr1_0) | (~c0_1(a463)) | (~c2_1(a463)) | (~c1_1(a484)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1994,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a484) | c2_1(a484) | (~c1_1(a484)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a463) | (~ndr1_0) | (~c0_1(a463)) | (~c2_1(a463)) | (~c1_1(a484))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[1993])).
% 0.84/1.03 tff(1995,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a484) | c2_1(a484) | (~c1_1(a484)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a463) | (~ndr1_0) | (~c0_1(a463)) | (~c2_1(a463)) | (~c1_1(a484)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[1994, 1992])).
% 0.84/1.03 tff(1996,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a484) | c2_1(a484) | (~c1_1(a484)) | c1_1(a463) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(1997,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp24 | c2_1(a484) | c3_1(a484) | c1_1(a463) | (~ndr1_0) | (~c0_1(a463)) | (~c2_1(a463)) | (~c1_1(a484))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1996, 1995])).
% 0.84/1.03 tff(1998,plain,
% 0.84/1.03 ($false),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1997, 204, 1384, 1991, 1980, 1979, 1990, 1989, 1967, 1360])).
% 0.84/1.03 tff(1999,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 0.84/1.03 tff(2000,plain,
% 0.84/1.03 (~c0_1(a486)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[119, 1999])).
% 0.84/1.03 tff(2001,plain,
% 0.84/1.03 (c1_1(a435)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1640, 1957])).
% 0.84/1.03 tff(2002,plain,
% 0.84/1.03 (c2_1(a486)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[127, 1999])).
% 0.84/1.03 tff(2003,plain,
% 0.84/1.03 (c1_1(a486)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[135, 1999])).
% 0.84/1.03 tff(2004,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c1_1(a445) | c3_1(a445) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a445) | c3_1(a445) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(2005,plain,
% 0.84/1.03 (((~ndr1_0) | c3_1(a445) | c1_1(a445) | (~c2_1(a445)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435))) <=> (c0_1(a486) | c1_1(a445) | c3_1(a445) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(2006,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a445) | c1_1(a445) | (~c2_1(a445)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c1_1(a445) | c3_1(a445) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[2005])).
% 0.84/1.03 tff(2007,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a445) | c1_1(a445) | (~c2_1(a445)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a445) | c3_1(a445) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[2006, 2004])).
% 0.84/1.03 tff(2008,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a445) | c1_1(a445) | (~c2_1(a445)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(2009,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a445) | c3_1(a445) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | (~c2_1(a445)) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 0.84/1.03 tff(2010,plain,
% 0.84/1.03 (~c2_1(a445)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[2009, 204, 2003, 2002, 2001, 2000, 1955, 1954, 1959, 1958, 10])).
% 0.84/1.03 tff(2011,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a463)) | (~c0_1(a463)) | (~c2_1(a463)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a463)) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(2012,plain,
% 0.84/1.03 (((~ndr1_0) | (~c2_1(a463)) | (~c3_1(a463)) | (~c0_1(a463)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a445) | c1_1(a445) | c0_1(a445)) <=> (c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a463)) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(2013,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a463)) | (~c3_1(a463)) | (~c0_1(a463)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a463)) | (~c0_1(a463)) | (~c2_1(a463))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[2012])).
% 0.84/1.03 tff(2014,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a463)) | (~c3_1(a463)) | (~c0_1(a463)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a445) | c1_1(a445) | c0_1(a445))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a463)) | (~c0_1(a463)) | (~c2_1(a463)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[2013, 2011])).
% 0.84/1.03 tff(2015,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a463)) | (~c3_1(a463)) | (~c0_1(a463)) | c1_1(a445) | c0_1(a445) | c3_1(a445) | c2_1(a445) | c1_1(a445) | c0_1(a445))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(2016,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a445) | c1_1(a445) | c3_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a463)) | (~c0_1(a463)) | (~c2_1(a463))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 0.84/1.03 tff(2017,plain,
% 0.84/1.03 (~c3_1(a463)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[2016, 204, 1980, 1979, 1956, 1955, 1954, 74, 2010])).
% 0.84/1.03 tff(2018,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(2019,plain,
% 0.84/1.03 (((~ndr1_0) | c3_1(a444) | c1_1(a444) | (~c2_1(a444)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435))) <=> (c0_1(a486) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(2020,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a444) | c1_1(a444) | (~c2_1(a444)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[2019])).
% 0.84/1.03 tff(2021,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a444) | c1_1(a444) | (~c2_1(a444)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[2020, 2018])).
% 0.84/1.03 tff(2022,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a444) | c1_1(a444) | (~c2_1(a444)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a435) | c3_1(a435) | (~c1_1(a435)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(2023,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c3_1(a444) | c0_1(a435) | c3_1(a435) | (~ndr1_0) | (~c1_1(a435)) | c1_1(a444) | (~c2_1(a444)) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 0.84/1.03 tff(2024,plain,
% 0.84/1.03 (c1_1(a444)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[2023, 204, 2003, 2002, 1933, 2001, 2000, 1931, 1959, 1958, 10])).
% 0.84/1.03 tff(2025,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c1_1(a463) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | c3_1(a463) | (~c2_1(a463)) | (~c1_1(a486)) | (~c2_1(a486)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a463) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | c3_1(a463) | (~c2_1(a463)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(2026,plain,
% 0.84/1.03 (((~ndr1_0) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444))) <=> (c0_1(a486) | c1_1(a463) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | c3_1(a463) | (~c2_1(a463)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(2027,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a486) | c1_1(a463) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | c3_1(a463) | (~c2_1(a463)) | (~c1_1(a486)) | (~c2_1(a486))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[2026])).
% 0.84/1.03 tff(2028,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a463) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | c3_1(a463) | (~c2_1(a463)) | (~c1_1(a486)) | (~c2_1(a486)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[2027, 2025])).
% 0.84/1.03 tff(2029,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c0_1(a486) | (~c1_1(a486)) | (~c2_1(a486)) | c0_1(a444) | c3_1(a444) | (~c1_1(a444)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(2030,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a486) | c1_1(a463) | c0_1(a444) | c3_1(a444) | (~ndr1_0) | (~c1_1(a444)) | c3_1(a463) | (~c2_1(a463)) | (~c1_1(a486)) | (~c2_1(a486))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[2029, 2028])).
% 0.84/1.03 tff(2031,plain,
% 0.84/1.03 ($false),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[2030, 204, 2003, 2002, 1979, 2000, 1967, 1932, 1931, 10, 2024, 2017])).
% 0.84/1.03 % SZS output end Proof
% 0.84/1.04 % E exiting
%------------------------------------------------------------------------------